Ultra-sensitive wideband diffraction-grating-coupled-mode Fabry-Pérot resonators for ultrasound and photoacoustic detection

Abstract

Optical ultrasound detectors offer broad bandwidth, high sensitivity, significantly reduced electrical and acoustic impedance mismatch, and seamless integration with transparent imaging platforms for biomedical and industrial ultrasound and photoacoustic applications. A diffraction-grating-coupled-mode Fabry-Pérot (GFP) resonator that enables wideband optical detection of ultrasound and photoacoustic signals employing a simple, low-cost fabrication flow is described. A 1D grating couples light between normal incidence and ±1^st orders that are confined by total-internal-reflection boundaries, forming an effective FP cavity as a coupled resonator operating in Fano resonance. For illustration, GFPs with 2.1-µm, 4.9-µm and 10.1-µm cavities have been fabricated and comprehensively characterized. The scalable design achieved a maximum calibrated bandwidth >130 MHz and a noise-equivalent pressure of ∼72 Pa over 100 MHz. By combining strong optical confinement, favorable acoustic impedance matching, and scalable fabrication, GFP offers a practical solution to advance photoacoustic and ultrasonic sensing with a tunable responsivity-bandwidth trade-off for multimodal biomedical imaging.

1. Introduction

Photoacoustic imaging has rapidly evolved into a compelling hybrid modality that combines the high contrast of optical imaging with the deep penetration and low scattering of ultrasound, making it highly appealing for a broad range of non-invasive biomedical applications [1], [2], [3], [4]. Similarly, conventional ultrasound imaging continues to play a central role in clinical diagnostics owing to its real-time capabilities and non-ionizing nature [5]. Central to both these modalities are piezoelectric transducers, which convert acoustic pressure waves into electrical signals and have long represented the state of the art in acoustic detection [6], [7]. However, despite their commercial maturity and widespread adoption, piezoelectric detectors exhibit practical limitations: (i) bandwidth remains intrinsically narrow without careful and labor-intensive damping procedures [8]; (ii) sensitivity can be limited without complex and time-consuming electrical and acoustic impedance matching [9]; (iii) their bulky form factor hinders seamless multimodal integration, e.g., with microscopy or OCT [10], [11]; and (iv) fabrication complexity increases at higher frequencies owing to stringent requirements on thickness control and layer uniformity [12]. These inherent limitations restrict performance, particularly in applications requiring high spatial resolution or integration with complementary imaging modalities, and motivate the exploration of alternative detection methods for acoustic signals that offer a viable route to overcome these challenges while enabling ultra-sensitive, wideband ultrasound detection [13].

Photonic ultrasound sensors present a transformative pathway offering several compelling advantages, e.g., high bandwidths, optical transparency, and device miniaturization capabilities [9], [14]. Furthermore, optical detectors obviate the need for complex electrical impedance-matching networks because the sensing mechanism relies on changes in the optical path length. Acoustic impedance mismatch can be significantly reduced because optical materials are readily available with an acoustic impedance close to that of water or biological tissues.

Several photonic approaches have been proposed to improve acoustic detection performance. Two main categories are of particular interest, i.e., membrane-based sensors and integrated sensors [15]. These optical sensors detect perturbations in their geometric dimensions, refractive index, or coupling distance between the waveguide and the cavity caused by acoustic pressure. These perturbations result in measurable resonance shifts. Membrane-based sensors utilize layered thin films for acoustic sensing, e.g., Fabry-Pérot (FP) cavities [16], [17], [18], surface plasmon resonators (SPR) [19], [20], evanescent field sensing [21], [22], etc., whereas integrated sensors rely on fabricated on-chip resonator-based structures such as π-phase-shifted Bragg gratings (BG) [23], microdisks [24], and whispering gallery mode (WGM) microcavities, e.g., micro-ring resonators [25], [26], [27], [28]. Integrated sensors, particularly microring- and other on-chip resonator-based devices, have developed rapidly in recent years and offer attractive advantages such as miniaturization, strong optical confinement and compact size, which make them highly interesting for future photoacoustic and ultrasound systems [29]. More recent studies have extended these concepts to optoacoustic micro-tomography and arrayed ultrasound imaging [30], [31], [32]. Overall, these studies highlight integrated photonics as a powerful route toward miniature, highly sensitive, and scalable ultrasound/photoacoustic sensing. At the same time, they also come with practical trade-offs, e.g., complex workflow for prototyping, tighter optical coupling and interrogation requirements, depending on the platform and application.

FP resonators, as thin-film sensors, have been widely adopted for photoacoustic and ultrasound sensing applications [16], [33], [34]. A typical FP structure comprises a thin dielectric spacer sandwiched between two reflective interfaces. The reflective interfaces can be realized with metallic films or engineered dielectric structures. In conventional FP structures, stacks of hard crystal materials of $\lambda /4$ thickness are deposited to form Bragg reflectors [35], [36]. Novel methods of light confinement have been achieved through total internal reflection with oblique incidence above the critical angle [37]. The resonance of an FP cavity is governed by the requirement that the round‑trip optical phase accumulation equals an integer multiple of 2π:

$$\begin{array}{c}2k_{z}L+{\varphi }_1+{\varphi }_2=2m\pi ,m=0,1,2,3,\dots \end{array}$$ (1)

where $k_z=\frac{2\pi n_s}{{\lambda }_0}\cos \theta$ denotes the z-component of the wave vector within the spacer, $L$ denotes the spacer thickness, $n_s$ is the refractive index of the spacer, ${\lambda }_0$ is the interrogation wavelength in free space, θ denotes the propagation angle, ${\varphi }_1$ and ${\varphi }_2$ are the phase changes at the upper and lower interfaces of the cavity, respectively, and $m$ specifies the resonance order. The primary detection mechanism for FP is the detection of deformation, the change in $L$, induced by the acoustic pressure. This dominates any change in refractive index of the resonator due to deformation. As bandwidth performance is mainly determined by the thickness of the cavity, $L$, the sensitivity is closely related to the finesse, which is jointly determined by the thickness of the cavity, $L$, and resonance quality, Q. For planar thin-film detectors, to achieve a higher Q, usually requires higher reflectivity from the mirrors, which effectively leads to a larger number of stack layers. Although this effect is often small in many practical designs, mirror thickness may still be a relevant design consideration because thicker mirrors can introduce additional acoustic discontinuity at the device surface for applications that require > 150 MHz bandwidth [38].

This study introduces a high-performance yet easy-to-fabricate optical detector, i.e., a diffraction-grating-coupled-mode Fabry-Pérot (GFP) resonator, designed for ultrasound detection in photoacoustic applications around the optical wavelength of 1550 nm, and evaluates its performance via theoretical analysis and experimental validation. Fig. 1(a) illustrates the layout of the proposed GFP structure. The GFP comprises a 1-dimensional (1D) grating and a uniform cavity. The presence of the grating breaks the polarization degeneracy of the cavity, so the optical response becomes polarization-dependent, and the resonator supports distinct TE and TM polarization responses. All investigations were carried out with TE polarization under normal incidence, the direction of which is shown in Fig. 1(a). Refractive indices of the layers were carefully selected to ensure that only the 0^th and ±1^st orders propagate in the cavity and only the 0^th order propagates outside the cavity and grating. The grating facilitates energy coupling between the 0^th and ±1^st orders, and FP resonance is formed by confining the ±1^st orders via total internal reflections enabled by carefully selected refractive indices. Although this structure looks very similar to a conventional FP resonator, in fact its operation is rather different as discussed at length in Appendix B and C. The structure operates as two coupled resonators: one involving the normally propagating beam and the other involving the diffracted orders. The diffracted-order resonator has a much higher $Q$than the normal-incidence one. Therefore, over most of the operating range, the low-$Q$ resonator predominates; however, as the round-trip phase of the diffracted orders approaches an integer multiple of $2\pi$, energy builds up in the diffracted orders and produces a sharp reflectivity peak. This can be seen in Fig. 1(b) where there are periodic sharp reflectivity peaks surrounded by areas of low reflectivity.

Fig. 1.

(a) Configuration overview of the GFP resonator for photoacoustic sensing and imaging. (b) A typical responsivity map of the GFP with respect to wavelength and grating thickness.

Conventional FP ultrasound detectors are already a well-established and highly effective platform for photoacoustic and ultrasound sensing. The motivation for the present GFP design is not to replace conventional FP structures, but rather to explore a complementary resonator architecture that combines normal-incidence interrogation, simple planar fabrication, and the ability to maintain useful resonances in relatively thin cavities for high-bandwidth applications. The combination is achieved through the use of coupling between low and high Q yielding Fano resonance for the high-Q resonance via the coupling grating.

The complete GFP assembly was directly fabricated on a standard 725-µm-thick fused silica wafer to ensure compatibility with existing optical platforms. The entire fabrication process involved only DUV lithography, etching and a single spin-coating process. Compared with a conventional FP resonator, the GFP architecture avoids dedicated mirror-coating layers, which may reduce additional acoustic discontinuities associated with such coatings, while significantly simplifying fabrication and reducing overall cost.

This paper is organized into five sections. In Section 2, a theoretical framework and an intuitive overview of the proposed structure are presented, detailing its operating principles and evaluating its respective strengths and limitations. Section 3 describes the experimental characterization of responsivity and bandwidth, including both ultrasound and photoacoustic evaluations of the proposed sensor, and evaluates the sensitivity in terms of noise-equivalent pressure. Section 4 summarizes and discusses the key findings and provides a vision for future work. Finally, the conclusions are presented in Section 5.

2. Theoretical analysis of working principles

As described in the introduction, the proposed resonator operates as an FP cavity wherein the grating layer functions as a coupler, and the interfaces between the spacer and surrounding media form two total internal reflection interfaces that serve as reflectors. This section begins with a detailed explanation of the formation of the FP cavity, followed by simplified models of GFP and an evaluation of GFP resonances in terms of acoustic wave detection.

2.1. Brief revisit of FP operation principles

The primary operating mechanism of an FP resonator for acoustic detection is the pressure-induced variation in cavity thickness as the acoustic wave impinges on the detector [39]. As the transducer thickness increases, the strain induced by the ultrasound accumulates constructively, thereby enhancing the overall response. Within its operation range, the response scales linearly with the total displacement of the transducer, $∆h$:

$$\begin{array}{c}∆h={\int }_0^h\frac{P_{\mathit{tot}}\left(x\right)}{M}\mathit{dx}=\frac{\nu }{2\pi \mathit{fM}}{\int }_0^{{\alpha }_m}{P}_{\mathit{tot}}\left(\alpha \right)d\alpha \end{array}$$ (2)

where $P_{\mathit{tot}}$ denotes the pressure distribution in the transducer resulting from a unit input pressure wave. The value of $P_{\mathit{tot}}$ is the vector sum of the forward propagating and backward propagating waves within the transducer, $\alpha$ is the phase of the acoustic wave as it propagates along the transducer, $\nu$ is the acoustic velocity in the transducer, $f$ is the frequency, and $\frac{\nu }{2\pi \mathit{fM}}$ is the accumulated phase of the sound wave as it propagates in the transducer, $M$ is the longitudinal modulus which depends on the material and physical constraints, ${\alpha }_m$ is the value of the phase of the acoustic wave at the end of the transducer corresponding to $x=h$. The second integral in the equation has units of pressure and physically represents a vectorial summation of the pressure distribution within the transducer.

However, when the thickness becomes comparable to the acoustic wavelength, the strain wave begins to exhibit significant phase variation across the depth of the transducer. This variation can result in a partial or complete phase cancellation of the acoustic contributions, particularly when the transducer thickness exceeds half the wavelength, ultimately reducing the detection efficiency.

Two primary factors determine the actual pressure experienced by the resonator. The first factor is the backing material. When the backing layer is compliant and the sample is thin, the resonator deformation is little, and the pressure is not transferred to the resonator. For layers considerably thinner than the acoustic wavelength, a stiff backing layer implies that the transducer sees approximately double the input pressure, whereas for a backing layer with an acoustic impedance similar to that of the transducer, the pressure imparted to the transducer is similar to the input pressure of the sound wave. However, a stiff backing also introduces stronger acoustic discontinuity, which can lead to a slight reduction in detection bandwidth. A detailed discussion on the effect of backing has been given in Appendix A. The second factor is transducer thickness. As the transducer thickness increases, the strain induced by the ultrasound accumulates constructively, enhancing the overall change in thickness and, hence, the optical response. However, when the thickness becomes comparable to the acoustic wavelength, phase variation across the transducer causes partial cancellation of the acoustic contribution to the deformation, ultimately reducing the detection efficiency. The analysis in Appendix A quantifies these effects and applies equally to both GFP and conventional FP resonators.

2.2. Optical mode analysis of GFP

Fig. 2 shows a schematic of the simplified GFP structure divided into three regions. Region 1 corresponds to the substrate with a refractive index of $n_1$, through which the interrogation optical beam is incident. Region 2 represents the GFP cavity consisting of a homogeneous polymer cavity with a 1D grating along the x-axis at the bottom of the cavity sandwiched between region 1 and 3. Here, the grating and homogeneous layer are considered to share the same refractive index, $n_2$. Region 3, with a refractive index of $n_3$, corresponds to the superstrate of the structure, i.e., water, through which an acoustic wave is projected onto the structure.

Fig. 2.

Schematic of simplified GFP structures.

Forward diffraction at 1D grating from medium 1 to medium 2 follows the grating equation given by

$$\begin{array}{c}{k}_2=k_1+N{k}_g,k_i=\frac{2\pi }{\lambda }{n}_i\sin {\theta }_i,i=1,2\end{array}$$ (3)

Where $k_i$ is the tangential component of the wave vector in media, $k_g=2\pi /d$ is the grating vector, $\mathrm{d}$ is the period of grating, $n$ is the refractive index and $N$ is the diffraction order.

Assuming normal incidence, the relationship between the refractive indices and the wavelength can be summarized from Eq. ($3$) in terms of the grating k-vector as:

$$\begin{array}{c}{k}_g>\frac{2\pi n_L}{{\lambda }_0}\mathit{and}\frac{2\pi n_2}{{\lambda }_0}>k_g>\frac{\pi n_2}{{\lambda }_0},k_g=2\pi /d,n_{\mathrm{L}}=\max (n_1,n_3)\end{array}$$ (4)

where ${\lambda }_0$ is the incident wavelength in vacuum, $n_L$ is the higher refractive index between the substrate and superstrate, and $n_2$ is the refractive index of the cavity.

The first inequality ensures that only one propagating wave is allowed in Region 1 and 3, and the second inequality ensures that three waves are allowed in Region 2, i.e. the 0th, −1st and 1st diffracted orders, while the second diffracted orders are evanescent. It can be further expressed in terms of wavelength and refractive indices:

$$\begin{array}{c}{\lambda }_0>n_{\mathrm{L}}d\mathit{and}\frac{n_{2}d}{2}<{\lambda }_0<n_{2}d,\end{array}$$ (5)

By combining Eq. $1$ and $3$, the round-trip phase accumulation relation with respect to the wavelength for the first diffracted order can be given:

$$\begin{array}{c}m=L\bullet \sqrt{\frac{n_2^2}{{\lambda }^2}-\frac{1}{d^2}}+\frac{{\varphi }_1+{\varphi }_2}{2\pi }\end{array}$$ (6)

where m is the relative phase multiplier with respect to $2\pi$, $\lambda$ is the wavelength in vacuum, $\mathrm{d}$ is the period of grating, $n_2$ is the refractive index of the cavity layer, $L$ is the thickness of the resonator, $\varphi$ is the phase of the reflection coefficient at the interface.

For a cavity of $10\mathrm{\mu }\mathrm{m}$ and a grating period of $1\mathrm{\mu }\mathrm{m}$, phase accumulation for the first diffracted order with respect to wavelength is shown in Fig. 3. The zeroth order is incident normally and follows Eq. $1$ ($m=n_{2}L/\lambda$), which is exactly the same as a conventional FP. The intersections of the curves with the horizontal lines representing integers mark the resonance wavelengths for GFP. It can be seen that phase accumulates faster along wavelength domain for the first diffracted order than for the zero-th order FP, indicating that GFP can potentially have more resonances than FP given the same cavity thickness. It also indicates that GFP can have resonances with a much thinner cavity.

Fig. 3.

The phase accumulation with respect to wavelength for the zero-th and first diffracted order inside GFP structure for a cavity thickness of $10\mathrm{\mu }\mathrm{m}.$

2.2.1. Coupled-bloch-mode model of GFP

The optical response of the resonator structure to a particular change in resonator thickness can be calculated employing rigorous coupled wave analysis (RCWA). However, instead of solving the entire structure, scattering at individual interfaces is computed and incorporated into a matrix model. This approach offers two significant advantages over the use of RCWA for the entire structure. First, the terms used in our model are more explicit, making it easier to analyze the underlying physical mechanisms. Second, once the canonical problem of scattering at the interface is solved, it can be easily solved for various structures with different thicknesses without repeating the full electromagnetic calculation. The coupled-Bloch-mode model can be applied to simplify the study of the behavior of GFP, which is similar to the approach of Lalanne et al. for deep lamellar gratings [40]. The optical field within the cavity is modeled as a superposition of two counterpropagating fields: one propagating in the positive z-direction and one propagating in the negative z-direction. The field propagating in the positive z-direction within the resonator is represented as ${\mathit{E}}^{+}$, which is a $3\times 1$ matrix representing only the propagating modes, i.e., −1, 0 and +1 diffracted orders. The propagation of evanescent waves is completely neglected because their penetration depth is significantly smaller than the polymer thickness and these waves do not reach the other side of the cavity where energy exchange between modes occurs. Similarly, the field propagating in the negative z-direction within the resonator is represented as ${\mathit{E}}^{-}$, which is also a $3\times 1$ matrix. A $3\times 3$ diagonal matrix is defined as $\mathbf{\Phi }$ to represent the accumulated phase during propagation from the interface of Region 1 and 2 to the interface of Regions 2 and 3 as follows:

$$\begin{array}{c}\mathbf{\Phi }=\left[\begin{array}{ccc}{e}^{i{k}_{z}L}& 0& 0\\ 0& e^{i\frac{2\mathrm{\pi }{n}_2}{\lambda }L}& 0\\ 0& 0& e^{i{k}_{z}L}\end{array}\right]\end{array}$$ (7)

where $k_z=\sqrt{{\left(2\mathrm{\pi }{n}_2/\lambda \right)}^2-{k_g}^2}$, $L$ is the thickness of the resonator, and $k_g$ is the grating vector.

Because only one propagating mode exists in Regions 1 and 3, the reflectivity $\mathit{ref}$ and transmissivity $\mathit{trans}$ are scalar quantities and can be expressed as

$$\begin{array}{c}\mathit{ref}={\mathit{r}}_{\mathbf{12}}+{\mathit{t}}_{\mathbf{21}}\mathbf{\Phi }{\mathit{E}}^{-}\end{array}$$ (8)

$$\begin{array}{c}\mathit{trans}={\mathit{t}}_{\mathbf{23}}\mathbf{\Phi }{\mathit{E}}^{+}\end{array}$$ (9)

where $\mathit{r}$ and $\mathit{t}$ are reflection and transmission coefficient matrices, and can be calculated via RCWA for scattering involving a single isolated grating and Fresnel’s equations between two homogeneous semi-infinite media, and subscripts indicate the propagation direction from the region denoted by the first index to that of the second index.

According to this definition, the fields propagating in the positive and negative z-directions can be expressed as

$$\begin{array}{c}{\mathit{E}}^{-}={\mathit{r}}_{\mathbf{23}}\mathbf{\Phi }{\mathit{E}}^{+}\end{array}$$ (10)

$$\begin{array}{c}{\mathit{E}}^{+}={\mathit{t}}_{\mathbf{12}}+{\mathit{r}}_{\mathbf{21}}\mathbf{\Phi }{\mathit{E}}^{-}\end{array}$$ (11)

Substituting Eq. (10) into Eq. (11) gives

$$\begin{array}{c}{\mathit{E}}^{+}={\mathit{A}}^{-\mathbf{1}}{\mathit{t}}_{\mathbf{12}}\end{array}$$ (12)

where $\mathit{A}=\mathit{I}-{\mathit{r}}_{\mathbf{21}}\mathbf{\Phi }{\mathit{r}}_{\mathbf{23}}\mathbf{\Phi }$.

Further substitution of Eq. (12) into Eq. (8) and (9) yields

$$\begin{array}{c}\mathit{ref}={\mathit{r}}_{\mathbf{12}}+{\mathit{t}}_{\mathbf{21}}\mathbf{\Phi }{\mathit{r}}_{\mathbf{23}}\mathbf{\Phi }{\mathit{A}}^{-\mathbf{1}}{\mathit{t}}_{\mathbf{12}}\end{array}$$ (13)

$$\begin{array}{c}\mathit{trans}={\mathit{t}}_{\mathbf{23}}\mathbf{\Phi }{\mathit{A}}^{-\mathbf{1}}{\mathit{t}}_{\mathbf{12}}\end{array}$$ (14)

Comparison with a full 81-order RCWA indicates that within the wavelength defined by Eq. ($5$), the model is consistent with the RCWA for the complete GFP structure. Once scattering with a single isolated grating layer is calculated, the matrix approach significantly reduces the computation time by at least two orders of magnitude, enabling efficient exploration of the parameter domains.

2.2.2. Optical performance of GFP

Fig. 4(a) shows the optical reflectivity for transverse electric (TE) polarization calculated for the structure with a single grating with a cavity refractive index of 1.58 with respect to grating thickness and wavelength. TE refers to the polarization where the electric field is oriented along the y-axis only. The refractive indices of the superstrate and substrate were chosen to match those of fused silica and water. The orange vertical line indicates the cut-off wavelength determined using Eq.$5$. To the left to the orange line, the first diffracted orders are no longer confined in the cavity, therefore, no GFP modes are supported. A detailed description can be found in Appendix B. Related to the theme of this research is the field distribution for the two points of interest marked A and B in Fig. 4(a). Marker A corresponds to normal incidence resonance peak wavelength, and marker B corresponds to left half-maximum position of the resonance. Their respective field distributions are shown in Fig. 4(c) and (d). It can be observed that, for both cases, at normal incidence, when around and in resonance, a standing wave pattern is formed both longitudinally and laterally, only the field intensity is different. The longitudinal and lateral standing wave formation at normal incidence provides additional confinement of energy along grating direction, i.e., x-axis, whereas for y-axis, which is perpendicular to the grating direction, no additional confinement is available, so 1D GFP behaves similarly to a conventional FP along the y-direction. Fig. 4(b) shows the reflectivity map as a function of cavity thickness and wavelength. It can be observed that the resonance trace generally follows Eq. $6$.

Fig. 4.

(a) Reflectivity map as a function of wavelength and grating thickness for TE polarization with a cavity of 5 $\mathrm{\mu }\mathrm{m}$. Marker A corresponds to the resonance peak wavelength; marker B corresponds to left half maximum resonance position. (b) Reflectivity map as a function of wavelength and cavity thickness varying from 2 $\mathrm{\mu }\mathrm{m}$ to 6 $\mathrm{\mu }\mathrm{m}$. Field distribution corresponding to (c) A and (d) B markers in (a), respectively.

For the fabricated experimental sample, a fit was implemented. It should be noted that, to match the precise measured spectrum with experimental results, it was necessary to fit the optical path length ($n_2\times \mathrm{L}$) as there was uncertainty in these values individually. The simulations were excellent predictors of the resonant linewidth and spectra. As Eq. $6$ indicates, the resonance trace is non-linear in wavelength domain, and resonance linewidth is strongly related to the resonance wavelength. Therefore, a slight deviation from the actual experimental parameters can introduce significant differences. However, the simulation and prediction remain informative for revealing the resonance linewidths and spectra.

Fig. 5 shows the simulated reflectivity with parameters listed in the figure caption. From Fig. 5, an asymmetry in the skirts of the sharp resonance are characteristic of a Fano resonance, which results from the interference between a high-Q first order resonance and low-Q background zeroth order resonance. Different phase relations between these contributions lead to different asymmetries in the line shape. The cavity thickness and refractive index were selected by minimizing the difference in free spectral range between the simulation and the experiment. The fill factor was chosen based on SEM images of the grating structure. The fitted cavity thicknesses in these simulations were somewhat slightly larger than those estimated from SEM images, which is understandable because the SEM cross sections may have been taken tilted at a slight angle from the vertical. The resonance marked A at 1500.02 nm in Fig. 5(a) has a FWHM of 1.43 nm; the resonance marked B at 1558.38 nm in Fig. 5(a) has a FWHM of 0.39 nm; the resonance marked C in Fig. 5(b) at 1533.88 nm has a FWHM of 0.35 nm and the resonance marked D in Fig. 5(c) at 1522.54 nm has a FWHM of 0.26 nm. The FSR between A and B is 58 nm, the FSR of Resonance C is 32.7 nm on the left and 25.0 nm on the right, and the FSR of Resonance D is 19.1 nm on the left, 16.82 nm on the right and 14.24 nm for the next adjacent peak.

Fig. 5.

Simulated reflectivity with a 500-nm grating with a PMMA fill factor of 67% and fused silica fill factor of 33% and a cavity of (a) $2.29\mathrm{\mu }\mathrm{m}$, (b) $5.36\mathrm{\mu }\mathrm{m}$ and (c) $10.1\mathrm{\mu }\mathrm{m}$. Refractive index of the cavity is set to 1.58, that of water is set to 1.318, and that of fused silica is 1.444.

2.3. GFP as an acoustic detector

The performance of optical resonators in acoustic detection is assessed primarily by three key parameters, i.e., responsivity, bandwidth, and sensitivity. In this context, responsivity is defined as the change in reflectivity per unit incident pressure. The responsivity and bandwidth are related to the resonator design and can generally be determined via a theoretical analysis. It is widely acknowledged that an intrinsic trade-off exists between responsivity and bandwidth for FP-based acoustic detection [18]. Sensitivity is commonly characterized by the noise-equivalent pressure (NEP), which is defined as the minimum detectable pressure level corresponding to an SNR of unity, and is determined jointly by the responsivity of the transducer and intrinsic noise of the experimental system. The responsivity $R_p$ is defined as

$$\begin{array}{c}{R}_p=\frac{\mathrm{d}I}{\mathrm{d}p}=\frac{\mathrm{d}I}{\mathrm{d}\lambda }\frac{\mathrm{d}\lambda }{\mathrm{d}L}\frac{\mathrm{d}L}{\mathrm{d}p}\end{array}$$ (15)

where $I$ denotes normalized optical intensity, $p$ denotes input pressure, $\lambda$ denotes the optical wavelength and $L$ denotes the length of the cavity. $\mathrm{d}I/\mathrm{d}\lambda$ represents the slope of the optical reflectivity with respect to wavelength, $d\lambda /\mathrm{d}L$ represents the shift of reflectivity caused by pressure-induced cavity thickness change, and $\mathit{dL}/\mathrm{d}p$ corresponds to the acoustic response, i.e., the change of cavity thickness induced by acoustic pressure.

The characterization of GFP as a pressure sensor proceeds through investigations of its acoustic behavior and optical response. The physical configuration of the GFP resonator resembles that of a conventional FP cavity, and its detection principle is likewise based on monitoring optical variations resulting from longitudinal dimensional distortions induced by acoustic pressure. Effectively, acoustically induced longitudinal dimension distortion is related to strain distribution and longitudinal elastic constant, $c_{11}$, since the layer is constrained from dimensional changes in the plane of incidence. To calculate the acoustically induced dimension distortion, it is necessary to calculate the pressure distribution, $P_{\mathit{tot}}$, in Eq. 2, throughout the cavity.

The pressure field can be computed numerically utilizing finite element software such as COMSOL. Nevertheless, the present configuration permits a more straightforward analytical description based on acoustic impedance. Fig. 6(a) shows the equivalent transfer matrix model of the layered GFP structure. The acoustic reflection and transmission coefficients of the layered structure can be determined using acoustic impedance, which is defined as the product of the material density and the acoustic velocity. This formulation yields forward and backward propagating waves, i.e., P⁺ and P^- at this interface. The total pressure at any point is simply given by the sum of these two complex quantities multiplied by the propagation phase factors.

Fig. 6.

(a) Transfer matrix model of the GFP structure and (b) normalized simulated frequency response for 2.5 μm, 5 μm and 10 μm cavity thickness.

Because the grating dimensions were significantly smaller than the wavelengths of typical medical or industrial ultrasonic waves, the acoustic impact is negligible except at frequencies exceeding 500 MHz. Consequently, the grating was modeled using the effective medium approximation (EMA) where a weighted average is calculated for the inverse of the effective bulk modulus and effective density as follows

$$\begin{array}{c}\frac{1}{K_{\mathit{eff}}}=\sum _i\frac{{\varphi }_i}{K_i},{\rho }_{\mathit{eff}}=\sum _i{\varphi }_i{\rho }_i\left(i=1,2,\dots \right)\end{array}$$ (17)

where $K_{\mathit{eff}}$ and ${\rho }_{\mathit{eff}}$ are the effective bulk modulus and effective density of the grating region modeled as an equivalent medium, respectively; $K_i$, ${\rho }_i$, and ${\varphi }_i$are the bulk modulus, density, and volume fraction of the $i$-th constituent material; $i$ denotes the material component in the grating composite.

The effective velocity and impedance are then given by

$$\begin{array}{c}{c}_{\mathit{eff}}=\sqrt{\frac{K_{\mathit{eff}}}{{\rho }_{\mathit{eff}}}},Z_{\mathit{eff}}={\rho }_{\mathit{eff}}{c}_{\mathit{eff}}\end{array}$$ (18)

where $c_{\mathit{eff}}$ is the effective acoustic velocity and $Z_{\mathit{eff}}$ is the effective acoustic impedance.

Fig. 6(b) shows the acoustic frequency response in terms of thickness displacement per pascal for the total cavity thicknesses of 2.5 μm, 5 μm and 10 μm with respect to acoustic frequency and incidence angle from water given that acoustic velocity is frequency independent. It can be observed that at normal incidence, bandwidths of 381 MHz, 192 MHz and 97 MHz can be expected for 2.5 μm, 5 μm and 10 μm cavity, respectively.

3. Experimental results

3.1. Fabrication

The GFP structure was fabricated on a fused silica substrate by deep-ultraviolet (DUV) lithography followed by dry etching for the grating layer and spin-coating for the cavity layer. DUV lithography was chosen over serial methods like electron beam lithography because it provides rapid prototyping of grating geometries with high pattern fidelity, excellent critical-dimension control, and good large-area uniformity, which are important for obtaining reproducible optical resonance performance. Three batches of GFP devices were fabricated to evaluate the effects of the cavity thickness on the optical performance and demonstrate the trade-off between responsivity/sensitivity and bandwidth.

Fig. 7(a) shows a schematic for the fabrication process. The substrate fused silica wafer was primed with HMDS at 125 °C for 60 s and stabilized at 20 °C for 30 s. UV135G photoresist was then spin coated at 3500 rpm for 45 s, followed by a soft bake at 120 °C for 60 s and cooling at 20 °C for 30 s to form a layer of 490 nm. The grating pattern was defined using a DUV 3030EX6 stepper (Canon Inc., Japan) with an exposure dose of $360\mathrm{mJ}\bullet {\mathrm{cm}}^{-2}$, followed by a post-exposure bake at 130 °C for 60 s and cooling at 20 °C for 30 s. After development in TMAH for 60 s and rinsing in deionized water for 1 min, the pattern was transferred into the fused silica using a GDE C200 dry etcher (NAURA Technology Group, China) with a ${\mathrm{CF}}_4/{\mathrm{C}}_4{\mathrm{F}}_8/\mathrm{Ar}$ plasma process at an etch rate of approximately $300\mathrm{nm}\bullet {\min }^{-1}$ for 90 s, producing a surface grating with a linewidth of 500 nm, a period of 1 μm, and a groove depth of approximately 500 nm over an die size of 20 mm × 20 mm. Subsequently, a proprietary UV-curable polymer coating resist, OHR1600 (Prinano, China), was spin coated onto the etched fused silica at 1000, 2000 and 4000 rpm for 60 s, and the coated sample was then cured under ultraviolet illumination in vacuum to complete the polymer layer of the GFP resonator for ultrasound detection. Fig. 7 shows the cross sections of the fabricated GFP devices with different spin speed forming an approximately 2.1 μm, 4.9 μm and 10.1 μm thick uniform polymer layer, respectively. It should be noted that the surface roughness in Fig. 7(b)-(d) is partly due to uncleaned surface residual after experiments and cleaving.

Fig. 7.

(a) Schematic for the fabrication process. (b) SEM images of the fabricated GFP devices with a spin coating speed of (b) 1000 rpm, (c) 2000 rpm and (d) 4000 rpm, yielding a cavity thickness of (b) 10.1 μm, (c) 4.9 μm, and (d) 2.1 μm, respectively.

In practice, exposure was performed on a 6-inch fused silica wafer, which was then cut into $2\times 2$ die pieces rather than single die pieces to mitigate the edge effect from spin coating. OHR1600 is a UV-curable polymer with a refractive index of around 1.6 at visible wavelengths and 1.58 at around 1550 nm wavelength. It was selected as the FP cavity material owing to its excellent optical transparency and its suitable combination of acoustic compliance and mechanical stability, which are similar to those of PMMA, for thin-film ultrasound sensing.

This fabrication route combines high pattern fidelity, and good wafer-scale repeatability with a relatively simple process flow consisting of a single DUV-defined grating, dry etching, and spin-coating of the cavity layer. After prototyping, fabrication of the grating can be further streamlined through nano-imprinting lithography for future standardized industrial mass production.

3.2. System

The optical resonances of the GFP structures feature narrow spectral linewidths and high angular selectivity. To characterize the performance of the transducer, a wavelength-interrogation setup with high angular stability was implemented, as shown in Fig. 8. The system operates in a forward-propagation photoacoustic configuration with an excitation wavelength of 532 nm and a probe wavelength for the GFPs, tunable around 1550 nm to avoid crosstalk while maintaining high resolution at visible wavelengths.

Fig. 8.

Experimental Setup. IRTL: infrared tunable laser; LP: linear polarizer; HWP: half-wave plate; BS: beamsplitter; PL: nanosecond pulse laser; VPD: photodetector at visible wavelength; IRCam: infrared camera; IRPD: infrared photodetector; OL: objective lens; L: lens. Inset: A sample reflected beam captured by IRCAM.

Wavelength interrogation was performed using a fiber-coupled, linearly polarized infrared tunable laser (TSL−710, Santec, Japan) centered at 1550 nm with a tuning range of 1480–1640 nm and a typical linewidth of 200 kHz, and a maximum output power of 30 mW at 1550 nm. The output polarization was filtered using an achromatic linear polarizer (LPNIR100-MP2, Thorlabs, USA) and adjusted using an achromatic half-wave plate (AHWP10M−1600, Thorlabs, USA) to ensure consistent polarization throughout the measurement. Subsequently, the collimated beam was propagated through a pair of lenses, L1 (f = 100 mm, Thorlabs, USA) and L2 (f = 100 mm, Thorlabs, USA), to achieve the desired beam diameter of 1.5 mm for uniform illumination of the sample and fine adjustment of the beam collimation. The beam was subsequently directed without expansion using a polarizing beamsplitter (PBS, CCM1-PBS254/M, Thorlabs, USA) and a pair of projection lenses, L3 and L4 (f = 100 mm, Thorlabs, USA). A half-wave plate was placed between the PBS and the projection lenses to rotate the polarization to 45° to ensure that the light reflected from the GFP was reflected by the PBS. After a right-angle mirror, the beam was projected onto the fabricated GFP structure. Reflected light was redirected by the PBS and projected utilizing collection lenses, L5 (f = 50 mm, Thorlabs, USA), and L6 (f = 150 mm, Thorlabs, USA) carrying a threefold expansion of the beam, then through an optical zero-aperture iris (ID37Z, Thorlabs, USA) between L6 and BS, and split by a beamsplitter and then propagated onto a photodetector (PD, FPD610-FS-NIR, Menlo Systems, Germany) and a NIR camera for data acquisition monitoring. The output of the photodetector was fed into a low-noise amplifier with a bandwidth of 150 MHz prior to acquisition. The amplified signal was digitized using an oscilloscope (MSOS254A, Keysight, USA) and an 8-bit computer-controlled data acquisition card (PCIE8920, ART Technology, China) for imaging. The zero-aperture iris allows the system to adjust the interrogation element size from 0, but for its two-aperture design, the shape is not always a circle. The actual acoustic element size on the GFP is no larger than 150 µm × 150 µm as indicated in the inset of Fig. 8.

Photoacoustic excitation was achieved utilizing fast laser pulses from a passively Q-switched Nd:YAG laser operating at 532 nm (Changguang, China), focused onto samples mounted on a customized motorized XYZ stage. During experiments, the maximum pulse energy was attenuated to below 200 nJ with a pulse repetition rate of 1 kHz and a pulse width of 3.5 ns. Focusing was achieved utilizing an objective lens (Plan N, 10×, 0.25 NA, Olympus, Japan). The sample was mounted to ensure that its bottom surface remained in direct contact with a thin water layer, thereby serving as an efficient acoustic coupling medium. This configuration enables the photoacoustically generated pressure waves to propagate from the sample into the GFP sensors with minimal attenuation or reflection loss, thereby ensuring accurate detection of the acoustic signals and maintaining high signal-to-noise performance in the imaging measurements. The stability and vibration resistance of the system were improved by reinforcing the optical and mechanical framework with additional cage-structure components (Raycage, China) to ensure consistent optical alignment and measurement repeatability during extended experiments.

A 100-nm-thick graphene film coating on a glass slide (Sixcarbon Technology, Shenzhen, China) was employed to characterize the bandwidth and directivity performance of the GFP devices by converting the incident laser intensity into acoustic waves. The multilayer graphene was synthesized on nickel foil by a high-temperature carbon dissolution-precipitation process. The nickel foil was first heated to 1000 °C under a hydrogen atmosphere and annealed for 30 min to remove surface impurities and improve crystallinity. Subsequently, methane (10 sccm) was introduced for 30 min, allowing carbon to dissolve into the nickel substrate. After the carbon dissolution step, the sample was cooled at a rate of 2 °C min⁻¹ . Upon reaching 600 °C, rapid cooling was applied. During the cooling process, dissolved carbon precipitated from the nickel and formed graphene layers on the foil surface. For graphene transfer, a PMMA supporting layer was first spin-coated onto the graphene surface. The underlying nickel foil was then removed by hydrochloric acid etching, leaving the graphene supported by the PMMA film. The resulting PMMA-graphene film was transferred onto a glass slide, followed by removal of the PMMA using acetone.

System trigger and synchronization were achieved using a Python script. This configuration enables the system to support reliable acquisition and analysis of both ultrasound and photoacoustic signals, providing the necessary temporal and spectral fidelity for responsivity and bandwidth characterization of the GFP.

3.3. Reflectivity

Before characterization, wavelength-scanning measurements were initially conducted to identify the resonance peaks in the reflection spectra of all devices and then fined-tuned for a maximum response. The spectral separation between adjacent reflectivity peaks corresponds to the optical thickness of the cavity layer and is directly related to the physical optical path length. Fig. 9(a), (d) and (g) show the measured reflectivity spectra (blue solid line) of the GFP configurations with cavity thicknesses of 2.1 μm, 4.9 μm, and 10.1 μm, respectively. The yellow dashed lines mark the simulated reflectivity spectra as shown in Section 2.2.2. Fig. 9(a) shows that for a cavity of 2.1 µm, the resonance around 1500.02 nm has a FWHM of 1.18 nm, giving a Q of 1271. With the free spectral range to the nearest peak being 59 nm, the finesse of the resonance is 50. The visibility of the peak is close to 1 as the background reflection is mostly coupled out by the wedge. It can be noted that visibility is low for the resonance around 1560 nm, because the GFP mode is sensitive to the optical incident angle.

Fig. 9.

Reflectivity and responsivity results for GFP with various cavity thickness. (a) Reflectivity spectrum for GFP with a 2.1-µm-thick cavity, (b) temporal responses to a 25 MHz UT driven by a pulse receiver, and (c) response maxima versus input pressures with linear regression for GFP with the peak near 1500.02 nm. (d)-(f) corresponding reflectivity for GFP with a 4.9-µm-thick cavity and responsivity results with the peak near 1533.88 nm. (g)-(i) corresponding reflectivity for GFP with a 10.1-µm-thick cavity and responsivity results with the peak near 1522.54 nm.

Fig. 9(d) shows the reflectivity for a cavity thickness of 4.9 µm, the resonance around 1533.88 nm has a FWHM of 0.4 nm, giving a Q of 3835. With the average free spectral range to the nearest peak at 28.8 nm, the finesse of the resonance is 72. The visibility of the peak is close to 1. Fig. 9(g) shows the reflectivity for a cavity of 10.1 µm, the resonance around 1522.54 nm has a FWHM of 0.23 nm, giving a Q of 6620. With the average free spectral range to the nearest peak at 18 nm, the finesse of the resonance is 78.

The measured spectra of GFP configurations are generally similar, exhibiting well-defined GFP resonance peaks within the scanned wavelength range. The measured spectra show good alignment with simulated resonance linewidths and FSRs reported in Section 2.2.2. The small differences in the peak amplitude and spectral contrast can be attributed to variations in the field confinement and surface scattering introduced by the imperfect grating profile.

3.4. Responsivity

The performance of the GFP is characterized by four key parameters: responsivity, bandwidth, sensitivity, and resolution. The first two parameters are primarily determined by the optical and acoustic design of the structure. Responsivity, $R_p$, is defined as the change in measured optical intensity per unit applied acoustic pressure:

$$\begin{array}{c}{R}_p=\frac{\mathit{dI}}{\mathit{dp}}\end{array}$$ (19)

where $\mathit{dI}$ is the change in detected optical intensity, and $\mathit{dp}$ is the applied acoustic pressure.

It quantifies the efficiency with which mechanical changes in pressure or deformation are converted into measurable signals normalized to the full maximum. Responsivity is also an important figure of interest because it reflects the intrinsic transduction efficiency of the detector, largely independent of the specific noise conditions of the readout system. As such, it provides a useful basis for lateral comparison between different acoustic sensing mechanisms and device architecture, even when their absolute NEP values are measured under different experimental conditions.

Responsivity characterization employed acoustic excitation generated by an ultrasound transducer (UT) at a center frequency of 25 MHz. The transducer was driven by a series of electrical pulses generated using a pulse generator (DPR300, JSR, USA) at 16 discrete voltage amplitudes to produce different acoustic output levels. The output acoustic pressures corresponding to these 16 amplitude levels ranged from 134 kPa to 614 kPa, as calibrated using a reference hydrophone (HMB−200, Onda, USA). The transducer and pulse generator were calibrated prior to measurements to ensure linearity and reproducibility. This configuration enabled the systematic evaluation of the GFP responsivity to varying acoustic pressures, establishing a relationship between the optical signal change and the incident acoustic amplitude. Fig. 9(b), (e) and (h) show the temporal responses of GFP devices with cavity thicknesses of 2.1 μm, 4.9 μm, and 10.1 μm, respectively. It can be observed from Fig. 9(h) and (i) that both upper and lower maxima experienced saturation.

The response maxima were plotted against the input pressure and shown in Fig. 9(c), (f) and (i), respectively. Linear regression was performed on the maxima of the responses to extract the slope, which is the responsivity of the GFPs. The responsivity is $9.11\times {10}^{-7}{\mathrm{Pa}}^{-1}$ for a 10.1-μm-thick cavity, $3.711\times {10}^{-7}{\mathrm{Pa}}^{-1}$ for a 4.9-μm-thick cavity, and $1.714\times {10}^{-7}{\mathrm{Pa}}^{-1}$ for a 2.1-μm-thick cavity. The observed contrast in responsivity provides a clear and quantitative indication of the difference in cavity thickness between the three fabricated GFP devices, confirming that the structural thickness plays a dominant role in governing the overall sensitivity of the GFP sensors because responsivity ratio is similar to the ratio of thickness as reflected in Eq. 15.

3.5. Bandwidth

Bandwidth characterization was performed employing broadband photoacoustic excitation in place of the ultrasound transducer with a 100-nm thick graphene layer on glass serving as the acoustic source. The −6 dB bandwidth of the laser was 119 MHz as shown in Fig. 10. The broadband nature of excitation ensures that a wide range of acoustic frequencies is generated, enabling a comprehensive evaluation of the temporal and spectral responses of the sensor. The detected waveform was analyzed in the frequency domain, and its spectrum was compared with that of a recorded laser-pulse signal. The overlap and attenuation characteristics of these two spectra provide a direct measure of the operational bandwidth of the sensor and reveal the frequency range over which the GFP structure can efficiently detect acoustic waves. The calibrated bandwidth is given by $f_{\mathit{GFP}}=f_{\mathit{Measurement}}/f_{\mathit{laser}}.$ $f_{\mathit{GFP}}$ was marked in yellow as calibrated response, $f_{\mathit{Measurement}}$ is shown in blue as measurement response, and $f_{\mathit{laser}}$ was marked in orange as laser pulse response in Fig. 10(d)-(f).

Fig. 10.

Bandwidth analysis for GFP. Measured temporal photoacoustic response of GFP to excitation of a 100-nm-thick graphene layer for a cavity thickness of (a) 2.1 μm, (b) 4.9 μm, and (c) 10.1 μm. Measured frequency responses of GFP (blue), measured frequency response of the excitation laser (orange) and calibrated response incorporating frequency response of the excitation laser (yellow) for a cavity thickness of (d) 2.1 μm, (e) 4.9 μm, and (f) 10.1 μm.

Fig. 10(a)-(c) show the temporal profiles of the photoacoustic signals detected using the fabricated 2.1-μm, 4.9-μm and 10.1-μm GFP devices, respectively. Fig. 10(d)-(f) show the corresponding frequency-domain spectra obtained by fast Fourier transform (FFT) of the temporal signal. Via the FFT analysis, the measured −6 dB bandwidth of the 2.1-μm GFP was determined to be 103 MHz, and the calibrated bandwidth was 132 MHz; the measured −6 dB bandwidth of the 4.9-μm GFP was determined to be 100 MHz, and the calibrated bandwidth was 110 MHz due to a lower cut-off frequency at 10 MHz. The measured −6 dB bandwidth of the 10.1-μm GFP was determined to be 67 MHz from 9 MHz to 76 MHz, and the calibrated bandwidth was 71 MHz from 10 MHz to 81 MHz.

Notably, the bandwidth performance of the GFPs is not inversely proportional to cavity thickness owing to the bandwidth limit imposed by the pulse laser. These results confirm that the proposed device is capable of broadband ultrasound detection and demonstrates its strong potential for high-resolution applications in photoacoustic microscopy and imaging.

3.6. Directional frequency response

The directional response of the GFP sensor was characterized by measuring its response as the acoustic source was laterally displaced relative to the detector along two orthogonal directions. Specifically, line scans were performed along the $x$- and $y$-axes, where the $x$-direction was aligned with the grating vector and the $y$-direction was perpendicular to it as shown in Fig. 11. The graphene film was positioned at approximately 1.96 mm above the 4.9-μm GFP device calculated from the time delay from the temporal response map.

Fig. 11.

Directivity Analysis. (a) Schematic for directivity analysis where x-axis is along the grating direction and y-axis is perpendicular to the grating direction. (b) Temporal and (c) frequency response maps for the x-axis scan. (d) Temporal and (e) frequency response maps for the y-axis scan. The white line marks the directional response for a conventional FP with 150-μm disk element.

The directivity measurements revealed a noticeable directional difference between the two orthogonal scan axes. Along the $y$-axis, perpendicular to the grating vector, the response resembles that of a conventional FP sensor, since no grating diffraction is involved in this direction and the grating layer acts approximately as an effective homogeneous layer. Along the $x$-axis, however, a plateau-like region was observed over approximately $-0.15$ to $0.15$ mm, within which the signal arrival time, amplitude, and bandwidth remained nearly unchanged. This behavior suggests relatively low angular selectivity and limited bandwidth degradation in the grating direction, which may be beneficial for optical-resolution photoacoustic microscopy (OR-PAM) applications requiring robust broadband detection over a finite angular range.

As indicated by the anisotropic directional response, the actual effective acoustic element size is not circularly symmetric. Such an asymmetric effective aperture will itself produce a direction-dependent directional response, independent of any acoustic interaction with the subwavelength grating. Therefore, the measured directional asymmetry can be attributed to the non-circular effective sensing region rather than to acoustic scattering by the grating.

3.7. Sensitivity

To accurately determine the sensitivity of the GFP device, the noise-equivalent pressure (NEP), defined as the equivalent pressure level with unit signal-to-noise ratio, was quantified by extending the measured responsivity curve to a noise threshold corresponding to a signal-to-noise ratio (SNR) of 1. This approach identifies the minimum acoustic pressure that can be reliably detected by a sensor. To achieve a reliable NEP estimate, a set of fine-grained responsivity measurements was performed within the low-pressure regime (<1 kPa), wherein the sensor operates near its noise floor. In this experiment, a function generator (33622 A, Keysight, USA) produced low-amplitude electrical pulses to drive an ultrasound transducer, generating weak broadband acoustic waves for detection by the fabricated GFP device. A series of small, calibrated pressure levels were produced by systematically varying the pulse amplitude. The transducer-generator assembly was calibrated using a reference hydrophone (HMB−200, Onda, USA) from 1 to 10 V and extrapolated to 100 mV to ensure accurate pressure estimation. By comparing the detected optical signals with the corresponding acoustic pressures, the responsivity curve was extended into the low-pressure regime in conjunction with the noise measurements, revealing the intrinsic sensitivity limit of the device. An additional variable-gain amplifier was employed with amplifier gain adjusted for different devices to avoid clipping at the amplifier output.

To reduce random fluctuations and evaluate the linearity of the GFP transducer more accurately, each response was acquired by averaging over 16 acquisitions. The temporal responses are shown in Fig. 12(a)-(c) for three structures, respectively. The voltage responsivity was 527.1 $\mathrm{mV}/\mathrm{kPa}$, $1.255\mathrm{V}/\mathrm{kPa}$, and 956.6 $\mathrm{mV}/\mathrm{kPa}$ for the 2.1-μm cavity, the 4.9-μm cavity and the 10.1-μm cavity, respectively. Averaging statistically improves the SNR by approximately a factor of 4, enabling a more reliable assessment of device voltage responsivity. However, for noise characterization, no averaging was applied to ensure that the intrinsic background noise of the system could be directly measured. Fig. 12(e)-(g) shows the 16 unaveraged response maxima plotted against the input pressure. Linear regression was performed on all maxima points, yielding the fitted response marked in red in Fig. 12(e) to (g).

Fig. 12.

NEP based sensitivity analysis. Temporal responses averaged over 16 acquisitions for a 25 MHz UT driven by a function generator emitting electric pulses for (a) 2.1 μm, (b) 4.9 μm, and (c) 10.1 μm. Unaveraged response maxima plotted against input pressure for (e) 2.1 μm, (f) 4.9 μm, and (g) 10.1 μm: blue dots represent the recorded maxima; the yellow line represents the linearly fitted response, and red lines represent the 3$\sigma$ boundaries of the response, where $\sigma =204.3\mathrm{mV}$ for the 2.1-μm cavity, $\sigma =122.5\mathrm{mV}$ for the 4.9-μm cavity, and $\sigma =68.57\mathrm{mV}$ for the 10.1-μm cavity, is the standard deviation from mean values. (d) Recorded temporal signal captured prior to triggers with 3$\sigma$ boundaries outlined in red for the 2.1-μm cavity and (h) its frequency response demonstrating the noise bandwidth.

The noise level was further evaluated within a pre-pulse interval from −1.4 µs to −0.4 µs, corresponding to the time window before the arrival of the excitation pulse, and was estimated to be $\sigma =204.3\mathrm{mV}$ for the 2.1-μm cavity, $\sigma =122.5\mathrm{mV}$ for the 4.9-μm cavity, and $\sigma =68.57\mathrm{mV}$ for the 10.1-μm cavity, where $\sigma$ denotes the one-standard-deviation ($1\sigma$) noise level over a 100 MHz noise bandwidth. Fig. 12(d) and (h) show the temporal noise signal captured prior to triggers with 3$\sigma$ boundaries outlined in red where $\sigma =204.3\mathrm{mV}$ for the 2.1-μm cavity and its frequency response demonstrating the noise bandwidth. From these data, the $1\sigma$ noise-equivalent pressure (NEP) of the system was estimated as 388 Pa for the 2.1-μm GFP, 98 Pa for the 4.9-μm GFP, and 72 Pa for the 10.1-μm GFP over a bandwidth of 100 MHz, which is equivalent to $38.8\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$, $9.8\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$ and $7.2\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$ for the three GFP structures over a 100 MHz bandwidth, respectively. The peak NEP was 1161 Pa for the 2.1-μm cavity, 287 Pa for the 4.9-μm cavity, and 225 Pa for the 10.1-μm cavity over a bandwidth of 100 MHz. Noise spectrum analysis indicated that the dominant contribution originated from additive Gaussian noise, as no prominent deviation in proportionality was observed in the NEP for the 2.1-μm GFP and the 4.9-μm GFP relative to the responsivity measurement. However, the weaker-than-expected NEP improvement of the 10.1- µm cavity is likely due to the increased sensitivity of its narrower, higher-Q resonance to interrogation-point drift and to local cavity non-uniformity, together with the more stringent collimation required to match the resonant wavevector. Because the responsivity is evaluated at the reflectivity peak whereas the NEP is referenced to the measured noise and the actual operating reflectivity, a small reduction in the latter for the high-Q cavity contributes to the NEP not improving in proportion to the responsivity.

3.8. Resolution

In OR-PAM, the lateral resolution is determined primarily by the numerical aperture of the optical excitation system rather than by the acoustic detector itself, whereas the axial resolution is governed mainly by the bandwidth of the acoustic detector. To quantitatively evaluate the spatial resolution of the GFP-based photoacoustic system, the knife-edge method was employed to determine the lateral resolution, and the shift-and-sum method was used to estimate the axial resolution (z direction) [41], [42], [43]. A 100-nm-thick Cr lithography mask deposited on a 1-mm-thick glass slide containing block patterns served as the knife edge, and it was positioned at the focal plane of the detection system and mounted on a precision motorized translation stage to ensure controlled linear movement across the optical focus. The 4.9-µm GFP sensor recorded the reflected or transmitted optical signal as the block pattern gradually obscured the illuminated area.

As shown in Fig. 13(a), the measured photoacoustic amplitudes obtained across the block edge were fitted using a nonlinear error-function model to construct the edge-spread function (ESF). The first derivative of the fitted ESF, corresponding to the line-spread function (LSF), yielded an estimated lateral resolution of approximately 3.5 µm. The slight deviation from the theoretical value, 2.12 µm, determined by $\lambda /\mathit{NA}$, is primarily attributed to diffraction and multiple reflections through thick cover glass slide and water. Fig. 13(b) shows an estimate of the axial resolution for the 4.9-µm GFP employing the shift-and-sum method, wherein a replica of the axial response is shifted and added to the unshifted results. The axial resolution is the axially shifted distance at which the dip of the summed signal reaches $1/\sqrt{2}$, yielding a value of 11.6 µm, which generally aligns with the resolution set by $0.88c_w/\mathit{BW}$, where $c_w$ is the acoustic velocity.

Fig. 13.

Resolution characterization of the GFP imaging system. (a) Lateral resolution determination with knife-edge method. (b) Axial resolution determination with shift-and-sum method.

3.9. Multiple-reflection analysis

In the photoacoustic bandwidth and directivity measurements, the acoustic excitation was generated by a 100-nm-thick graphene layer on a 1-mm-thick glass substrate. Fig. 14(a) shows the detailed experimental configuration for the bandwidth and directivity measurements. In addition to the main photoacoustic response, delayed echoes were observed in the extended temporal traces obtained during the bandwidth and directivity measurements as the generated acoustic wave propagated through the coupling water layer and was detected by the GFP device fabricated on a 725-μm-thick fused silica substrate as shown in Fig. 14(a).

Fig. 14.

Multiple-reflection analysis. (a) The detailed experimental configuration for bandwidth and directivity measurements. Acoustic propagation demonstration for the PA signal (coral), reflection from GFP substrate (green) and reflection from graphene sample substrate (yellow). (b) An extended temporal response for a 4.9-μm GFP including the desired PA signal and reflections from GFP substrate (marked in green) and graphene substrate (marked in yellow).

To suppress parasitic optical reflections, the GFP substrate was mounted on a fused silica wedge using optical coupling oil. Under this configuration, in addition to the desired photoacoustic signal, delayed echoes arising from acoustic reflections at the GFP substrate/coupling-medium interface (marked in green in Fig. 14) and the graphene-substrate/air interface (marked in yellow in Fig. 14) can still be observed in the extended temporal response. These delayed features were identified by their arrival times relative to the main photoacoustic pulse and are marked separately in Fig. 14(b).

Such multiple reflections are a general consequence of finite-thickness solid substrates in laser-ultrasound measurements and may become a source of clutter in imaging modalities with a large acoustic depth of view, such as photoacoustic computed tomography (PACT). In the present work, however, their influence on the OR-PAM demonstration is limited because the effective imaging depth is constrained mainly by the optical focal depth of the excitation objective, so these delayed echoes fall largely outside the useful depth range. For future extension to PACT or other large-depth imaging applications, direct fabrication on a fused silica wedge would be a more suitable approach for suppressing substrate-related back-reflections and avoiding clutter. These results indicate that, although substrate-related echoes are present, they do not prevent accurate characterization or proof-of-concept OR-PAM imaging in the current system.

3.10. OR-PAM demonstration

To demonstrate the volumetric imaging capability of the system, a phantom composed of fine tungsten wires with a diameter of approximately 15 μm was imaged. Volumetric data were acquired by raster scanning the sample using a motorized 3-axis stage while recording the photoacoustic A-line signal at each position. The in-focus information was recorded for reconstruction to visualize the spatial distribution of the absorbing structures. The tungsten-wire phantom was selected as a convenient absorbing target because its strong optical absorption and well-defined fine features make it suitable for assessing the ability of the system to reconstruct spatially distributed structures and resolve details.

Fig. 15(a) shows the maximum-amplitude-projection (MAP) image in the $\mathit{xy}$-plane, obtained by projecting the maximum photoacoustic amplitude at each lateral position along the depth direction. The tungsten wires are clearly resolved, confirming that the system is capable of volumetric imaging of micrometer-scale absorbers. With 532 nm excitation and an objective of NA = 0.25, the optical excitation is tightly confined near the focal plane. To further illustrate the three-dimensional imaging performance, Fig. 15(b) shows representative $\mathit{xz}$-plane cross sections extracted at the lateral positions indicated by the orange and green dashed lines in Fig. 15(a). The 3-frame green cross sections demonstrated the process where two tungsten wires overlap and part. The wire below, therefore, cannot be clearly identified due to the strong optical absorption nature of tungsten wires.

Fig. 15.

Photoacoustic image of a tungsten-wire phantom. (a) The maximum amplitude projection (MAP) view of xy plane. (b) xz plane cross sections with y positions indicated by orange and green dashed lines in (a). (c) y-axis and z-axis linscans for the tungsten wire marked by the magenta rectangle in (b) demonstrating the quantitative measurement of the tungsten wire dimensions in depth (green) and lateral (yellow) direction.

These cross sections show the depth-resolved distributions of the tungsten wires and confirm the ability of the system to distinguish multiple absorbing features in the volumetric dataset. Fig. 15(c) shows corresponding lateral and axial line profiles for the wire marked by the magenta rectangle in Fig. 15(b), enabling a quantitative estimate of the apparent wire dimensions in the lateral and depth directions. These results provide a proof-of-concept demonstration that the GFP detector can be integrated into an OR-PAM system for volumetric imaging with micrometer-scale spatial resolution.

4. Discussion

The proposed GFP devices demonstrated strong performance as optically interrogated ultrasound sensors for photoacoustic and ultrasound applications, combining narrow optical resonances, broadband acoustic response, and high responsivity in a simple planar structure. The measured reflectivity spectra confirm that the GFP can sustain well-defined resonances with useful $Q$, finesse, and visibility, while the responsivity measurements show linear operation over a wide pressure range, indicating that the devices operate within the linear-elastic regime of the constituent materials. Together, these results confirm that the GFP can efficiently transduce acoustic-pressure-induced cavity deformation into measurable optical intensity changes.

The bandwidth measurements further highlight the suitability of the GFP for high-resolution detection of photoacoustically generated ultrasound. The measured and calibrated responses show that the 2.1-μm GFP, 4.9-μm GFP and 10.1-μm GFP devices provide sensitivity of $38.8\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$, $9.7\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$and $7.2\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$ with bandwidth extending up to 132 MHz, 110 MHz and 71 MHz, demonstrating the expected bandwidth-responsivity trade-off, with thinner cavities favoring broader bandwidth and thicker cavities favoring improved responsivity and lower NEP. The bandwidth for the 2.1-μm GFP and the 4.9-μm GFP were primarily limited by the laser pulse bandwidth, whereas that for the 10.1-μm GFP was primarily limited by the bandwidth-responsivity trade-off. The agreement between the measured optical spectra and theoretical analysis in terms of linewidth, free spectral range, and finesse as shown in Fig. 9 supports the physical picture developed in Section 2.

Conventional FP ultrasound detectors are a well-established and highly effective platform for ultrasound and photoacoustic sensing, with mature fabrication workflows, excellent repeatability, and strong demonstrated performance in applications such as photoacoustic computed tomography and microscopy [16], [36], [38]. The GFP architecture proposed here is therefore best viewed as a complementary alternative rather than a replacement. Its main advantages are a relatively simple planar fabrication route and the ability to retain visible resonances with useful Q and sensitivity even for very thin cavity layers, which is attractive for high-bandwidth applications such as PAM. At the same time, because the GFP resonance relies on grating-mediated coupling between the zero and diffracted orders, it is more sensitive to alignment and incident angle than a conventional normal-incidence FP cavity. The GFP thus offers a different balance of bandwidth, fabrication simplicity, and alignment tolerance, making it suitable for applications where these trade-offs are favorable.

A comparison between GFP and recently developed thin-film ultrasound detectors, including optical resonant sensors and piezoelectric PVDF-based detectors, is summarized in Table 1 in terms of bandwidth (BW), noise-equivalent pressure (NEP), and fabrication complexity. It should be noted that direct numerical comparisons should be interpreted with care because NEP and BW are not always reported under identical definitions and quantified under identical circumstances. Across thin-film detection platforms, an intrinsic design trade-off exists between BW and NEP: for a given detection principle, increasing the effective cavity thickness (or acoustic interaction length/compliance) typically improves pressure responsivity and thus reduces NEP, but at the expense of a narrower usable bandwidth. This trend is directly reflected by the two GFP implementations in this work, where the thinner GFP configuration favors ultrawideband response, while the thicker GFP shifts the operating point toward improved sensitivity with a reduced BW. Importantly, among planar thin-film detectors listed in Table 1, GFP achieves a particularly attractive and scalable BW-NEP balance while retaining a comparatively simple and scalable fabrication flow (spin-coating and nanoimprinting), providing a practical knob to tailor performance to application needs by adjusting cavity thickness.

Table 1.

Comparison of performance between recently reported detectors.

Type	Structure	Cavity	CF (MHz)	BW	NEP	Fabrication Complexity	Note
Optical	GFP (this work)	2.1-µm mix polymer 4.9-µm mix polymer 10.1-µm mix polymer		103 MHz (−6dB) 100 MHz (−6dB) 67 MHz (−6dB)	$38.8\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$ $9.8\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$ $7.2\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	low: DUV+etching+ spin-coating
	total-internal-reflection FP [17]	3.4 µm PDMS		75 MHz (−3dB)	$35.8\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	low: sputtering+ spin-coating
	Planar FP [36]	22 µm Parylene		39 MHz (−3dB)	$23.1\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	medium: sputtering+CVD+ sputtering
		38 µm Parylene		22 MHz (−3dB)	$15.7\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$
	Polymeric waveguide [44]	350 nm PDMS		201 MHz (−6dB)	$17\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	low: spin-coating
	Acoustic guiding FP [38]	25 µm SU−8		30 MHz	$32.5\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	medium: spin-coating +EBE+Photolithography
	Plano-concave microresonator [16]	30 µm Polymer		∼32 MHz (−3dB)	$12.7\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	medium: sputtering+stamping+ sputtering	A series of scalable thin-film transducers
		250 µm Polymer		3.8 MHz (−3dB)	$2.05\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$
		16 µm Polymer		40 MHz	$2.08\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	medium: sputtering+ dip coating+sputtering	Fiber-tip
	Buckled-dome microcavities [45]	0.8 µm fluorocarbon		15 MHz	$0.5-3\mathrm{m}\mathrm{P}\mathrm{a}\bullet \mathrm{H}{\mathrm{z}}^{\mathrm{-}\mathrm{1}\mathrm{/}\mathrm{2}}$	high: sputtering+ ICP-RIE+sputtering+ adhesion treatment
	Microbubble FP [46]	microbubble		∼0.8 MHz	$3.4\mathrm{m}\mathrm{P}\mathrm{a}\bullet \mathrm{H}{\mathrm{z}}^{-1/2}$	medium: coating+ heating+filling
	Surface plasmon resonator [20]	Gold film		125 MHz	$10.8\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	low: sputtering
	Bragg Grating Optical Fiber [47]	Bragg grating		160 MHz	$2.5\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	medium: precise polishing+coating
Piezo-electric	planar PVDF TrFE [48]	100 µm PVDF TrFe 28 µm PVDF TrFe	11 40	10 MHz 75 MHz	Not Rated	medium: deposition+ sputtering+wiring+ deposition	PCB array
	Fisheye PVDF [49], [50]	25 µm PVDF	15	29 MHz	$1.21\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	medium	spherical shape
	Spherical PVDF [51]	25 µm PVDF		29.7 MHz	$0.97\mathrm{mPa}\bullet {\mathrm{Hz}}^{-1/2}$	medium: bending+ sputtering+wiring	spherical shape

CF: center frequency; BW: bandwidth; NEP: noise-equivalent pressure.

Beyond planar implementations, GFP is also structurally compatible with geometric strategies reported for other high-performance optical thin-film detectors, such as spherical and plano-concave resonator designs, as well as acoustic-guiding structures [16], [38], [51]. Adopting curvature-enabled or focusing geometries can increase the effective receive aperture and improve collection efficiency, offering a pathway to further reduce NEP without proportionally sacrificing bandwidth. Therefore, future GFP development can leverage these established design concepts, in combination with continued optimization of cavity thickness and interrogation conditions, to push the BW-NEP frontier toward higher sensitivity and wider bandwidth simultaneously.

Thermal stability is a practical consideration for wavelength-interrogated polymer resonators, because both the refractive index and thickness of polymer layers exhibit temperature dependence [52], [53]. In GFP, resonance drift may manifest as baseline fluctuation in reflectivity when operating on a steep spectral slope under continuous illumination from the interrogation laser, potentially generating low-frequency noise in long-duration acquisitions. In practice, wavelength drift induced operating point shift was monitored with the detector where the DC level of received optical signal indicates the wavelength drift. In the present experiments, the 2.1-µm GFP device maintained stable performance across continuously repeated measurements over a period of 10 h, a maximum of 5% of response drift has been observed as shown in Fig. 16(a), suggesting that the current material stack and curing/post-curing steps provide adequate stability for current state ultrasound detection. A theoretical thermal drift analysis is calculated for a temperature drift from $-20°\mathrm{C}$ to $80°\mathrm{C}$ with a thermo-optic coefficient of $-1.3\times {10}^{-4}{°\mathrm{C}}^{-1}$ and a thermal expansion coefficient of $7\times {10}^{-5}{°\mathrm{C}}^{-1}$ shown in Fig. 16(b) [52]. The result indicates that the temperature-related resonance blue-shift happens at an approximate speed of 0.01 nm per degree Celsius. For future system-level deployment with improved sensitivity, thermal drift can be mitigated in real time by (i) temperature regulation of the coupling medium and sensor mount, and (ii) referencing strategies for wavelength locking onto the resonance peak position intermittently. Such measures are particularly relevant for array operation and in vivo imaging, where ambient and coupling conditions can vary over time.

Fig. 16.

(a) Overnight stability measurement for 10 h with the 2.1-µm GFP of a 25-MHz ultrasound transducer driven by a pulser. (b) Simulated reflectivity map varying temperature from −20 °C to 80 °C with a thermooptic coefficient of $-1.3\times {10}^{-4}{°\mathrm{C}}^{-1}$ and a thermal expansion coefficient of $7\times {10}^{-5}{°\mathrm{C}}^{-1}$. (c) A ∼0.25-linewidth resonance recorded with 4.9-µm GFP and TM polarization around 1536 nm. (d) Simulated reflectivity for a dual-grating GFP with 10-µm cavity and 500 nm grating.

Several practical limitations should also be noted. First, the directivity measurements show anisotropic behavior. This anisotropy is optical in origin: the one-dimensional grating renders the effective optical sensing region direction-dependent, structured by grating-coupled diffraction and lateral standing-wave confinement along the grating direction (x-axis), and behaving as a conventional FP cavity perpendicular to it (y-axis), and this should be considered in system design. This direction-dependent response can be further attributed to an asymmetric effective aperture. Second, delayed echoes arising from finite-thickness substrates remain observable in the bandwidth and directivity measurements. Although these reflections do not prevent reliable characterization or proof-of-concept OR-PAM imaging in the current forward-mode configuration, they could become a more significant source of clutter in larger-depth imaging modalities such as PACT.

Future work will focus on improving both the intrinsic performance of the GFP transducer and its implementation in an efficient OR-PAM system. On the transducer side, the structure requires only a simple spin-coated overlayer on top of the grating, enabling the potential use of softer materials and substantially thinner films. Such optimization is expected to preserve responsivity and sensitivity while shifting the sensitivity-bandwidth trade-off toward a higher bandwidth and broader detection range. Further gains can be achieved by tailoring the acoustic impedance and cavity geometry to improve the frequency response. Theoretical analysis indicates that sensitivity can be increased by approximately a factor of 8 via the use of a softer material, for example, a PDMS-based cavity, to significantly enhance the strain-induced thickness modulation, thereby improving responsivity. Currently, detection is performed using only the TE polarization. Fig. 16(c) shows an TM resonance peak recorded with the 4.9-µm demonstrating the system’s angular alignment quality. However, the linewidth is still an order of magnitude larger than simulated TM resonance. Finer control over position and tilt will be needed for further experiment. Furthermore, the TM signal can be introduced to form a differential signal for phase interrogation, which further enhances the responsivity, NEP, and signal-to-noise ratio without compromising the bandwidth [19]. Further fine-tuning of the responsivity and bandwidth can be achieved by fine-tuning the FP cavity thickness. More substantial performance potential can be achieved by involving an additional grating layer on top of the current GFP for a dual-grating structure as shown in Fig. 16(d) [54]. This potentially can allow the detector to simultaneously increase both the sensitivity and dynamic range in a single structure.

Array detection can greatly improve detection and scanning efficiency but usually comes with complex wiring design and expensive multichannel DAQs [48], [55]. Optical array detection can be realized through parallel discrete sensor array and parallelized interrogation [26], [56], [57]. Versatile optical means, e.g., beam multiplexing and beam modulation, can greatly relax and circumvent the necessity for strenuous design and expensive equipment [18], [26], [58]. On the discrete sensor array side, GFP is intrinsically compatible with planar, large-area array fabrication because the structure is realized with straightforward spin-coating and nanoimprinting on a standard coverslip, which provides potential for standardized mass array production with high repeatability and throughput. On the parallelized interrogation side, although the narrow resonance linewidth and high angular selectivity favor well-collimated/telecentric illumination, these constraints are compatible with modern beam-delivery optics and, importantly, can be turned into an advantage for multiplexing. In particular, a beam-modulation stack, e.g., spatial light modulator and digital micromirror, can generate multi-beam excitation for simultaneous interrogation of multiple pixels, or enable high-speed beam scanning to sequentially address a dense array without the electrical interconnect burden typical of piezoelectric arrays [59]. Implementation of advanced beam modulation techniques on photoacoustic excitation can further decrease the required time for imaging [60]. This strategy allows a single tunable source and shared detection chain to interrogate many sensing sites with flexible trade-offs between parallelism and speed, providing a practical pathway toward scalable GFP arrays for fast video-framerate photoacoustic/ultrasound imaging.

The directional measurements reveal an anisotropic response: along the direction perpendicular to the grating the behavior is consistent with a conventional FP element of approximately 150 µm, whereas along the grating direction the response is markedly broader. We attribute this anisotropy to the non-circular effective sensing region arising from the optical anisotropy of the one-dimensional grating, the grating itself being acoustically negligible over the frequency range studied. The broadened angular response along the grating direction may be advantageous for OR-PAM, where it increases the angular acceptance and could relax the lateral scanning step, although the consequences of this asymmetry for PACT, in which signals arrive over a wide range of incidence angles, remain to be investigated. With regard to bandwidth, it should be emphasized that the simulated response (Fig. 6) represents the intrinsic potential of the design, whereas the measured response (Fig. 10) is bound by the characterization configuration, in particular the tightly focused excitation source and the 150 MHz readout amplifier, therefore constitutes a lower bound on the achievable bandwidth. Feasibility evaluation of GFP for PACT with a rigorous determination of the intrinsic frequency response and directivity, using a large-area, spatially uniform, laser-generated planar source that can provide a unipolar waveform, is identified as an important step for future work [61].

5. Conclusion

In this study, a diffraction-grating-coupled-mode Fabry-Pérot resonator was proposed and experimentally validated as a simple, robust, and high-performance optical ultrasound and photoacoustic detector. By integrating a 1D polymer grating with a polymer FP cavity on a standard coverslip, the GFP architecture achieved efficient acoustic-to-optical transduction while maintaining optical transparency and straightforward fabrication via spin-coating and nanoimprinting. Theoretical modeling based on acoustic transfer matrix analysis and coupled-mode optics accurately predicted the mechanical and optical responses and closely aligned with experimental measurements. The fabricated devices exhibited high responsivity, broadband detection (calibrated bandwidths up to >130 MHz), low noise-equivalent pressure on the order of 72 Pa over 100 MHz for a cavity size of approximately 10.1 µm, and micrometer-scale lateral and axial resolution in an OR-PAM configuration. Collectively, these results demonstrate that GFP transducers have the potential to be a complementary alternative to the already well-established FP polymer sensors for high bandwidth applications.

CRediT authorship contribution statement

Michael Geoffrey Somekh: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Shibiao Wei: Writing – review & editing, Validation, Resources, Funding acquisition, Data curation. Mengqi Shen: Writing – review & editing, Resources, Methodology, Investigation, Funding acquisition. Xiaoping Jiang: Writing – original draft, Validation, Software, Methodology, Investigation, Formal analysis.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

Biographies

Xiaoping Jiang received the Ph.D. in biophotonics from The Hong Kong Polytechnic University in 2023. He is currently a postdoctoral research fellow at the Nanophotonics Research Center, Institute of Microscale Optoelectronics and State Key Laboratory of Radio Frequency Heterogeneous, Shenzhen University. His research interests include optical sensors, photoacoustics, sensing and imaging.

Mengqi Shen completed her Ph.D. at the University of Nottingham in 2018. After a period of working as Research Assistant in The Hong Kong Polytechnic University, she joined Shenzhen University as a postdoctoral researcher. She is currently a senior lecturer at Shenzhen MSU-BIT University. Her research interests include imaging, sensors, measurement and detectors.

Shibiao Wei received the Ph.D. degree from the Nankai University, Tianjin, China in 2015. After a period of working in Australia, he joined Shenzhen University and is currently an associate professor with the Nanophotonics Research Center, Institute of Microscale Optoelectronics and State Key Laboratory of Radio Frequency Heterogeneous, Shenzhen University. His research interests include plasmonic optics, photonic sensors and optical metasurface devices.

Michael G. Somekh received the first degree in Metallurgy and Science of Materials from Oxford University and the Ph.D. in Microwave Electronics from Lancaster University UK. After research fellowships at Oxford University, his first academic position was in University College London. He then joined the University of Nottingham, Nottingham, U.K., where he founded the Applied Optics group. After a period working in Hong Kong and Shenzhen, he currently holds a position in Nottingham University as Professor of Optical Engineering. He is a Fellow of the Institute of Physics and was elected Fellow of the Royal Academy of Engineering (the UK National Engineering Academy) in 2012 in recognition of his interdisciplinary work. His research interests include imaging, sensors and ultrasonics.

Appendix A. Analysis of Backing Strength on the Performance of FP-type Ultrasound Detectors

Two primary factors determine the actual pressure experienced by the resonator. The first factor is the backing material. When the backing layer is compliant and the sample is thin, the resonator does not deform, and the pressure is not transferred to the resonator. For layers considerably thinner than the acoustic wavelength, a stiff backing layer implies that the transducer sees approximately double the input pressure, whereas for a backing layer with an acoustic impedance similar to that of the transducer, the pressure imparted to the transducer is similar to the input pressure of the sound wave. The second factor is transducer thickness. As the transducer thickness increases, the strain induced by the ultrasound accumulates constructively, enhancing the overall change in thickness and, hence, the optical response. However, when the thickness becomes comparable to the acoustic wavelength, it cancels the acoustic contribution to the deformation, ultimately reducing the detection efficiency. The following analysis quantifies these effects and applies equally to both GFP and conventional FP resonators.

Fig. A1.

(a) Integrated pressure as a function of normalized thickness of transducer across the transducer with different backing materials for a unit pressure wave input. The total thickness is normalized to the acoustic wavelength of 2π. The incident medium, i.e., water, has a normalized impedance of 1, whereas the transducer medium has a normalized impedance of 2. The blue line corresponds to the integrated pressure for hard backing where the impedance of water is negligible compared with that of the backing medium. The orange, yellow, purple, green and cyan curves indicate the integrated pressure curves for media with normalized impedances of 8, 4, 2, 1 and 0.5, respectively. The magenta curve represents a compliant backing medium with negligible acoustic impedance. (b) Acoustic response comparison for soft- (solid) and hard-backing (dash) and GFP (blue) and a conventional FP (orange) of 10-μm cavity thickness, respectively

Therefore, for a typical conventional FP resonator consisting of a polymer film of various thicknesses sandwiched between a 20% reflective aluminum coating and a 75% reflective aluminum coating, the mechanical response to a given acoustic pressure can be estimated. Fig. A 1(a) shows the integrated pressures given by Eq. 2 for different thicknesses of a polymethyl methacrylate (PMMA) film with total thickness normalized to the acoustic wavelength of 2π and the acoustic impedance of the incident medium (water) normalized to 1. The acoustic impedance of the resonator cavity is 2. The blue curve corresponds to a rigid backing layer with a normalized acoustic impedance exceeding 10⁴. The orange, yellow, purple, green, and cyan curves correspond to backing layers with normalized backing impedances of 8, 4, 2, 1, and 0.5, respectively, with a normalized acoustic impedance of 1. The magenta curve represents a backing layer with a normalized acoustic impedance of 0. The analysis focused on the linear operation region, where the bandwidth effect is not significant. A harder backing can constructively contribute to the total pressure distribution within the cavity. For a small thickness, the gradient of the hard backing was twice that of the matched backing (acoustic impedance of 2) because the reflected field doubled the pressure. By contrast, compliant backing (acoustic impedance of zero) results in cancellation of pressure between the forward-propagating field and reflected field. For a small thickness, the signal is represented by the integrated pressure, which becomes non-zero when the phase difference between the incident and reflected beams ceases in the antiphase.

A brief acoustic-response comparison between the GFP and a conventional FP resonator is shown in Fig. A 1(b) for both soft and hard backing conditions. The conventional FP was assumed to consist of double dielectric mirrors, each formed by eight alternating layers with refractive indices of 2.27 and 1.34, an effective sound velocity of $5000\mathrm{m}/\mathrm{s}$ and effective density of $3\mathrm{g}/{\mathrm{cm}}^3$. In Fig. A 1(b), the soft backing case is shown with solid lines, whereas the hard-backing case is shown with dashed lines. It can be observed that hard backing provides additional response at the cost of a slight reduction in bandwidth. Although the conventional FP is already well matched acoustically, the discontinuity introduced by the mirror stacks has a minor effect near the cutoff frequency.

Appendix B. Physical Interpretation of the GFP

To provide additional physical insight into the operation of the grating Fabry-Pérot resonator (GFP), we consider a representative structure consisting of a 1-µm-period grating with a depth of 0.5 µm, a fused silica substrate ($n=1.444$), a polymer cavity layer ($n=1.6$) with a thickness of 5.2 µm, and water as the superstrate ($n=1.318$). Although the exact dimensions differ slightly from those used in the experiments, the physical mechanisms discussed below are generally applicable to the class of grating-coupled resonators introduced in this work.

Fig. A2.

(a) Reflection coefficient vs wavelength for a 1-µm-period grating with a depth of 0.5 µm, a fused silica substrate ($n=1.444$), a polymer cavity layer ($n=1.6$) with a thickness of 5.2 µm, and water as the superstrate ($n=1.318$). (b) Complex-plane evolution of the reflected field with increasing round-trip number at resonance ($\lambda =1578.24$ nm). The black circles mark increments of 10 round trips. The short black line from the origin denotes the first reflected component, $r_{12}$, corresponding to the portion of the incident field that does not enter the cavity. (c) Complex-plane evolution of the intracavity modal fields at resonance for the same case as (b). The green curve represents the zero-order field, while the blue curve represents the $\pm 1$diffracted orders, which are identical and therefore overlap. The unit circle corresponds to the input-field amplitude. At resonance, the zero-order field is progressively suppressed, whereas the diffracted-order field builds up strongly. (d) Complex-plane evolution of the reflected-field contributions slightly off resonance ($\lambda =1578.4$ nm). (e) Complex-plane evolution of the intracavity modal fields slightly off resonance ($\lambda =1578.4$ nm)

As shown in Fig. A2(a), the calculated reflection spectrum shows a sequence of sharp reflectivity maxima separated by low-reflectivity regions, indicating that the structure can support resonances with very high spectral selectivity. For a representative resonance near 1552.6 nm, the simulated quality factor reaches approximately $1.58\times {10}^4$, while the corresponding finesse is on the order of 120, demonstrating that a simple grating-assisted structure can support much sharper resonances than would be expected from a conventional single-mode cavity of comparable thickness.

A useful way to understand the origin of this high-$Q$ behavior is to rewrite the reflected field as a sum of contributions from successive round trips inside the cavity using the coupled Bloch mode model:

$$\begin{array}{c}\mathit{ref}={\mathit{r}}_{\mathbf{23}}+\sum _{\mathit{n}}{{\mathit{t}}_{\mathbf{21}}\left(\mathit{\varphi }{\mathit{r}}_{\mathbf{23}}\mathit{\varphi }{\mathit{r}}_{\mathbf{21}}\right)}^{\mathit{n}-\mathbf{1}}\mathit{\varphi }{\mathit{r}}_{\mathbf{23}}\mathit{\varphi }{\mathit{t}}_{\mathbf{21}}\end{array}$$ (A1)

Under this interpretation, the total reflectivity is built up gradually through coherent addition of many cavity returns. Fig. A 2(b) shows the buildup of $\mathit{ref}$with multiple reflections in the cavity at the peak of the reflectivity 1578.24 nm wavelength. At resonance, the reflected field requires several hundred effective round trips before converging, consistent with the large $Q$ factor. Fig. A 2(c) show an examination of the intracavity fields that further reveals that the zero-order component is initially dominant but is progressively suppressed with increasing round-trip number, while the $\pm 1$diffracted orders build up strongly and eventually dominate the resonant response. Fig. A 2(d) and (e) show those for a wavelength 0.16 nm off resonance. It can be seen that the reflection contributions are not quite in phase, resulting in a lower reflection, and similar effect occurs for the internal field. The diffracted orders grow steadily with each component close to being in phase with the last and eventually, the field becomes far greater than the input beam.

In an earlier publication [17], we presented a cavity based on total internal reflection. Here there were only oblique modes, so if the input beam was totally internally reflected it was necessary to insert a lossy layer (12 nm of gold) to give a reflectivity variation that could be used for transduction. The Q of the cavity in this case was of the order of 120 (more than two orders of magnitude less than the current configuration) so the combination of swapping between modes and use of only lossless materials gave the present resonator a vastly higher Q with an associated increase in sensitivity. In order to obtain highly sensitive detection it was necessary in [17] to employ a highly compliant cavity layer, which deformed strongly under incident field. In the previous work with the low Q, the walk-off of the beam was limited by the small number of reflections of the order of 4 compared to 360 in the present case. In the GFP, the walk-off is limited by examining the field pattern as shown in Fig. 4(c) and (d), where there is a standing wave parallel to the propagation direction which means that there is considerable confinement in the present structure. Another way of visualizing the confinement is by noting that there is mode swapping so that a +1 mode becomes −1 mode and vice versa, this means that walk-off of the beam reverses itself so that the field is much more confined than one would otherwise expect.

Thus, the GFP structure in whole acts as a coupled resonator where the grating is not merely acting as an input coupler; rather, it enables coherent energy exchange between the normally propagating mode and the diffracted modes. The high-$Q$ resonance is therefore associated with gradual transfer of energy into the diffracted-order cavity, which stores optical energy much more efficiently than the zero-order channel.

Appendix C. Coupled-Resonator Interpretation and Periodicity of the GFP Resonance

To further clarify the resonance condition of the grating Fabry–Pérot resonator (GFP), it is useful to examine the optical response as a function of cavity thickness rather than wavelength. This representation is cleaner because the scattering properties of the interfaces remain fixed, while only the propagation phases inside the cavity vary with thickness. In this way, the periodicity of the resonance can be understood more directly.

Fig. C1.

(a) Reflection (blue) and transmission (red) coefficients as functions of cavity thickness at a wavelength of 1480 nm for a GFP with a 1 μm grating period and 0.5 μm grating height. (b) Intracavity modal amplitudes as functions of cavity thickness for the same structure. The red curve represents the diffracted orders ($+1$ and $-1$, which overlap), and the blue curve represents the zeroth order. (c) Reflection (blue) and transmission (red) coefficients as functions of cavity thickness at a wavelength of 1549 nm for a GFP with a 1 μm grating period and 0.5 μm grating height

To illustrate this behavior, we consider a representative GFP structure with a 1 μm grating period and 0.5 μm grating height, and calculate the reflection and transmission coefficients as the cavity thickness varies. Fig. C 1(a) and (c) show the reflection and transmission spectra versus cavity thickness at wavelengths of 1480 nm and 1549 nm, respectively. In both cases, sharp reflection maxima coincide with transmission minima, as required by energy conservation. This confirms that the structure supports well-defined resonant states at discrete cavity thicknesses. Fig. C 1(b) shows the corresponding intracavity modal amplitudes as functions of cavity thickness. The red curves represent the diffracted orders ($+1$ and $-1$, which are degenerate here), and the blue curve represents the zeroth order. At the condition for complete reflection, the diffracted-order field exhibits a sharp maximum, while the zeroth-order component vanishes. The disappearance of the zeroth order is essential for unity reflection, because otherwise finite transmission through the cavity–water interface would remain and energy would leak into a non-resonant channel.

Table C1.

Resonance Periodicity

Wavelength (nm)	Period $z_1$(nm)	$2k_{\pm 1}{z}_1$	$2k_{\mathrm{n}\mathrm{ormal}}{z}_1$
1480	1217.2	$2\pi$	16.5362 (2.63182 ×2π)
1549	1932.6	$2\pi$	$25.0862$ $(7.985\times 2\pi )$

The periodicity of the GFP resonance can be understood by examining the round-trip phase delays of the zeroth and diffracted orders. Representative values are listed in Table C1. Here, $k_{\pm 1}$ and $k_{\mathrm{n}\mathrm{ormal}}$ denote the propagation constants of the diffracted and zeroth orders, respectively, and $z_1$ is the spacing between adjacent resonance peaks. $z_1$ It is clear from Table C1 that the resonance condition is governed primarily by the diffracted-order round-trip phase being an integer multiple of $2\pi$, i.e., $2k_{\pm 1}{z}_1=2n\pi .$

For the forward-propagating intracavity field ${\mathit{E}}^{\mathit{+}}$, the coupled-mode relation is given by Eq.$12$. Because of symmetry and ${\mathit{r}}_{\mathit{12}}$ is diagonal, assume ${\mathit{r}}_{\mathit{12}}=\mathit{diag}(\left[h,k,h\right])$, the reflection matrix ${\mathit{r}}_{\mathbf{21}}$ may be written as

$$\begin{array}{c}{\mathit{r}}_{\mathbf{21}}=\left[\begin{array}{ccc}a& b& c\\ d& g& d\\ c& b& a\end{array}\right]\end{array}$$ (C1)

Substituting these expressions into Eq.$12$ gives

$$\mathit{I}-{\mathit{r}}_{\mathbf{21}}\mathbf{\Phi }{\mathit{r}}_{\mathbf{23}}\mathbf{\Phi }=\left[\begin{array}{ccc}1-\mathit{ah}{e}^{2i{k}_{\pm 1}z}& -\mathit{bk}{e}^{2i{k}_{n\mathit{ormal}}z}& -\mathit{ch}{e}^{2i{k}_{\pm 1}z}\\ -\mathit{dh}{e}^{2i{k}_{\pm 1}z}& 1-\mathit{fk}{e}^{2i{k}_{n\mathit{ormal}}z}& -\mathit{dh}{e}^{2i{k}_{\pm 1}z}\\ -\mathit{ch}{e}^{2i{k}_{\pm 1}z}& -\mathit{bk}{e}^{2i{k}_{n\mathit{ormal}}z}& 1-\mathit{ah}{e}^{2i{k}_{\pm 1}z}\end{array}\right]$$ (C2)

At resonance, the zeroth-order field vanishes, so the field vector has the form

$${\mathit{E}}^{+}=\left[\begin{array}{c}\mathit{E}\\ \mathbf{0}\\ \mathit{E}\end{array}\right]$$ (C3)

Substituting this form into the matrix equation yields the resonance conditions:

$$\left(1-\mathit{ah}{e}^{2i{k}_{\pm 1}z}-\mathit{ch}{e}^{2i{k}_{\pm 1}z}\right)E=t_{12}\mathit{and}-\mathit{dh}{e}^{2i{k}_{\pm 1}z}E=t_{12}$$ (C4)

These equations depend only on the factor $e^{2i{k}_{1}z}$. Therefore, if they are satisfied for some thickness $z$, they remain satisfied when $2k_{\pm 1}z$ is increased by $2\pi$. This proves that the GFP resonance is periodic with respect to the diffracted-order round-trip phase.

When the system is slightly off resonance, the zeroth-order field no longer vanishes, and the factor $e^{2i{k}_{n\mathit{ormal}}z}$ enters explicitly into the field relations. This explains the behavior of the resonance skirts in Fig. C 1(a) and Fig. C 1(c). Near resonance, the line shape depends on the interference between the high-$Q$ diffracted-order channel and the lower-$Q$ zeroth-order channel.

At 1480 nm, the term $2k_{n\mathit{ormal}}z$ is relatively far from an integer multiple of $2\pi$, so the phase of the zeroth-order contribution changes significantly from one resonance to the next. As a result, the line shapes near adjacent resonances can differ substantially. By contrast, when the zeroth-order phase also lies close to an integer multiple of $2\pi$, the relative phase between the channels varies little, and the response around neighboring resonances becomes much more similar.

Therefore, the GFP can be understood as a coupled-resonator system consisting of one low-Q resonator associated with the zeroth order, and a high-Q resonator associated with the first diffracted order. For most cavity thicknesses, the zeroth-order response dominates. However, as the condition $2k_{\pm 1}{z}_1=2n\pi$ is approached, energy is progressively transferred into the diffracted orders, while the zeroth order component is suppressed. The Q of the diffracted order cavity is much higher since energy cannot leak out at the planar interface. In this sense, the resonator operates by switching energy between two coupled resonators, one of these has a very high Q and finesse resulting in sensitive ultrasound detection.

Data availability

Data will be made available on request.