Chiral lasing enabled by strong coupling

Abstract

Chiral quasi-bound states in the continuum are spin-dependent high-Q resonances in meta-photonic structures that are realized by perturbing symmetry-protected optical states by engineering in-plane and out-of-plane asymmetries, and they support chiral lasing in the vertical direction. Here, we explore the coupling between two resonances in a chiral metasurface and introduce a mechanism for high-purity chiral laser emission. We reveal that two resonances with nearly orthogonal polarizations become strongly coupled in an engineered chiral metasurface. The inherent phase difference of the resonances, associated with the coherent destruction on the decay channel, can endow high-Q factor and maximize chirality to one of the hybrid modes. We verify this approach experimentally by measuring transmission spectra, angle-resolved photoluminescence, and laser emission. We believe that this mechanism allows breaking restrictions on conventional chiral quasi-BIC lasing, enabling the realization of chiral emission at any designed direction.

Chiral quasi-BIC with high-Q and maximized chirality has been realized at off-Γ point in momentum space.

INTRODUCTION

The localization and manipulation of light in artificial nanostructures is critical to the advancement of next-generation optical communication and information processing. Over the past decades, various mechanisms for controlling electromagnetic fields in nanophotonic devices have been developed and used (1–6). Bound state in the continuum (BIC), a concept proposed by von Neumann and Wigner, is a prominent representative (7). BIC in photonics corresponds to some particular resonances confined via far-field destructive interference (8–11). By tailoring the system symmetry or the coupling between different resonances, light can be trapped for a long time in nanostructures, and the corresponding light-matter interactions are thus significantly enhanced, transforming nano-devices and photonic integrated circuits (12–19). Chiral quasi-BICs have recently attracted substantial attention for their ability to manipulate the spectral and spin-dependent characteristics of radiation (20–25). Chiral quasi-BICs have been proposed and experimentally demonstrated by simultaneously introducing in-plane and out-of-plane asymmetries to resonant metasurfaces. The combination of high-quality (Q, Q ∝ ωτ) factor and near-unity circular dichroism (CD) triggers the selective enhancement/suppression of chiral local density of states (LDOS), leading to high-purity chiral emission and large nonlinear chirality (26–30). Despite the progress, current chiral quasi-BICs are all constructed by perturbing the symmetry-protected BICs. Their practical applications are hindered by the restricted positions (near Γ-point) in momentum space.

With the advancement of nanophotonics, another chiral phenomenon known as superchiral fields has also attracted widespread attention. Optical chirality was first introduced by Lipkin in 1964 and then simplified to $\tilde{C}=-0.5{\mathrm{\epsilon }}_0\mathrm{\omega Im}({\mathbf{E}}^{*}·\mathbf{B})$ (31, 32). Apparently, the optical chirality can be greatly enhanced if the electrical and magnetic components in nanostructures are spectrally and spatially overlapping, parallel, and π/2 out of phase. This guiding rule has been exploited to produce superchiral fields in complexly designed plasmonic or dielectric nanostructures (33–39). Soon after, it was realized that mixing two near-orthogonal resonances with similar mode profiles was a more straightforward and effective approach (40–42). By adjusting the structural parameters, the chirality of electromagnetic field in the photonic crystal membrane is significantly enhanced by several orders of magnitude around the crossing points including exceptional point (40–42). Several novel phenomena such as chiral mode splitting were also proposed (40, 41). So far, mode-mixing method has achieved a series of breakthroughs in constructing near-field superchiral fields. Several challenges still remain in manipulating the chirality of radiation because of the inconsistency between near-field chirality and CD. Superchirality and CD do not have a complete one-to-one correspondence but are still closely related because both of them are proportioned to E^*·B. As a consequence, the mixing and accurate excitation of two eigenmodes with orthogonal polarizations might also be exploited to produce the chiral quasi-BIC in metasurfaces. Here and below, we use the concept of mode coupling and demonstrate a mechanism to construct chiral quasi-BIC and realize chiral emissions.

RESULTS

In a non-Hermitian system with finite size based on lossless material, the TE (transverse electric) resonance and TM (transverse magnetic) resonance do not strictly follow their definitions and can couple one another. Their interaction can be described by coupled mode theory with a non-Hermitian Hamiltonian

$$H=\left[\begin{array}{cc}{E}_1& W\\ V& E_2\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\omega }}_1+i^{*}{\mathrm{\gamma }}_1& W\\ V& {\mathrm{\omega }}_2+i^{*}{\mathrm{\gamma }}_2\end{array}\right]$$ (1)

where E_1,2 are the energy of two resonances and $\sqrt{\mathit{VW}}$ is the coupling constant. They are all complex in this case. ω_1,2 is the real parts of E_1,2 representing resonance frequency, while γ_1,2 is the imaginary parts of E_1,2, representing the radiation loss. The corresponding eigenvalues and eigenvectors can be expressed

$$E_{\pm }=\frac{E_1+E_2}{2}\pm \frac{1}{2}\sqrt{{(E_1-E_2)}^2+4\mathit{VW}}$$ (2)

$$V_{\pm }=\left(\begin{array}{c}\frac{E_1-E_2}{2\sqrt{\mathit{VW}}}\pm \sqrt{\frac{{(E_1-E_2)}^2}{4\mathit{VW}}+1}\\ 1\end{array}\right)$$ (3)

We consider a metasurface that supports TE and TM two linearly polarized modes with similar complexed numbered resonant frequencies ω_1,2 + i * γ_1,2. Their corresponding far field polarization states Ø_1,2 are written as

$$\left[\begin{array}{c}{\varnothing }_1\\ {\varnothing }_2\end{array}\right]=\left\{\begin{array}{c}{\mathrm{\gamma }}_1·\left[\text{cos}\left({\mathrm{\beta }}_1\right)·\widehat{x}+\text{sin}\left({\mathrm{\beta }}_1\right)·\widehat{y}\right]\\ {\mathrm{\gamma }}_2·\left[\text{cos}\left({\mathrm{\beta }}_2\right)·\widehat{x}+\text{sin}\left({\mathrm{\beta }}_2\right)·\widehat{y}\right]·e^{i\mathrm{\delta }}\end{array}\right\}$$ (4)

Here, because there are no intrinsic loss in material, the amplitude of radiation is proportional to γ_1,2, and β_1,2 are the polarization directions of uncoupled modes to the x axis. Their phase difference is denoted as δ. As a consequence, the polarization states of the hybrid modes of mode interaction are obtained with the following expression

$${\varnothing }_{\pm }={V_{\pm }}^{†}\left[\begin{array}{c}{\varnothing }_1\\ {\varnothing }_2\end{array}\right]$$ (5)

It is straightforward to know from Eq. 5 that the polarization states of hybrid modes can be well controlled by tailoring the polarization states of uncoupled modes and their far field phase difference. As depicted in section S1, to accurately describe the interaction between the two modes of metasurface, it is necessary to obtain the resonance complex frequency and polarization of the two modes before coupling by fitting the numerical simulation results, which is used as the input of the coupling mode model. Besides, as the derivation shown in section S1, one hybrid mode is able to reach the north pole on the surface of Poincare sphere when $\frac{\mid V\left(2\right)\mid }{\mid V\left(1\right)\mid }=\frac{{\mathrm{\gamma }}_1}{{\mathrm{\gamma }}_2}$ and δ = ∆β where ∆β = β₂ − β₁, demonstrating the generation of chiral state with S₃ = 1. In addition, the coupling constant in non-Hermitian system is a complex number. As discussed before, the mode interaction also has the capability of tailoring the decay rates of the hybrid modes, leading to an enhanced Q factor around the crossing or anti-crossing point (43–45). Therefore, both the Q factors and the polarization states of hybrid modes can be tailored by the mode interactions. With a proper design of nanostructure, a chiral quasi-BIC with both enhanced Q factor and maximized CD can thus be expected.

In numerical simulation, we start with a metasurface that supports a series of quasi-BICs. Figure 1A illustrates the schematic of our metasurface. It is composed of square latticed periodic nanostructures on a K9 glass substrate. Figure 1B shows the top-view and side-view images of each unit cell. It contains two shallow-etched Si₃N₄ nanopillars covered by dye (PM597)–doped polymethyl methacrylate (PMMA). Two nanopillars are separated by an angle θ and rotated by an angle φ around the center of unit cell. The refractive indices of PMMA, Si₃N₄, and K9 glass are set to 1.49, 2.01, and 1.52, respectively. Their detailed structural parameters are listed in the figure caption. The metasurface supports one TE₀ BIC and one TM₀ BIC in the gain spectral range of PM597 (from 565 to 600 nm, see details in section S2) at θ = φ = 0°. With the increase of angle θ, e.g., θ = 20° while keeping φ = 0°, the BICs quickly degrade to quasi-BICs, and the polarizations of their far-field radiation in normal direction are linearly polarized along two directions with a difference around π/2 (45, 46).

Fig. 1. Chiral quasi-BIC lasing via mode interaction.

(A) Schematic of the designed metasurface chiral laser emission. (B) Top-view (top) and side-view (bottom) of one unit cell with a lattice size of P = 339 nm. Each unit cells contains two identical Si₃N₄ ellipses with R_l = 231 nm and R_s = 110 nm on a glass substrate. Two ellipses with a center-to-center distance of 170 nm are separated by an angle of θ = 20° and rotated by an angle φ around the center of the unit cell. In the vertical direction, the Si₃N₄ membrane has a thickness of H = 267 nm and shallow etched by a depth of 190 nm. The Si₃N₄ nanostructures are covered by a dye-doped PMMA with a thickness of 370 nm. (C and D) The real and imaginary parts of TE₀ and TM₀ modes in the metasurface as a function of rotation angle φ. The solid lines are the fitted curves following coupled mode theory. (E) The mode profiles at the parameter marked on (C), and arrows represent the direction of the electric field. (F) The radiation S₃ from theory (The.) and simulation (Sim.) of two modes.

The situation gets more interesting when the rotation angle φ is changed. In such a case, the global square lattice is still preserved along the x and y directions to maintain the topological properties of the BIC modes. The rotation of local nanostructures, however, affects the field distributions of the resonances and modifies their resonant wavelengths. Figure 1 (C and D) shows the evolution of real and imaginary parts of the eigenfrequencies of TE₀ and TM₀ resonances. Two modes respond oppositely to the rotation angle and gradually approach in Fig. 1C. Due to the finite thickness and asymmetry in vertical direction, TE quasi-BIC and TM quasi-BIC are not orthogonal in our metasurface. Considering the spatial overlap of their field patterns (Fig. 1E, i and ii), the interaction between two resonances can thus be expected. With the increase of rotation angle φ, a repulsion in real parts of eigenfrequencies and a crossing in the imaginary parts are observed at around φ = 20.5°. Meanwhile, an obvious exchange in the field distribution occurs in Fig. 1E. All these numerical results are consistent with the theoretical model and confirm the strong coupling between two quasi-BICs.

In Fig. 1E, panels iii and iv are the numerically calculated field patterns of two hybrid modes. We can see that the mode interaction strongly mixes two modes around the anti-crossing point. Due to the phase difference between TE and TM polarizations, the requirements for superchiral field can be fully matched here, and a marked enhancement factor of 350 has been achieved for the near-field chirality (section S3). As discussed above in Eq. 5, the phase difference between their radiation fields also enables the control of polarization states of the hybrid modes. As shown in Fig. 1F, the Stokes parameter S₃ of one mode increases with the rotation angle and reaches a maximal value of S₃ = 1 around the anti-crossing point. The corresponding imaginary part also increases and approaches to 0, giving a local maximum of Q factor of Q = 13,000. Both the Q factor and S₃ reduce at larger φ, and all the numerical results match the theoretical model (solid lines) well. We thus know that the chiral quasi-BIC has been constructed by the strong coupling for the first time. Compared with the control of in-plane and out-of-plane asymmetries, strong coupling can occur at any designed angle (section S4), not just near the Γ-point in momentum space (47). Meanwhile such chiral quasi-BICs have the ability to control chiral LDOS (section S5), enabling high-purity and highly directional chiral photoluminescence and chiral lasing (26). We note that the main role of φ and θ is to adjust the coupling between TE and TM modes. The chiral quasi-BIC can also be constructed by tuning θ individually. We fix θ = 20° for the feasibility of fabrication.

On the basis of the above theoretical model and numerical simulation, we have fabricated the metasurfaces with a combined process of electron-beam lithography, reactive ion etching, and spin coating (see details in Materials and Methods). Figure 2 (A and B) shows the top-view and tilt-view scanning electron microscopy (SEM) images of one metasurface before coating the PMMA layer. The lattice size p, separation angle θ, rotation angle φ, and all the other structural parameters follow the numerical designs of hybrid modes very well. The metasurface is optically characterized with a homemade microscope system. Figure 2C depicts the transmission spectra under the illumination of light with left-handed circular polarization (LCP) and right-handed circular polarization (RCP), respectively. For the LCP incident light, two resonances dips can be observed at 582.4 and 583.3 nm. The RCP transmission, however, only one dip appears at 583.3 nm. Then, we know that the metasurface is almost completely decoupled from RCP light at the wavelength of 582.4 nm. Following the definition in (24), the CD and Q factor at 582.4 nm are CD = 0.98 and Q = 2100, respectively, while those at 583.3 nm are only CD = −0.06 and Q = 1300. Then, we know that a high-Q chiral resonance has been generated in our metasurface. The relatively low Q factor in the experiment is mainly attributed to the finite size of the metasurface and the additional scattering losses caused by the surface roughness.

Fig. 2. Transmission spectrum characterization of intrinsic chirality.

(A and B) The top-view and tilt-view SEM images of metasurface with φ = 20.5°. Scale bars, 300 nm. (C) The corresponding transmission spectrum in experiment (Exp.) and its fitted (Fit.) curve. (D to F) The experimentally recorded resonant wavelength, Q factor, and the CD of metasurfaces with different rotation angle φ. The corresponding simulation results are shown as solid and dashed lines. Two y axes are used in (E) for numerical simulation (left, y axis) and experimental results (right, y axis), respectively. a.u., arbitrary units.

To confirm the strong coupling induced chiral quasi-BIC, a series of metasurfaces with different rotation angle φ have been experimentally fabricated and optically characterized. The detail information on SEM images and transmission curves can be found in section S6. Figure 2 (D and E) summarizes the resonant wavelengths and Q factors of two resonances in different samples. With the increase of rotation angle φ, two resonances gradually approach and repel one another at around φ = 20.5°, and a crossing in Q factor can also be observed. Because of the nanofabrication deviations, the wavelengths of two resonances do not change very smoothly in different samples. The mode with weaker RCP dip always has shorter wavelengths at small φ and is in good agreement with the simulated results (solid lines in Fig. 2, D and E). Then, strong coupling between two resonances can be confirmed. The extracted CD values are plotted in Fig. 2F, where a maximized CD can be seen around the anti-crossing point. Then, we can confirm that chiral quasi-BIC has been constructed by the strong coupling.

Then, the photoluminescence of the metasurface with a chiral quasi-BIC is examined by pumping it with a continuous wave laser at 520 nm. The angle-resolved emission spectra are recorded by a CCD coupled to a monochromator via the back focal plane imaging technique (Materials and Methods). Figure 3A shows the experimentally recorded angle-resolved spectra of LCP and RCP photoluminescence. The band structure of TE₀, TM₀, and TE₁ resonances along the k_y direction can be observed. The different field distributions of three modes make them response differently to the emission angle. As a consequence, three apparent anti-crossings can be found at ~0.5° and ±2°. The LCP and RCP emissions in Fig. 3A have identical wavelengths but significantly different intensities, especially around the anti-crossings. The emission spectra of designed hybrid modes are shown and fitted in Fig. 3B. Similar to the transmission, two peaks at 582.3 and 583.4 nm can be seen in the LCP emission spectrum. The corresponding RCP spectrum only has one peak at 583.4 nm. Using the definition of $\text{CD}=\frac{I_{\text{LCP}}-I_{\text{RCP}}}{I_{\text{LCP}}+I_{\text{RCP}}}=S_3$, the corresponding CD is as high as 0.929 at 582.3 nm.

Fig. 3. Angle-resolved photoluminescence from the resonant metasurface.

(A) Experimentally measured angle-resolved LCP and RCP photoluminescence spectrum. (B to D) Spectra of LCP and RCP photoluminescence and the fitted results around three anti-crossings marked by vertical dashed lines in (A). (E) The corresponding CD of emissions in (A).

Similarly, the emission spectra around the other two anti-crossings (−2.1° and 2.6°) have also been extracted and plotted in Fig. 3 (C and D). The emission at 2.6° is also dominated by the LCP emission and gives a CD of 0.936 at 582.4 nm. For the emission at −2.1°, the spectra at 582.4 nm are dominated by its RCP component and result in an opposite CD value of −0.915. Then, all the spectra in Fig. 3A are fitted and the corresponding CD values are calculated and plotted in Fig. 3E. We can see that three modes show chiral responses at almost all the angles and reach the maximized values around three anti-crossings. Then, we know that the strong coupling induced chiral quasi-BIC is not limited to Γ-point. Instead, it is quite universal and flexible. Note that the spectra in Fig. 3 are recorded at a small angle of 0.5° from Γ-point in the x direction. This has resulted from a balance between Q factor and the LDOS in the luminescent materials.

The metasurface has been further pumped by a frequency doubled Nd:YAG laser (532 nm, repetition rate of 10 Hz, pulse width of 8 ns) to explore its lasing characteristics. When the pump fluence is increased to 135 μJ/cm², the LCP emission at 582.7 nm increases rapidly and dominates the entire emission spectra at higher pump fluences (Fig. 4A, top). The corresponding chirality related emission is summarized as a function of pump fluence and plotted in Fig. 4B. A superliner curve can be observed from the LCP component and a kink can be seen at 135 μJ/cm², indicating the threshold behaviors very well (section S7). Associated with the far field directionality and interference pattern, we know that lasing actions have been achieved from the designed metasurface (section S7). As shown in Fig. 4 (A and B), the corresponding RCP emission is always more than an order of magnitude lower than its LCP counterparts and can be neglected.

Fig. 4. Circularly polarized metasurface emitting laser.

(A) Experimentally recorded LCP (blue solid line) and RCP (red dashed line) emission spectra at a pump fluence of 135 μJ/cm² (top) and 195 μJ/cm² (bottom), respectively. (B) The integrated intensities of LCP (dots) and RCP (open squares) emissions as a function of pump fluence. The solid squares represent the corresponding CD values of laser emissions. (C) Experimentally recorded angle resolved LCP (bottom) and RCP (top) laser spectrum at a pump fluence of 195 μJ/cm².

According to the emission wavelength, we know that the lasing action happens at the anti-crossing point near the Γ-point. This result can be easily understood with the Q factors. The central anti-crossing is closer to the top of the band. It has a Q factor four to five times larger than that in the other two (section S8) and, thus, has much lower laser thresholds. The exact position of lasing actions in momentum space is also determined by the LDOS in the gain materials (48, 49). Similar to the spontaneous emission in Fig. 3, the lasing action also deviates a little bit from Γ-point. Figure 4C shows the angle-resolved laser spectra that are recorded at the back-focal plane of objective lens. Here, the pump fluence is 195 μJ/cm². It is straightforward to see that the emission is dominated by the LCP components and concentrated at a tiny angle of 0.5°, consistent with the laser spectra in Fig. 4A well. Then, the CD of the laser emission is calculated and plotted as open squares in Fig. 4B. It is obvious that the CD value is close to 1 around the laser threshold.

With the further increase of pump fluence, we notice a slight reduction of CD value. This reduction is related to the increase of optical gain. Around the threshold, the optical gain balances the total loss and reaches the condition of chiral quasi-BIC. At higher pump power, the system is dominated by the gain and slightly deviates from the perfect condition. However, the chirality is still as high as CD = 0.94 when the laser reaches the gain saturation. Meanwhile, a slight blue shift of lasing wavelength can be seen. It is caused by the thermal effect under high pump fluence. We also note that chiral laser emission can also be tuned to arbitrary direction by the strong coupling. As shown in section S4, the chiral quasi-BIC can be realized at a large angle and has a locally maximal Q factor. While the top of band still has much higher Q value, the narrow spectral range of gain materials can ensure the laser emissions at the designed wavelengths and angles.

DISCUSSION

We have demonstrated a generic approach to construct high-Q chiral quasi-BIC resonances in dielectric metasurfaces. In contrast to the control of in-plane and out-of-plane asymmetries, here, we have revealed that interaction between optical resonances is also able to tailor simultaneously the Q factor and CD, leading to chiral quasi-BIC resonances, high-purity chiral photoluminescence, and chiral lasing. Owing to the universality of the mode interaction in nanostructures, our mechanism is not restricted to the symmetry protected BIC and the vicinity of Γ-point in the momentum space. It can be extended to arbitrary direction, and, thus, it provides a new degree of freedom for the construction of high-purity chiral light sources and their applications. In addition to mode coupling, some other phenomenon in non-Hermitian system, e.g., parity-time symmetry can also be exploited to construct chiral lasing as well.

MATERIALS AND METHODS

Numerical simulations

The complex numbered eigenfrequencies (ω) of photonics crystal structure are directly calculated with the radio-frequency module of a commercial software for the finite element method (COMSOL Multiphysics). Periodic boundary conditions are applied in the x and y directions to mimic the infinitely large periodic nanostructures. Perfectly matched layers are used in the vertical direction to absorb the outgoing waves. The Q factors are calculated with Q = Re(ω)/Im(ω)/2. The far field radiation is directly obtained by analyzing the electric field radiated from the eigenmodes.

Sample fabrication

The Si₃N₄ nanostructures are prepared using a combined process of electron-beam lithography (EBL) and reactive ion etching. Silicon nitride thin film was deposited on a K9 substrate via plasma-enhanced chemical vapor deposition. A 20-nm chromium layer was evaporated onto the silicon nitride. Then, PMMA A2 was spin coated at 4000 revolutions (r)/s for 60 s and baked at 180°C for 15 min. The desired pattern exposed to the PMMA by EBL. A 15-nm silicon dioxide layer was evaporated onto the sample and lifted off. Last, chromium and silicon nitride were etched by two reactive ion etchings, respectively. The flow of fabrication is shown in section S9.

The dye-doped PMMA was homemade as required. The macromolecular PMMA particles were dissolved in an anisole solution with a concentration of 0.14 g/ml and centrifuged at 8000 r/s to prepare a PMMA precursor. Then, laser dye PM597 is dissolved into the PMMA precursor with mass ratio of 2% to PMMA and magnetic stirred for 3 hours. Then, the dye-doped PMMA layer with a thickness of 370 nm is achieved by spin coating the solution onto Si₃N₄ nanostructures with a speed of 6000 r/s.

Optical characterization

Two kinds of homemade optical microscopy system are used to characterize the transmission spectrum and the angular resolved emission spectrum, respectively. In the transmission measurement setup, a supercontinuum laser is used as the light source. After passing through a Glan prism and a quarter-wave plate, the circularly polarized laser is focused to a spot with radius of 15 μm at the center of the metasurface. The transmission spectrum is obtained by collecting the passing light into fiber spectrometer. In the angular resolved emission spectrum measurement, the light source was replaced by the 520-nm continuous-wave laser or a 532-nm nanosecond-pulsed laser. By projecting the back focal plane on the CCD spectrometer, the angular resolved emission spectrum can be directly measured. The schematic diagrams are shown in section S10.

Supplementary Materials

This PDF file includes:

Sections S1 to S13

Figs. S1 to S19