Polarization control enabled by on-chip three-dimensional rotator

Abstract

Precise polarization control is fundamental for applications such as optical communication and quantum information processing. Femtosecond-laser written photonic integrated circuits (PICs) offer the ability to both maintain and manipulate the state of polarization (SOP) on-chip, making them a promising platform for integrated and flexible polarization control. However, current polarization control devices are either inefficient in rotating polarization or limited to adjusting the birefringence and optical axis orientation of the waveguides. In this study, we introduce and demonstrate a new type of three-dimensional polarization rotator, built from composite waveguides with varied optical axis orientations. By varying the rotation length and angle of the rotators, we efficiently rotate the horizontal and vertical polarization states between 5° and 180°, achieving output SOPs with a linear polarization degree exceeding 99.5 %. Moreover, when other linear polarization states were introduced, the rotators not only preserved the rotation angle but also enabled additional control over the ellipticity of the output SOPs, ranging from −6° to 7° These novel waveguide rotators allow for both efficient polarization rotation and ellipticity control, marking a major advancement in on-chip polarization management and paving the way for full polarization utilization.

Graphical abstract

1. Introduction

Polarization, one of the most significant degrees of freedom of photons, has been widely utilized in medical diagnosis [1], remote sensing [2], materials analysis [3], optical communication [4], and quantum information processing [5]. In optical communication, the polarization division multiplexing (PDM) scheme uses two orthogonal polarization states (SOPs) to transmit more information through a single fiber. Recently, a pseudo-PDM system utilizing four linear SOPs demonstrated the ability to transmit 100-Gbps signals, significantly increasing channel capacity compared to the PDM scheme [6]. In quantum information, polarization-entangled qubits enable secure quantum communication and faster computation [5,7]. These applications depend on the arbitrary control of the SOP of light, underscoring the pressing need for precise and efficient polarization control systems.

Currently, two primary methods are used to achieve polarization control: one relying on bulky optical components [8], and the other on photonic integrated circuits (PICs) [[9], [10], [11], [12]]. In the first approach, polarization control is achieved by rotating large components such as waveplates, polarization beam splitters (PBS), and fiber polarization controllers. However, this method lacks integration and is vulnerable to external environmental factors. In contrast, PIC-based polarization control devices offer greater compactness, stability, and reconfigurability, making them a promising platform for future polarization control. On one hand, researchers have developed high-performance on-chip polarization control devices such as polarization splitting rotators (PSRs) [11], waveplates [12], and PBSs [13]. On the other hand, planar PICs integrating PSRs with reconfigurable Mach-Zehnder interferometers (MZIs) can generate arbitrary SOPs [9]. The basic principle is to decompose the incident polarization into light propagating along different paths with different intensities by PSRs, and subsequently manipulate the phase between paths with MZIs to successfully compose arbitrary SOPs at the output. However, stable propagation of arbitrary SOPs on planar PICs is limited by the fixed optical axes and high birefringence of rectangular waveguides, making it challenging [14].

To overcome these limitations, the femtosecond laser direct writing (FsLDW) technique presents a promising approach for achieving on-chip propagation and control of arbitrary SOPs [[15], [16], [17], [18], [19], [20]]. FsLDW enables direct fabrication of arbitrary three-dimensional (3D) photonic circuits by inducing permanent refractive index changes in transparent materials using tightly focused femtosecond pulses, combined with a high-precision 3D translation stage. Using its 3D processing capabilities, FsLDW allows for the adjustment of optical axis orientations (0–180°) and birefringence (10^–7–10^–5) in femtosecond laser-written waveguides by controlling their cross-sectional shapes [[21], [22], [23], [24], [25]]. As a result, polarization-independent devices such as directional couplers [24] and polarization-dependent devices like waveplates [12,22], polarization beam splitters (PBS) [18,26,27], light attenuator [28], among others, can be integrated on a single PIC simultaneously. Nevertheless, polarization rotators using FsLDW are currently limited to converting between horizontal (H) and vertical (V) SOPs, with a low conversion efficiency of up to 60 % [29]. Furthermore, few studies have explored FsLDW devices that provide both high-efficiency polarization rotation and ellipticity control, indicating that PICs based on FsLDW have not yet fully realized their potential for polarization control.

In this study, we present a novel three-dimensional polarization rotator based on rotating the cross-section of composite waveguides (CWGs) [30]. Each segment of the rotating CWGs acts as a waveplate with varying optical axes, enabling control over the incident SOPs. By adjusting the rotation length and angle, the rotators achieve 5°−180° rotation for both horizontal (H) and vertical (V) polarizations, while maintaining a degree of linear polarization (DOLP) above 99.5 %. Additionally, the rotator can rotate all incident linear SOPs and add a phase to the output, enabling simultaneous control of polarization ellipticity. These rotators provide a practical solution for high-efficiency polarization rotation and ellipticity control, advancing the development of arbitrary on-chip polarization management.

2. Design and experimental fabrication of rotators

2.1. Device design

The schematic of the polarization rotators is illustrated in Fig. 1. Unlike the rotators in Ref [29], the devices presented here consist of three main segments: input circular waveguides, a taper, and rotating waveguides, with the entire rotator constructed from two writing tracks. Before the taper, the two writing tracks overlap to form an input circular waveguide with low birefringence, preserving the input SOPs. The tracks then gradually diverge, reaching a central distance of d_w, forming a taper that minimizes coupling loss between the circular waveguide and the CWG. Here, to maintain device compactness while ensuring low mode coupling loss between the input circular waveguide and the rotating waveguide, a taper length of 1.5 mm was selected, beyond which the mode coupling loss becomes nearly constant [30]. Finally, as depicted in Fig. 1(b), the central distance d_w stays constant, while the rectangular CWG rotates along the z-axis with a length L_r and a rotation angle α.

Fig. 1.

(a) A three-dimensional schematic of the rotators with a rotation angle α of 0°, 45°, 90°, and 135°, respectively. (b) Schematic of the rotator composed of CWGs with a central distance of d_w and a rotation angle α at o-yz plane. Here, L_p, L_t, and L_r represents the length of input circular waveguides, the taper, and the rotating CWGs, respectively. The insets illustrate the cross-sections of the device at different position.

2.2. The FsLDW of device

The FsLDW process for fabricating the waveguides and rotators was performed using a custom-built femtosecond laser writing system. The femtosecond laser pulses were generated by a commercial solid-state system (CARBIDE CB5, Light Conversion Ltd) with a central wavelength of 1030 nm, a repetition rate of 1 MHz, and a pulse duration of 290 fs. Then, the previously developed MFSFP method was utilized, where a spatial light modulator (SLM) transformed the single laser focus into a multi-foci array for the inscription of individual circular tracks [31]. These shaped pulses were then focused by a 40 × objective lens (NA = 0.75, WD = 0.51 mm; UPlanFL N, Olympus) to a depth of 190 µm inside a borosilicate glass substrate (EAGLE XG, Corning). All waveguides and devices, composed of these fundamental circular tracks, were inscribed using a pulse energy of 390 nJ and a writing velocity of 40 mm/s. After fabrication, the sample cross-sections were finely polished for further characterization of the cross-sectional profiles, mode fields, and polarization properties.

3. Results and discussions

3.1. Cross-sectional profiles and mode fields of circular waveguides and CWGs

To prevent the excitation of higher-order modes during rotation, all waveguides in the rotators must be single-mode. Specifically, the rotator can be divided into three types of waveguides: the input circular waveguides, the taper, and the rotating waveguides. Here, the initial CWG in the rotation section, starting with a combined angle of 0°, undergoes a gradual rotation by α along the propagation path. the rotation angle α determines the variation range of the combined angle θ. We used a metallurgical microscope and a beam analyzer to characterize the cross-sectional profiles and mode fields of each waveguide. As shown in Fig. 2, the mode fields of all waveguides display Gaussian intensity distributions, confirming their single-mode characteristics. The width and height of the circular waveguide shown in Fig. 2(a1) are 5 µm and 4.8 µm, respectively, while the diameter of the corresponding mode field is approximately 6.15 µm. As shown in Figs. 2(a2)-(a4), the central distance d_w between the two written tracks gradually increases in the taper region, resulting in a smooth transition of the cross-section from the circular waveguide to the CWG. In the CWGs, the major axes of the elliptical mode fields align with the combined angles θ. Additionally, as the central distance d_w of the two tracks increases from 3.2 µm to 3.6 µm in Figs. 2(b1)-(e1) and (b2)-(e2), the mode fields of CWGs becoming more elliptical.

Fig. 2.

The cross-sectional profiles and mode fields of the waveguides in the rotator. (a1) The input circular waveguide. (a2) The 1/4 position, (a3) the 1/2 position, and (a4) the 3/4 position along the taper. The CWGs with a central distance d_w of (b1)-(e1) 3.2 µm and (b2)-(e2) 3.6 µm. All scale bars are 5 µm.

3.2. Optical axes and birefringence intensity of waveguides

To further characterize the polarization properties of the waveguides shown in Fig. 2, we utilized our previous setup from Ref [24] to experimentally determine their birefringence and optical axis angles. For the circular waveguides, the measured birefringence was 1.14 × 10⁻⁵, with the fast (f) and slow (s) axes oriented horizontally and vertically, respectively. This relatively low birefringence allows the input circular waveguide to preserve the input SOP. In the CWGs with varying combined angles θ, the f and s axes align with the major and minor axes of the CWG, showing a strong linear correlation with θ as depicted in Fig. 3(a). Additionally, as the central distance d_w increases from 3.2 µm to 3.6 µm, the more elliptical modes of the CWGs result in a larger form birefringence, as illustrated in Fig. 3(b). Specifically, the birefringence exhibits a notable increase from 2.08 × 10^–5 to 3.65 × 10^–5 as θ varies from 0° to 180°, indicating an approximate 2- to 3-times enhancement compared to circular waveguides. Therefore, the input SOP can be viewed as passing through multiple waveplates with continuously varying optical axis angles.

Fig. 3.

Fundamental polarization characteristics of the CWGs. (a) Relationship between the optical axis angles and the combined angle θ of CWGs. (b) Birefringence intensity of CWGs with central distances of 3.2 µm and 3.6 µm as a function of the combined angle θ.

3.3. Highly efficient rotation of linear SOPs

Based on the analysis of the optical axes and birefringence intensity of CWGs, the main principle can be explained as follows: Initially, as depicted in Fig. 4(a), a rotating CWG comprises a series of short, straight CWGs, each with a distinct combined angle θ. Consequently, the input polarization states effectively traverse multiple waveplates with continuously changing optical axis angles, where the length of each CWG segment L₀ determines its phase delay δ. The Mueller matrix for the ith waveplate can therefore be expressed as:

$$M_i=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& {\cos }^2\left(2{\theta }_i\right)+{\sin }^2\left(2{\theta }_i\right)\cos \left({\delta }_i\right)& \cos \left(2{\theta }_i\right)\sin \left(2{\theta }_i\right)(\cos \left({\delta }_i\right)-1)& -\sin \left(2{\theta }_i\right)\sin \left({\delta }_i\right)\\ 0& \cos \left(2{\theta }_i\right)\sin \left(2{\theta }_i\right)(\cos \left({\delta }_i\right)-1)& {\cos }^2\left(2{\theta }_i\right)\cos \left({\delta }_i\right)+{\sin }^2\left(2{\theta }_i\right)& -\cos \left(2{\theta }_i\right)\sin \left({\delta }_i\right)\\ 0& \sin \left(2{\theta }_i\right)\sin \left({\delta }_i\right)& \cos \left(2{\theta }_i\right)\sin \left({\delta }_i\right)& \cos \left({\delta }_i\right)\end{array}\right]$$ (1)

Fig. 4.

(a) The rotating CWG is composed of multiple segments of waveplate with optical axis along its major and minor axis, while the phase delay δ is determined by the length of each segment L₀. (b) Polarization rotation angle and (c) ellipticity of the output SOPs when V-polarized light is injected into the rotators. The device rotation angle α was set to 45°, while the rotation length L_r varied between 5 mm and 45 mm. The insets illustrate the definitions of the polarization rotation angle and ellipticity.

Hence, the output SOP Sout can be written as:

$$S_{\text{out}}=\prod _{i=1}^n{M}_i·S_{\text{in}},$$ (2)

where S_in and S_out represent the Stokes vectors of the input and output SOP. In the design of the rotator, the increment of the combined angle θ was fixed at 1°, resulting in a fixed number of segments. As the rotation length L_r increases, the length of each segment L₀ also increases, consequently elevating the phase delay δ of each segment. Hence, deviations from the optimal rotation length (either lower or higher) lead to phase delays that are either too small or too large.

We next experimentally characterized the linear polarization control enabled by the rotators. The rotation angle α of the device was first set to 45° with V polarized light input, and the output SOP was then characterized. Here, the polarization rotation angle is defined as the angle between the input linear states and the major axes of output SOPs. In Fig. 4(b), the incident V state gradually rotated as the polarization rotation angles of output SOPs increased with rotation length L_r. In addition, the ellipticity of a polarization ellipse is rigorously defined as the arctangent of the ratio between the semi-minor axis $b$ and the semi-major axis $a$, as illustrated in the inset of Fig. 4(c). An ellipticity angle of 0° corresponds to linearly polarized light, whereas an angle of ±45° represents circular polarization. The results in Fig. 4(c) suggest that the ellipticity of the output SOPs exhibits a trend of increasing first and then decreasing. Hence, for the rotation of linear SOPs, there is an optimal rotation length at which the polarization rotation angle matches the device's rotation angle α, and the ellipticity of the output SOP approaches zero. Based on the results in Fig. 4, the optimal L_r decreased from 42.5 mm (when d_w = 3.2 µm) to 32.5 mm (when d_w = 3.6 µm). It is evident that the higher birefringence of the CWGs results in a shorter optimal L_r for achieving linear SOP rotation, which is advantageous for reducing the size of rotators in the z direction.

To achieve compact rotators, we set the central distance d_w to 3.6 µm in the following tests and for subsequent tests and characterized the rotators at their optimal rotation lengths, with rotation angles α ranging from −90° to 90° The output SOPs for V- and H-polarized input light from various rotators were directly recorded using a commercial polarimeter (PAX1000IR1, Thorlabs, Inc.) and plotted on the Poincaré sphere, as shown in Figs. 5(a) and (b). Notably, the rotation angles of polarization matched the rotation angles α of the devices and all output SOPs are located near the equator of the Poincaré sphere, suggesting that the input H and V states achieved the arbitrary rotation within a range of −90° to 90° The degree of linear polarization (DOLP) measures the fraction of light that is linearly polarized, ranging from 1 for perfect linear polarization to 0 for unpolarized light. Based on the Stokes parameters of each output SOP, we calculated the DOLP using the following equation:

$$\text{DOLP}=\sqrt{\frac{S_1^2+S_2^2}{S_0^2}}$$ (3)

Here, S₀ represents the total light intensity, S₁ represents the intensity of linear H or V polarization, and S₂ represents the intensity of linear +45° or −45° polarization. As illustrated in Fig. 5(c), the DOLP at all device rotation angles exceeds 99.5 %, confirming the linear polarization characteristics of the output SOPs. Specifically, the rotation efficiency refers to the proportion of the output optical power that aligns with a predefined target linear polarization. As the azimuth angle of the output SOP of the rotator aligns with that of the target linear polarization, the DOLP of the output SOP becomes equivalent to this rotation efficiency. In contrast to previously demonstrated laser-written rotators, which achieved a conversion efficiency of up to 60 % [29], our rotators demonstrate superior linear polarization rotation performance with an efficiency of 99.5 % and a rotation angle range of −90° to 90° Besides, as the rotation angle α increases, the optimal rotation length L_r increases slightly, leading to a corresponding rise in insertion loss. Nonetheless, all insertion losses of the rotators remain below 3.20 dB.

Fig. 5.

The output SOPs corresponding to different rotation angles α when the rotators were at their optimal rotation length L_r. The position of the output SOPs on the Poincaré sphere for (a) V-polarized and (b) H-polarized light inputs. The hollow circle and star indicate the input SOPs in each figure. (c) The calculated degree of linear polarization (DOLP) for the output SOPs. (d) The insertion losses of the polarization rotators.

3.4. The ellipticity control of SOPs

In addition to the H and V polarization states, other linearly polarized light was also injected into the rotators. For demonstration, the experimental results for rotators with rotation angles α of 45° and 90° were evaluated. Note that both the 45° and 90° rotators were set to their optimal rotation length L_r. The polarization rotation angles and the ellipticity of the output SOPs were recorded and are shown in Fig. 6. As shown in Fig. 6(a), when linearly polarized light with input angles ranging from 0° to 180° was injected, the rotators rotated the input polarization by angles closely matching the device rotation angles α of approximately 45° and 90°, respectively. Additionally, Fig. 6(b) illustrates that the ellipticity of the output SOPs varied in a sinusoidal pattern with respect to the input angles. This mechanism operates as follows: firstly, the taper functioned as a waveplate with vertical and horizontal optical axes. Then, an angular misalignment between the input linear polarization and these axes introduced a phase delay that, combined with a subsequent polarization rotation waveguide, could control the ellipticity of the output SOP. For the 45° and 90° rotators, the ellipticity of the output SOPs could be regulated within ranges of −6° to 7° and −2.5° to 5°, respectively. Thus, with varying linearly polarized light input, we achieve both highly efficient polarization rotation and precise ellipticity control of the SOPs within a single device, marking the first demonstration of this capability on femtosecond laser-written waveguides. This marks a significant advancement over previously reported laser-written waveplates, as the use of three-dimensional rotators enables more complex and versatile on-chip polarization control.

Fig. 6.

(a) The polarization rotation angle and (b) the ellipticity of the output SOPs when linearly polarized light, excluding H and V, is injected into the rotators. The rotation angles α of the devices were set to 45° and 90° for demonstration. The insets illustrate the definitions of the polarization rotation angle and ellipticity.

4. Conclusions

In conclusion, we developed a novel three-dimensional waveguide rotator that effectively enables on-chip polarization control. These devices consist of composite waveguides (CWGs) with optical axis angles ranging from 0° to 180° and birefringence values between 2.08 × 10⁻⁵ and 3.65 × 10⁻⁵. By adjusting the rotation angles and lengths of the rotators, we achieved highly efficient rotation of the input horizontal (H) and vertical (V) linear polarizations within a range of −90° to 90° The degree of linear polarization (DOLP) of the output states of polarization (SOPs) exceeded 99.5 %, marking the highest value reported for the femtosecond laser direct writing (FsLDW) waveguide platform. Additionally, the rotators can rotate other linearly polarized states (beyond just H and V) to angles closely matching the devices’ rotation angles, while also allowing simultaneous regulation of the ellipticity of the output SOPs, ranging from −6° to 7° for a rotation angle of 45°, and −2.5° to 5° for a rotation angle of 90° These three-dimensional waveguide rotators offer valuable insights into achieving arbitrary on-chip polarization control, which is essential for advancing applications in chip-based classical and quantum communication.

CRediT authorship contribution statement

Zezheng Li: Conceptualization, Data curation, Formal analysis. Shuaipeng Guo: Investigation. Yuexiao Yan: Formal analysis, Investigation. Hongfei Bu: Investigation, Software. Yixuan Zhang: Resources. Wenzhuo Niu: Validation, Visualization. Yang Ouyang: Methodology. Qidai Chen: Resources, Supervision. Zhennan Tian: Funding acquisition, Supervision. Hongbo Sun: Funding acquisition, Project administration.

Declaration of competing interest

The authors declare that they have no conflicts of interest in this work.

Biographies

Zezheng Li is currently a postdoc in the Department of Precision Instrument at Tsinghua University. He earned his Bachelor’s degree in Electronic Science and Technology from the College of Electronic Science and Engineering at Jilin University in 2019. In 2024, he completed his Ph.D. in Physical Electronics from the same institution. His research focuses on ultrafast laser direct writing of three-dimensional optical waveguide devices and topological waveguide arrays.

Zhennan Tian graduated from the College of Electronic Science and Engineering, Jilin University in 2017 with a doctoral degree, and has been promoted to professor since 2023. His research focuses on the femtosecond laser direct writing waveguide technology and its applications. With the work of on-chip control of photon states, photonic topological devices, and uniform waveguide array with large depth, he has been selected in the National Youth Talent Plan in 2023.

Hongbo Sun is a tenured professor in the Department of Precision Instrument at Tsinghua University. His research focuses on the application of femtosecond laser micro/nanofabrication technology in areas such as 3D photonic integration, nanomechanics, and the fabrication of micro/nano optoelectronic devices. He has received the second prize of the National Natural Science Award (first ranking for both 2020 and 2024).