• Photonics Research
  • Vol. 10, Issue 1, 76 (2022)
Yanxian Wei1, Hailong Zhou1、4, Yuntian Chen1, Yunhong Ding2、3, Jianji Dong1、*, and Xinliang Zhang1
Author Affiliations
  • 1Wuhan National Laboratory for Optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China
  • 2Department of Photonics Engineering, Technical University of Denmark, 2800 Lyngby, Denmark
  • 3SiPhotonIC ApS, 2830 Virum, Denmark
  • 4e-mail: hailongzhou@hust.edu.cn
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    DOI: 10.1364/PRJ.444075 Cite this Article Set citation alerts
    Yanxian Wei, Hailong Zhou, Yuntian Chen, Yunhong Ding, Jianji Dong, Xinliang Zhang, "Anti-parity-time symmetry enabled on-chip chiral polarizer," Photonics Res. 10, 76 (2022) Copy Citation Text show less

    Abstract

    Encircling an exceptional point (EP) in a parity-time (PT) symmetric system has shown great potential for chiral optical devices, such as chiral mode switching for symmetric and antisymmetric modes. However, to our best knowledge, chiral switching for polarization states has never been reported, although chiral polarization manipulation has significant applications in imaging, sensing, communication, etc. Here, inspired by the anti-PT symmetry, we demonstrate, for the first time to our best knowledge, an on-chip chiral polarizer by constructing a polarization-coupled anti-PT symmetric system. The transmission axes of the chiral polarizer are different for forward and backward propagation. A polarization extinction ratio of over 10 dB is achieved for both propagating directions. Moreover, a telecommunication experiment is performed to demonstrate the potential applications in polarization encoding signals. It provides a novel functionality for encircling-an-EP parametric evolution and offers a new approach for on-chip chiral polarization manipulation.

    1. INTRODUCTION

    Non-Hermitian systems, especially parity-time (PT) symmetric systems, have attracted widespread attention for their fascinating physical properties and broad applications. Fruitful advances have been achieved in the field of PT symmetry [1], such as unidirectional propagation and lasing [28], single-mode lasing [912], sense enhancement [1318], and optoelectronics oscillators [19,20]. Notably, owing to the non-Hermiticity-induced nonadiabatic transitions, chiral mode switching was achieved for symmetric and antisymmetric modes by encircling the exceptional point (EP) in a PT symmetric system [2129], exhibiting great potential for chiral devices [7,27,30]. However, different from the spatial modes, it is unsuitable to perform the encircling EP evolution in an on-chip PT symmetric system for chiral polarization switching, because the polarization modes are asymmetrical, and the coupling between two orthogonal polarization states needs not only the match of effective indexes of the two polarization modes but also the share of a common parallel polarization component between them. As a result, the chiral polarization switching to date has not been yielded. However, as a basic property of light, polarization has abundant applications, such as communication [3133], imaging [3436], and storage [37]. Thus, chiral polarization switching can inspire fascinating interest into handling polarization information.

    As the counterpart of PT symmetric systems, anti-PT symmetric systems were first proposed by Ge and Türeci in 2013 [38], conjugated to those observed in PT-symmetric ones [39]. Many novel phenomena about anti-PT symmetry have been observed, e.g., sensing enhancement [40], coherent perfect absorption lasing [41], heat transfer [42], topological superconductors [43], and chiral dynamics [44]. Different from the PT symmetry, the eigenmodes of anti-PT symmetric systems are asymmetrical when the real parts of the corresponding eigenvalue split, which exactly matches the polarization mode characteristics. Anti-PT symmetry shows great potential in physics and applications. For practical optical applications, anti-PT symmetry has harsh requirements of pure imaginary coupling coefficients, which were demonstrated by indirectly dissipative coupling [45], nonlinear coupling [46], spinning the resonator [47], etc. Benefiting from these breakthroughs, anti-PT symmetry can be heralded as a powerful tool to design optical devices with fascinating properties. Notably, the indirect coupling in anti-PT symmetric systems makes it possible to construct chiral polarization switching.

    In this paper, we propose and experimentally demonstrate a chiral polarizer based on an anti-PT symmetric system for the first time. Conventional polarizers operate by rejecting undesired polarization, and the transmission axes are the same for bidirectional propagation, whereas, our chiral polarizer operates by rotating the orthogonal polarization state to the transmission axis [48] and exhibits different transmission axes for forward and backward propagation. We induce a transitional mode between transverse electric (TE) and transverse magnetic (TM) modes and realize the encircling-an-EP parametric evolution in an integrated polarization-coupled anti-PT symmetric system. For arbitrary input polarization states, we achieve a polarization extinction ratio of 10 dB between the transmission of TE and TM modes over a bandwidth from 1550 to 1590 nm. Moreover, the application of polarization data formatting is also demonstrated by a communication experiment with a bit rate of 10 Gbit/s on-off keying signals. Our work demonstrates a practicable application for encircling EP in non-Hermitian systems and provides a novel tool for future polarization manipulating such as data formatting and polarization-multiplexing duplex communication.

    2. RESULT

    A. Principle of Chiral Polarization Switching

    Figure 1(a) shows the comparison between a conventional polarizer and our chiral polarizer. The chiral polarizer exhibits different transmission axes for forward and backward propagation. In forward propagation, the output polarization state will be rotated to the vertical direction no matter what the input polarization states are. However, in backward propagation, the output polarization state will be rotated to the horizontal direction. This chiral dynamic can be used for on-chip polarization data formatting or polarization multiplexing duplex operation. It should be noted that a conventional polarizer operates by rejecting undesired polarization, and the transmission axes are the same for bidirectional propagation. Figure 1(b) illustrates the chip structure of the chiral polarizer, constructed with a three-waveguide coupled region and two polarization beam splitters (PBSs). The three-waveguide coupled region consists of three waveguides, WG1, WG2, and WG3, where WG1 and WG3 support TE0 and TM0 modes, respectively, and WG2 supports the transitional TE1 mode. The coupled region is a dual-port system, in which the TE0 and TM0 modes are processed separately. When light is injected from the left, the output mode is TE0 regardless of TE0 or TM0 injection, whereas, when light is injected from the right, the output mode is TM0 for both TE0 and TM0 injection. The PBS is used to decompose the input light into TE0 and TM0 modes and combine the output light to handle arbitrary polarization. The anti-PT symmetry is realized by the indirect dissipate coupling between WG1 and WG3. We use the coupled-mode theory to analyze the system. The model Hamiltonian takes the form H=[β1κ10κ1β2+iγκ30κ3β3],where γ is the loss of WG2, which can be tuned by introducing a chromium (Cr) strip on top of WG2; β1, β2, and β3 are the propagation constants of modes in WG1, WG2, and WG3, respectively. κ1 is the coupling coefficient between WG1 and WG2, and κ3 is that between WG2 and WG3. The eigenvalue is given by λ=β1+β32+iκ1κ3γ±iκ12κ32γ2(β1β32+iκ12κ322γ)2with an assumption of |γ||λβ2|. The detailed analysis is described in Appendix A. The normalized complex-eigenvalue spectra ε=±iκEP2γκ12κ32κEP4[sign(β1β3)+iκ12κ322κEP2]2dependent on κ1/κEP and κ3/κEP form a Reimann surface, as shown in Figs. 1(c) and 1(d), where the EP point can be specified by κ12=κ32=γ|(β1β3)/2|=κEP2. The encircling-EP evolution can be acquired by suitably changing κ1 and κ3 along the propagation direction. In that case, chiral polarization switching can be achieved because of the non-Hermiticity-induced nonadiabatic transitions [49]. Due to the presence of absorption, the self-intersecting Reimann surface is separated into gain surface (red) and loss surface (blue). Each point on the surface represents an eigenvalue of the system. By changing the system parameters, the eigenvalue can move on the surface. The path can form a ring around the EP if the parameters are well managed, that is, the encircling EP evolution. The nonadiabatic hopping occurs only when the eigenvalue is moving on the loss surface, which leads to the different final states for encircling the EP clockwise and counterclockwise. Inspired by this chiral dynamic, it is possible to apply encircling EP evolution to guide the design of chiral polarizer.

    Concept and scheme of the chiral polarizer. (a) Comparison between conventional polarizer and our chiral polarizer. (b) Scheme of our chiral polarizer. The chiral polarizer is constructed with three waveguides WG1, WG2, and WG3; where WG1 and WG3 are supposed to be lossless, and WG2 has a high loss. (c) Encircling EP evolution clockwise. (d) Encircling EP evolution counterclockwise.

    Figure 1.Concept and scheme of the chiral polarizer. (a) Comparison between conventional polarizer and our chiral polarizer. (b) Scheme of our chiral polarizer. The chiral polarizer is constructed with three waveguides WG1, WG2, and WG3; where WG1 and WG3 are supposed to be lossless, and WG2 has a high loss. (c) Encircling EP evolution clockwise. (d) Encircling EP evolution counterclockwise.

    Figure 1(c) shows the process of the eigenvalue moving clockwise on the Reimann surface. In this direction, the TE0 mode moves on the loss surface. Due to the presence of absorption, the evolution of TE0 mode cannot maintain on the loss surface for the entire loop and hops to the gain surface during the evolution. As a result, the TE0 mode returns to itself without mode flipping. However, the TM0 mode moves on the gain surface, which indicates that the evolution of the TM0 mode can survive to the end without hopping and complete the mode flipping. Figure 1(d) demonstrates the evolution in counterclockwise direction. In contrast with the process in the clockwise direction, the TM0 mode moves on the loss surface, while the TE0 mode moves on the gain surface when encircling EP in the counterclockwise direction. Figures 1(c) and 1(d) indicate that the final polarization state of light for encircling EP clockwise is the TE0 mode and that for encircling EP counterclockwise is the TM0 mode, no matter the state of original polarization.

    B. Design of the Chiral Polarizer

    Figure 2 shows the design details of the proposed chiral polarizer. The device is designed on a silicon-on-insulator (SOI) platform with 250 nm top silicon and 2 μm buried oxide. We use the finite difference time domain method to calculate the mode field distribution and effective refractive index of each mode in waveguides with different widths, as shown in Fig. 2(a). In order to realize mode coupling, the effective refractive indexes of the three modes in respective waveguides must be approximately equal. On this premise, the widths of the waveguides are designed to be 315 nm for WG1, 441 nm for WG3, and 644 nm for WG2, which are marked by the dashed lines in Fig. 2(a). A Cr strip with a width of 100 nm and a thickness of 100 nm is deposited on the top of WG2 to induce the absorption loss (γ).

    Detailed design of chiral polarizer. (a) Effective refractive index of each mode versus the width of waveguide. (b) Optimized gap transform function that generates encircling EP parametric evolution. (c) Wavelength-dependent parametric loops for the design shown in (a) and (b).

    Figure 2.Detailed design of chiral polarizer. (a) Effective refractive index of each mode versus the width of waveguide. (b) Optimized gap transform function that generates encircling EP parametric evolution. (c) Wavelength-dependent parametric loops for the design shown in (a) and (b).

    The coupling coefficients κ1 and κ3 can be controlled by changing the gaps between waveguides. Figure 2(b) shows the gap variation along the propagation direction between WG1 and WG2 (gap12) and that between WG2 and WG3 (gap23), which are given by gap12=gap02+100  nm(gap02100  nm)×cos(zL34π),gap23=gap02+50  nm(gap0250  nm)×sin(zL34π),where z is the propagation distance, L is the total length of the coupled region, and gap0=600  nm is the maximum gap between the two waveguides. As the propagation distance of z increases from 0 to L, the parametric variation gives rise to a closed curve in the (κ1,κ3) plane. Figure 2(c) shows the closed loops around EPs at different wavelengths. EPs at different wavelengths are marked by the points in Fig. 2(c). The loops clearly encircle the EPs over a spectrum range from 1530 to 1570 nm, which covers the C-band for optical communication. It should be noted that an arbitrary polarization state can be decomposed into x and y polarization components with a particular amplitude ratio and phase difference. As a result, the input light with an arbitrary polarization state is first split into TE0 and TM0 modes by a PBS in our device and then starts the encircling EP evolution. The TE0 and TM0 modes enter the coupled region through WG1 and WG3, respectively, after PBS. The length of the coupling region is 110 μm, corresponding to the L in Eq. (2). A longer coupling region will lead to a higher extinct ratio but a higher loss. A 110 μm coupling length is a good trade-off between the extinction ratio and loss. Figure 3(a) shows the field distributions of TE0 and TM0 modes excited from different directions at 1540 nm. It can be seen clearly that TE0 and TM0 modes are both transmitted to the TE0 mode and output from WG1 when the light is injected from the left ports (i.e., forward propagation), whereas, they are both transmitted to the TM0 mode and output from WG3 when the light is injected from the right ports (i.e., backward propagation). The corresponding transmission spectra are shown in Fig. 3(b), which indicate that the chiral dynamics occurs over a spectrum range from 1520 to 1570 nm. A 10 dB extinction ratio is also accomplished from 1530 to 1560 nm, which can be used for the chiral polarizer.

    Simulation results of the chiral polarizer. (a) Simulation power distributions in the waveguides for forward and backward propagation. (b) Transmission spectra for different input.

    Figure 3.Simulation results of the chiral polarizer. (a) Simulation power distributions in the waveguides for forward and backward propagation. (b) Transmission spectra for different input.

    C. Fabrication and Experiment

    The device is fabricated by a standard electron-beam (e-beam) lithography-based nanofabrication process on the commercial 250 nm SOI platform. The scanning electron microscope (SEM) is used to determine the dimensions of the devices and confirm the obtained geometric shape, as shown in Fig. 4(a). The detailed structures of PBS and coupling region are presented as insets in Fig. 4(a) with the tested spectrum shown in Figs. 4(f) and 4(g); the fabrication of PBS is presented in the Appendix B [50]. The device is characterized by measuring the transmission spectra. The measured transmission spectra for TE0 and TM0 injection are shown in Figs. 4(b)–4(e). TE and TM denote the input or output mode from the left, and TE’ and TM’ denote the input or output mode from the right. Figures 4(b) and 4(c) demonstrate the output spectra for forward propagation. It can be seen clearly that the TE0 is the dominant output mode whichever TE0 or TM0 mode is inputted, whereas the TM0 mode becomes the dominant output mode for backward propagation, as shown in Figs. 4(d) and 4(e). The oscillations of the experimental spectra are due to the resonances between the facets of the coupling fiber. A 10 dB extinction ratio is achieved from 1550 to 1590 nm. The polarizer exhibits a loss of 25  dB for TE0 input from the left and TM0 input from the right. This loss is the intrinsic property of encircling EP in a passive system, which can be reduced by shortening the coupling length. It is a trade-off between insertion loss and extinction ratio. For more practical applications, the coupling length should be designed carefully or induce gain to balance the loss. Compared with the simulation results, the experiment spectra are redshifted, which is mainly caused by fabrication errors. According to Fig. 2(a), the refractive indexes dependent on waveguide width in TE0 and TE1 modes have high slopes, which indicate that the fabrication errors may manifest a vital impact on the performance of device. In fact, we have tested different devices with gradually varied parameters. The asymmetric mode switching phenomenon can be observed when the deviation of the widths of waveguides is lower than 10 nm. The insertion loss is mainly influenced by the width of the Cr strip. A wider Cr strip leads to higher insertion loss. For a well-performed device, the fabrication error should be controlled within 10  nm.

    SEM images of the chip and the experimentally measured spectra. (a) SEM images of the proposed chiral polarizer. Zoom-in images of polarization beam splitter and coupled region are shown in the subgraphs. (b)–(e) Experimentally measured spectra of the device for the (b), (c) forward propagation and (d), (e) backward propagation. TE and TM denote the modes input or output from the left; TE’ and TM’ denote the modes input or output from the right. (f), (g) Test results of the PBS.

    Figure 4.SEM images of the chip and the experimentally measured spectra. (a) SEM images of the proposed chiral polarizer. Zoom-in images of polarization beam splitter and coupled region are shown in the subgraphs. (b)–(e) Experimentally measured spectra of the device for the (b), (c) forward propagation and (d), (e) backward propagation. TE and TM denote the modes input or output from the left; TE’ and TM’ denote the modes input or output from the right. (f), (g) Test results of the PBS.

    To further verify the practical communication performances of the proposed chiral polarizer, a communication experiment is demonstrated to perform a function of formatting the data encoded on polarization channels into a particular polarization state. The experiment setup is illustrated in Fig. 5(a). The on–off keying (OOK) data are encoded on the TE0 and TM0 modes, where the TE0 mode indicates “1” and TM0 mode indicates “0.” Without loss of generality, the polarization encoded signals can be decomposed into data loaded on the TE0 mode and its inverted data loaded on the TM0 mode. In the experiment, the 10 GHz random OOK data and its inverted data are generated by an arbitrary waveform generator and loaded on the TE0 and TM0 modes by intensity modulator (IM), respectively. An erbium-doped fiber amplifier is used to compensate the power difference between TE0 and TM0 modes induced by the chiral polarizer. Data streams loaded on TE0 and TM0 modes are combined by the PBS and injected into the chip. The output light is decomposed into TE0 and TM0 modes and received by the oscilloscope. The input waveforms for forward and backward propagation is shown in Figs. 5(b) and 5(d), respectively. The output TE0 and TM0 polarization components of light are shown in Figs. 5(c) and 5(e). According to the analysis above, the data stream loaded on different polarization states transporting forward will be formatted into the TE0 mode. It can be seen clearly in Fig. 5(c) that most signal power is transferred to the TE0 mode, while only a little signal power remains in the TM0 mode. However, the TM0 mode becomes the dominant mode when the data transports backward. Figure 5(e) shows that most signal power transferred to TM0 mode rather than TE0 mode, which indicates the function of polarization data formatting with our chiral polarizer. An extinction ratio of 13 and 14 dB for forward and backward propagation is achieved, respectively.

    Experiment setup and results of communication experiment. (a) Experiment setup. (b) The 10 GHz OOK bits stream loaded on TE and TM modes for inputting forward. (c) Power summary of the output TE and TM modes. (d), (e) Result of inputting backward. TE and TM denote the input or output modes from the left; TE’ and TM’ denote the input or output modes from the right.

    Figure 5.Experiment setup and results of communication experiment. (a) Experiment setup. (b) The 10 GHz OOK bits stream loaded on TE and TM modes for inputting forward. (c) Power summary of the output TE and TM modes. (d), (e) Result of inputting backward. TE and TM denote the input or output modes from the left; TE’ and TM’ denote the input or output modes from the right.

    3. CONCLUSION

    In summary, we have proposed a chiral polarizer in an anti-PT symmetric system, which forms different polarized states dependent on light propagation direction. Based on the indirect coupling property of the anti-PT symmetric system, we successfully build an on-chip polarization-coupled anti-PT symmetric system for the first time. With the encircling EP evolution, we implement the chiral asymmetry polarization switch and chiral polarizer. The proposed chiral polarizer has been successfully applied to polarization data formatting for polarization encoding signals. The extinction ratio between the TE0 and TM0 modes for forward and backward propagation is 13 and 14 dB, respectively. Our work provides a new on-chip polarization manipulation method and demonstrates a practicable application in optics for encircling EP in non-Hermitian systems.

    Acknowledgment

    Acknowledgment. We thank Prof. Chengwei Qiu from National University of Singapore for the fruitful discussions.

    APPENDIX A: THEORY OF INDIRECT DISSIPATED COUPLING OF ANTI-PT SYMMETRIC SYSTEM

    For the three-waveguide-coupled system shown in Fig. 1(b), WG1 and WG3 are supposed to be lossless, and WG2 has a high loss. In this case, the complex amplitudes in these waveguides satisfy the mode coupling equation, given by [β1κ10κ1β2+iγκ30κ3β3][E1E2E3]=λ[E1E2E3],where E is the complex amplitude of each mode and β is the propagation coefficient. κ1 is the coupling coefficient between WG1 and WG2, while κ3 is the coupling coefficient between WG2 and WG3. By substituting E1 and E3 for E2, and, under the assumption of |γ||λβ2|, Eq. (A1) can be simplified as [β1+iκ12γiκ1κ3γiκ1κ3γβ3+iκ32γ][E1E3]=λ[E1E3].The eigenvalue of this degenerate second-order system can be written as λ=β1+β32+iκ1κ3γ±iκ12κ32γ2(β1β32+iκ12κ322γ)2.Equation (A3) indicates that the system has an EP at κ12=κ32=γ|β1β32|. Encircling EP evolution can be obtained by changing κ1 and κ3 along the propagation direction.

    In Eq. (A3), we suppose κ1=κ3, Δ=β1β32, and Ω2=κ12κ32γ2(β1β32)2. When Ω2>0, the imaginary part of the eigenvalue splits, and the eigenvector can be written as E1,3=[1,(±|Ω|+iΔ)γκ1κ3]T. The phase differences between two complex amplitudes in WG1 and WG3 are close to 0 and π, indicating that the symmetry of the system is unbroken. When Ω2<0, the real part of the eigenvalue splits, and the eigenvector of the system can be written as E1,3=[1,i(Δ|Ω|)γκ1κ3]T. The phase differences between two complex amplitudes in WG1 and WG3 are π2, indicating that the symmetry of the system is broken. Compared with the PT symmetric system, an anti-PT symmetric system shows the opposite degenerate condition of real and imaginary parts of the eigenvalue in broken and unbroken states. This property indicates that the indirect coupling in the three-waveguide-coupled system can be used to construct the anti-PT symmetric system, which lays the foundation of our work.

    APPENDIX B: FABRICATION AND TEST RESULT OF ON-CHIP PBS

    We use on-chip PBSs to split the input light into TE and TM modes and recombine the output light. The PBS is based on a directional coupler, which has a significantly larger TM0 coupling coefficient than the TE0 mode coupling coefficient. The coupling length is selected so that the TM0 mode achieves full coupling, while the TE0 mode remains negligible coupling. The PBS is fabricated by electron beam lithography (EBL) and inductively coupled plasma (ICP) etching. The insertion loss of the PBS for TE input is negligible and for TM input is about 1 dB; further, the extinction ratio is tested by TE and TM mode input, respectively. The extinction ratio is 35 dB for the TE mode input. For the TM mode input, the extinction ratio is 23 dB. The light splitting ability of PBS is enough for our chiral polarizer.

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    Yanxian Wei, Hailong Zhou, Yuntian Chen, Yunhong Ding, Jianji Dong, Xinliang Zhang, "Anti-parity-time symmetry enabled on-chip chiral polarizer," Photonics Res. 10, 76 (2022)
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