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Polarimetric Parity-Time Symmetry in a Photonic System Lingzhi Li1,Yuancao1,Yanyanzhi1, Jiejun Zhang 1,Yutingzou1, Xinhuan Feng1,Bai-Ouguan1 and Jianping Yao 1,2

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Polarimetric Parity-Time Symmetry in a Photonic System Lingzhi Li1,Yuancao1,Yanyanzhi1, Jiejun Zhang 1,Yutingzou1, Xinhuan Feng1,Bai-Ouguan1 and Jianping Yao 1,2 Li et al. Light: Science & Applications (2020) 9:169 Official journal of the CIOMP 2047-7538 https://doi.org/10.1038/s41377-020-00407-3 www.nature.com/lsa ARTICLE Open Access Polarimetric parity-time symmetry in a photonic system Lingzhi Li1,YuanCao1,YanyanZhi1, Jiejun Zhang 1,YutingZou1, Xinhuan Feng1,Bai-OuGuan1 and Jianping Yao 1,2 Abstract Parity-time (PT) symmetry has attracted intensive research interest in recent years. PT symmetry is conventionally implemented between two spatially distributed subspaces with identical localized eigenfrequencies and complementary gain and loss coefficients. The implementation is complicated. In this paper, we propose and demonstrate that PT symmetry can be implemented between two subspaces in a single spatial unit based on optical polarimetric diversity. By controlling the polarization states of light in the single spatial unit, the localized eigenfrequencies, gain, loss, and coupling coefficients of two polarimetric loops can be tuned, leading to PT symmetry breaking. As a demonstration, a fiber ring laser based on this concept supporting stable and single-mode lasing without using an ultranarrow bandpass filter is implemented. Introduction threshold5,6. An optical filter can be incorporated into a A parity-time (PT) symmetric system is a special non- laser cavity to reduce the number of modes above the Hermitian system of which its Hamiltonian possesses real threshold. If the optical filter has a sufficiently narrow 23,24 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; eigenvalues. Recently, PT symmetry has been investigated passband, single-mode lasing can be achieved . How- – extensively in photonic1 13 and optoelectronic14,15 sys- ever, for a long-cavity laser such as a fiber laser with a tems, one of the main reasons being its effectiveness for cavity length on the order of tens of meters, a high-Q – mode selection in an optical or optoelectronic system11 optical filter is needed, making the system costly and 15. For a high-performance continuous-wave laser, single- endowing it with poor stability25,26. mode operation is one of the fundamental requirements Parity-time symmetry has been proven to be an effective because it determines the coherence and power stability solution for achieving mode selection in a photonic sys- – of the laser output5,6,16. For a long-cavity laser, for which tem1 15. Conventionally, a PT-symmetric system is it is preferable to have low phase noise, a narrow line- implemented between two cross-coupled and spatially width, and high optical power, single-mode lasing is distributed optical subspaces, which are engineered to – challenging due to the small mode spacing5,6,16 24. Since have an identical geometry with complementary gain and the gain spectrum of a gain medium in a laser cavity is loss coefficients. A PT-symmetric system has a strongly usually several orders of magnitude broader than the enhanced gain difference between the dominant mode mode spacing of the laser, the round-trip gain difference and the side modes, thus making single-mode oscillation between adjacent modes is small, making it difficult to possible5,6,14,15. However, such a system requires two achieve single-mode oscillation by manipulating the lasing spatially distributed subspaces, which leads to increased structural complexity, high cost, and strong susceptibility to environmental perturbations. Recently, we demon- Correspondence: Jiejun Zhang ([email protected])or Jianping Yao ([email protected]) strated a new type of PT-symmetric system that is realized 1Guangdong Provincial Key Laboratory of Optical Fiber Sensing and in the parameter space of optical wavelength, where the Communications, Institute of Photonics Technology, Jinan University, spatial duplicity in a conventional PT-symmetric system is Guangzhou 511442, China 27 2Microwave Photonics Research Laboratory, School of Electrical Engineering eliminated . Since two wavelengths are employed, the and Computer Science, University of Ottawa, Ottawa, ON K1N 6N5, Canada © The Author(s) 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a linktotheCreativeCommons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Li et al. Light: Science & Applications (2020) 9:169 Page 2 of 8 concept is not applicable to a system where only a single and Pol. 2), are used to tune the gain and loss coefficients of wavelength is supported. the eigenvalues in the two polarimetric loops to achieve PT In this paper, we propose and demonstrate that a PT- symmetry. As the gain and loss coefficients are increased to symmetric system can be implemented in a single spatial values greater than the coupling coefficient, PT symmetry unit based on polarimetric diversity, which supports single- breaking occurs. The two polarimetric loops form a PT- wavelength operation. By controlling the polarization states symmetric fiber ring laser with one polarimetric loop of light in a single spatial unit, the localized eigen- supporting the gain modes and the other supporting the frequencies, gain, loss, and coupling coefficients can be loss modes. The polarimetric PT symmetry then strongly controlled to achieve PT symmetry breaking. As a demon- enhances the gain difference between the dominant mode stration, a long-cavity fiber ring laser supporting single- and the sidemodes, making single-mode lasing possible mode lasing without using a high-Q optical filter is imple- without using an ultranarrow bandpass filter. mented. In the experiment, the fiber ring laser has a cavity As shown in Fig. 1, the photonic system has a single length of 41.0 m with a mode spacing as small as 4.88 MHz. unidirectional physical fiber loop that supports two The employment of polarimetric PT symmetry enables polarimetric loops. An erbium-doped fiber amplifier effective suppression of the sidemodes with a suppression (EDFA) is incorporated to provide an optical gain. The ratio greater than 47.9 dB. The linewidth of the light gen- polarimetric diversity is implemented by controlling the erated by the fiber ring laser is measured to be 129 kHz with polarization states of light in the fiber loop. The dominant a wavelength tunable range of 35 nm. With active stabili- mode can be coarsely chosen with a tunable optical filter zation, the linewidth can be reduced to its Lorentzian line- (TOF). The output of the system is derived using a 3-dB width of 2.4 kHz. The proposed polarimetric PT symmetry optical coupler (OC), which is sent to an optical spectrum concept opens new avenues for the implementation of non- analyzer (OSA) for spectrum analysis, an optical homo- Hermitian photonic systems with increased functionalities. dyne system for mode analysis, and an optical self- heterodyne system for linewidth measurement. Results A three-paddle fiber-optic PC has a sandwiched struc- Figure 1 shows a schematic diagram of the proposed ture with a half-wave plate located between two quarter- polarimetric PT-symmetric photonic system consisting of wave plates. The transfer function of a three-paddle PC is two polarimetric loops. The two polarimetric loops, with given by28 independently adjustable eigenfrequencies and round-trip ðÞφ θ À θ ðÞφ gain coefficients, are implemented based on polarimetric exp i 2 0 cos sin exp i 1 0 FPC ¼ ´ ´ diversity in a single physical loop. Specifically, the bire- 01sin θ cos θ 01 fringent path in the fiber ring laser loop creates two ð1Þ polarimetric loops, and the coupled path allows coupling between the two polarimetric loops. Two polarization where φ1 and φ2 are the phase retardances introduced to controllers (PCs), in conjunction with two polarizers (Pol. 1 the two orthogonally polarized light waves by the two Birefringent path Coupled path Ex k EDFA E PC2 x k Ey OC1 E y Polarimetricloops TOF OC2 Pol. 2 λ Pol. 1 E x k Optical spectral Longitudinal PC1 analysis mode analysis Ey Fig. 1 Schematic diagram of the proposed polarimetric PT-symmetric photonic system. The system consists of a single spatial loop, in which two equivalent polarimetric loops are formed by recirculating light waves of orthogonal polarization states in the loop. To achieve PT symmetry, the phase retardance, power ratio, and coupling coefficient between the orthogonally polarized light waves are tuned by controlling PC1 in the birefringent path, and the lasing threshold is tuned by controlling PC2 in the coupled path. PC: polarization controller; Pol.: polarizer; EDFA: erbium- doped fiber amplifier; OC: optical coupler; TOF: tunable optical filter Li et al. Light: Science & Applications (2020) 9:169 Page 3 of 8 Table 1 The critical angles that are tuned to achieve polarimetric PT symmetry Angle Definition Functionality Tuning method θr Rotation angle of quarter-wave plate to tune PT symmetry of the real part of the eigenfrequency of the Quarter-wave plate of PC1 polarization phase retardance polarimetric loops θi Optical axis rotation angle from Pol. 1 to Pol. 2 PT symmetry of the imaginary part of the eigenfrequency of Half-wave plate of PC1 the polarimetric loops θt Optical axis rotation angle from Pol. 2 to Pol. 1 Lasing threshold Half-wave plate of PC2 a b 8 tuned by m r x 6 y x y Polarimetric ω loop Ex 4 Polarimetric 2 loop Ey 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 i (rad) c λ/4 (PC1) Pol.
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