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Liu X, Lin Z, Song W, Sun J, Huang C, Wu S, Xiao X, Xin H, Zhu S, Li T. Perfect Excitation of Topological States by Supersymmetric Waveguides. PHYSICAL REVIEW LETTERS 2024; 132:016601. [PMID: 38242675 DOI: 10.1103/physrevlett.132.016601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 11/20/2023] [Indexed: 01/21/2024]
Abstract
Topological photonic states provide intriguing strategies for robust light manipulations, however, it remains challenging to perfectly excite these topological eigenstates due to their complicated mode profiles. In this work, we propose to realize the exact eigenmode of the topological edge states by supersymmetric (SUSY) structures. By adiabatically transforming the SUSY partner to its main topological structure, the edge modes can be perfectly excited with simple single-site input. We experimentally verify our strategy in integrated silicon waveguides in telecommunication wavelength, showing a broad working bandwidth. Moreover, a shortcut-to-adiabaticity strategy is further applied to speed up the adiabatic pump process by inverse-design approaches, thus enabling fast mode evolutions and leading to reduced device size. Our method is universal and beneficial to the topology-based or complex eigenmodes systems, ranging from photonics and microwaves to cold atoms and acoustics.
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Affiliation(s)
- Xuanyu Liu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Zhiyuan Lin
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Wange Song
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Jiacheng Sun
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Chunyu Huang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Shengjie Wu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Xingjian Xiao
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Haoran Xin
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Shining Zhu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Tao Li
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, School of Physics, Nanjing University, Nanjing, 210093, China
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Fu T, Chen J, Wang Y, Zhou X, Qi A, Wang X, Dai Y, Wang M, Zheng W. Electrically driven supersymmetric semiconductor laser arrays with single-lobe far-field patterns. OPTICS EXPRESS 2023; 31:1858-1867. [PMID: 36785211 DOI: 10.1364/oe.479111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 12/15/2022] [Indexed: 06/18/2023]
Abstract
Semiconductor laser arrays based on the third-order supersymmetric (SUSY) transformation are proposed to increase the mode discrimination between fundamental supermode and high-order supermodes. The distance between the edge waveguide of the main array and that of the superpartners is optimized. Then, the electric field distributions of different modes are also calculated, which show that, except for the fundamental supermode, the high-order supermodes penetrate deeper into the superpartner arrays, which accounts for the increased loss of high-order supermodes. The fabricated third-order SUSY laser array can emit light with a single-lobe far-field pattern under an injection current of 70 mA, which is a promising candidate for optical couplings between lasers and optical elements.
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Viedma D, Queraltó G, Mompart J, Ahufinger V. High-efficiency topological pumping with discrete supersymmetry transformations. OPTICS EXPRESS 2022; 30:23531-23543. [PMID: 36225030 DOI: 10.1364/oe.460192] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2022] [Accepted: 05/24/2022] [Indexed: 06/16/2023]
Abstract
Making use of the isospectrality of Supersymmetry transformations, we propose a general and high-fidelity method to prepare gapped topological modes in discrete systems from a single-site excitation. The method consists of adiabatically connecting two superpartner structures, deforming the input state into the desired mode. We demonstrate the method by pumping topological states of the Su-Schrieffer-Heeger model in an optical waveguide array, where the adiabatic deformation is performed along the propagation direction. We obtain fidelities above F = 0.99 for a wide range of coupling strengths when pumping edge and interface states.
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Fu T, Qi A, Chen J, Wang Y, Zhou X, Wang X, Dai Y, Wang M, Zheng W. Electrically injected supersymmetric semiconductor lasers with narrow vertical divergence angle. OPTICS LETTERS 2022; 47:2991-2994. [PMID: 35709033 DOI: 10.1364/ol.459993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
Electrically injected supersymmetric (SUSY) semiconductor lasers are proposed and fabricated. Two successive SUSY transformations are applied to the main array arranged along the direction of epitaxial growth, which can remove the propagation constants of the fundamental mode and the leaky mode of the main array from the superpartner while keeping those of other high-order modes. The SUSY laser possesses an excellent mode discrimination and favors the lasing of the fundamental mode. The fabricated SUSY laser can emit light with a single-lobe vertical far-field pattern with the full width at half maximum of 16.87° under an injection current of 1.4 A.
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Viedma D, Ahufinger V, Mompart J. Supersymmetry-enhanced stark-chirped rapid-adiabatic-passage in multimode optical waveguides. OPTICS EXPRESS 2021; 29:39200-39213. [PMID: 34809289 DOI: 10.1364/oe.442475] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Accepted: 10/06/2021] [Indexed: 06/13/2023]
Abstract
We propose a method to efficiently pump an excited mode of a multimode optical waveguide starting from a fundamental-mode input by combining Stark-Chirped Rapid Adiabatic Passage (SCRAP) and Supersymmetry (SUSY) transformations. In a two-waveguide set, we implement SCRAP by modulating the core refractive index of one waveguide, which is evanescently coupled to its SUSY partner. SCRAP provides an efficient transfer of light intensity between the modes of different waveguides, while SUSY allows to control which modes are supported. Using both techniques allows to achieve fidelities above 99% for the pumping of the excited mode of a two-mode waveguide. Additionally, we show that SCRAP can be exploited to spatially separate superpositions of fundamental and excited modes, and how SUSY can also improve the results for this application.
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Qiao X, Midya B, Gao Z, Zhang Z, Zhao H, Wu T, Yim J, Agarwal R, Litchinitser NM, Feng L. Higher-dimensional supersymmetric microlaser arrays. Science 2021; 372:403-408. [PMID: 33888640 DOI: 10.1126/science.abg3904] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2021] [Accepted: 03/24/2021] [Indexed: 12/24/2022]
Abstract
The nonlinear scaling of complexity with the increased number of components in integrated photonics is a major obstacle impeding large-scale, phase-locked laser arrays. Here, we develop a higher-dimensional supersymmetry formalism for precise mode control and nonlinear power scaling. Our supersymmetric microlaser arrays feature phase-locked coherence and synchronization of all of the evanescently coupled microring lasers-collectively oscillating in the fundamental transverse supermode-which enables high-radiance, small-divergence, and single-frequency laser emission with a two-orders-of-magnitude enhancement in energy density. We also demonstrate the feasibility of structuring high-radiance vortex laser beams, which enhance the laser performance by taking full advantage of spatial degrees of freedom of light. Our approach provides a route for designing large-scale integrated photonic systems in both classical and quantum regimes.
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Affiliation(s)
- Xingdu Qiao
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Bikashkali Midya
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.,Department of Physical Sciences, Indian Institute of Science Education and Research, Berhampur 760010, India
| | - Zihe Gao
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Zhifeng Zhang
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Haoqi Zhao
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Tianwei Wu
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Jieun Yim
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Ritesh Agarwal
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Natalia M Litchinitser
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
| | - Liang Feng
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA. .,Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
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Gupta SK, Zou Y, Zhu XY, Lu MH, Zhang LJ, Liu XP, Chen YF. Parity-Time Symmetry in Non-Hermitian Complex Optical Media. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1903639. [PMID: 31830340 DOI: 10.1002/adma.201903639] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2019] [Revised: 09/25/2019] [Indexed: 06/10/2023]
Abstract
The exploration of quantum-inspired symmetries in optical and photonic systems has witnessed immense research interest both fundamentally and technologically in a wide range of subject areas in physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory and recently ramified into a diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant application prospects and engineering of novel materials. In addition, there has been increasing research interest in many emerging directions beyond optics and photonics. Here, the state-of-the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings are brought together, and key concepts, a background, and a detailed perspective on new emerging directions are described. It can be anticipated that this trendy field of interest will be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, optoelectronics, and beyond, and will offer distinctive application prospects in novel functional materials.
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Affiliation(s)
- Samit Kumar Gupta
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Yi Zou
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Xue-Yi Zhu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Ming-Hui Lu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Li-Jian Zhang
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Xiao-Ping Liu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Yan-Feng Chen
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
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Walasik W, Chandra N, Midya B, Feng L, Litchinitser NM. Mode-sorter design using continuous supersymmetric transformation. OPTICS EXPRESS 2019; 27:22429-22438. [PMID: 31510537 DOI: 10.1364/oe.27.022429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Accepted: 07/03/2019] [Indexed: 06/10/2023]
Abstract
We propose to use a continuous supersymmetric (SUSY) transformation of a dielectric permittivity profile in order to design a photonic mode sorter. The iso-spectrality of the SUSY transformation ensures that modes of the waveguide preserve their propagation constants while being spatially separated. This global matching of the propagation constants, in conjunction with the adiabatic modification of the refractive index landscape along the propagation direction, results in the negligible modal cross-talk and low scattering losses in the sorter. We show that a properly optimized SUSY mode sorter outperforms a standard asymmetric Y-splitter by reducing the cross-talk by at least two orders of magnitude. Moreover, the SUSY sorter is capable of sorting either transverse-electric or transverse-magnetic polarized modes and operates in a broad range of wavelengths. At the telecommunication wavelength, the 300-μm-long SUSY sorter provides the cross-talk of -35 dB and a broad operation bandwidth. The design proposed here paves the way toward efficient signal manipulation in integrated photonic devices.
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Smirnova DA, Padmanabhan P, Leykam D. Parity anomaly laser. OPTICS LETTERS 2019; 44:1120-1123. [PMID: 30821785 DOI: 10.1364/ol.44.001120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Accepted: 01/22/2019] [Indexed: 06/09/2023]
Abstract
We propose a novel supersymmetry-inspired scheme for achieving robust single-mode lasing in arrays of coupled microcavities, based on factorizing a given array Hamiltonian into its "supercharge" partner array. Pumping a single sublattice of the partner array preferentially induces lasing of an unpaired zero mode. A chiral symmetry protects the zero mode similar to 1D topological arrays, but it need not be localized to domain walls or edges. We demonstrate single-mode lasing over a wider parameter regime by designing the zero mode to have a uniform intensity profile.
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Hokmabadi MP, Nye NS, El-Ganainy R, Christodoulides DN, Khajavikhan M. Supersymmetric laser arrays. Science 2019; 363:623-626. [DOI: 10.1126/science.aav5103] [Citation(s) in RCA: 51] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Accepted: 12/14/2018] [Indexed: 11/02/2022]
Abstract
Scaling up the radiance of coupled laser arrays has been a long-standing challenge in photonics. In this study, we demonstrate that notions from supersymmetry—a theoretical framework developed in high-energy physics—can be strategically used in optics to address this problem. In this regard, a supersymmetric laser array is realized that is capable of emitting exclusively in its fundamental transverse mode in a stable manner. Our results not only pave the way toward devising new schemes for scaling up radiance in integrated lasers, but also, on a more fundamental level, could shed light on the intriguing synergy between non-Hermiticity and supersymmetry.
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Queraltó G, Ahufinger V, Mompart J. Integrated photonic devices based on adiabatic transitions between supersymmetric structures. OPTICS EXPRESS 2018; 26:33797-33806. [PMID: 30650812 DOI: 10.1364/oe.26.033797] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Accepted: 11/11/2018] [Indexed: 06/09/2023]
Abstract
We introduce adiabatic transitions connecting two supersymmetric partner profiles by smoothly modifying the transverse refractive index profile along the propagation direction. With this transformation, one of the transverse electric modes evolves adapting its shape and propagation constant without being coupled to other guided or radiated modes while the rest of the modes are radiated. This technique offers a systematic way to manipulate the modal content in systems of optical waveguides and engineer efficient and robust photonic devices such as tapered waveguides, single-waveguide mode filters, beam splitters and interferometers. Numerical simulations show that very high fidelities and transmitted powers are obtained for a broad range of devices lengths and light's wavelengths.
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Walasik W, Midya B, Feng L, Litchintser NM. Supersymmetry-guided method for mode selection and optimization in coupled systems: publisher's note. OPTICS LETTERS 2018; 43:5250. [PMID: 30382979 DOI: 10.1364/ol.43.005250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Indexed: 06/08/2023]
Abstract
This publisher's note corrects an error in the funding section of Opt. Lett.43, 3758 (2018)OPLEDP0146-959210.1364/OL.43.003758.
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Midya B, Walasik W, Litchinitser NM, Feng L. Supercharge optical arrays. OPTICS LETTERS 2018; 43:4927-4930. [PMID: 30320785 DOI: 10.1364/ol.43.004927] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2018] [Accepted: 09/15/2018] [Indexed: 06/08/2023]
Abstract
We introduce the notion of a supercharge optical array synthesized according to supersymmetric charge operators. Starting from an arbitrary array, mathematical supersymmetry transformation can be used systematically to create a zero-energy physical state below the ground state of the super-partner array. This zero mode, which is pinned deep in the mid-gap of the corresponding supercharge array owing to the square-root spectral relationship between a supercharge and a super-Hamiltonian array, is shown to be protected because of the chiral symmetry inherent to a supercharge array. A supercharge array can be used in practical applications to design a discrete optical system of waveguides or coupled resonators where the mid-gap zero mode facilitates robust light dynamics in either spatial or time domain.
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