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Amelio I, Goldman N. Lasing in Non-Hermitian Flat Bands: Quantum Geometry, Coherence, and the Fate of Kardar-Parisi-Zhang Physics. PHYSICAL REVIEW LETTERS 2024; 132:186902. [PMID: 38759172 DOI: 10.1103/physrevlett.132.186902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Revised: 04/03/2024] [Accepted: 04/08/2024] [Indexed: 05/19/2024]
Abstract
We show that lasing in flat-band lattices can be stabilized by means of the geometrical properties of the Bloch states, in settings where the single-particle dispersion is flat in both its real and imaginary parts. We illustrate a general projection method and compute the collective excitations, which display a diffusive behavior ruled by quantum geometry through a peculiar coefficient involving gain, losses and interactions, and entailing resilience against modulational instabilities. Then, we derive an equation of motion for the phase dynamics and identify a Kardar-Parisi-Zhang term of geometric origin. This term is shown to exactly cancel whenever the real and imaginary parts of the laser nonlinearity are proportional to each other, or when the uniform-pairing condition is satisfied. We confirm our results through numerical studies of the π-flux diamond chain. This Letter highlights the key role of Bloch geometric effects in nonlinear dissipative systems and KPZ physics, with direct implications for the design of laser arrays with enhanced coherence.
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Affiliation(s)
- Ivan Amelio
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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Yoshimi H, Yamaguchi T, Ishida S, Ota Y, Iwamoto S. Efficient light couplers to topological slow light waveguides in valley photonic crystals. OPTICS EXPRESS 2024; 32:6382-6390. [PMID: 38439342 DOI: 10.1364/oe.512196] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Accepted: 01/26/2024] [Indexed: 03/06/2024]
Abstract
We numerically and experimentally demonstrate efficient light couplers between topological slow light waveguides in valley photonic crystals (VPhCs) and wire waveguides. By numerical simulations, we obtained a high coupling efficiency of -0.84 dB/coupler on average in the slow light regime of a group index ng = 10 - 30. Experimentally, we fabricated the couplers in a Si slab and measured the transmitted power of the devices. We realized a high coupling efficiency of approximately -1.2 dB/coupler in the slow light region of ng = 10 - 30, which is close to the result from the numerical simulations. These demonstrations will lay the groundwork for low-loss photonic integrated circuits using topological slow light waveguides.
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Ma J, Zhou T, Tang M, Li H, Zhang Z, Xi X, Martin M, Baron T, Liu H, Zhang Z, Chen S, Sun X. Room-temperature continuous-wave topological Dirac-vortex microcavity lasers on silicon. LIGHT, SCIENCE & APPLICATIONS 2023; 12:255. [PMID: 37872140 PMCID: PMC10593858 DOI: 10.1038/s41377-023-01290-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Revised: 09/17/2023] [Accepted: 09/20/2023] [Indexed: 10/25/2023]
Abstract
Robust laser sources are a fundamental building block for contemporary information technologies. Originating from condensed-matter physics, the concept of topology has recently entered the realm of optics, offering fundamentally new design principles for lasers with enhanced robustness. In analogy to the well-known Majorana fermions in topological superconductors, Dirac-vortex states have recently been investigated in passive photonic systems and are now considered as a promising candidate for robust lasers. Here, we experimentally realize the topological Dirac-vortex microcavity lasers in InAs/InGaAs quantum-dot materials monolithically grown on a silicon substrate. We observe room-temperature continuous-wave linearly polarized vertical laser emission at a telecom wavelength. We confirm that the wavelength of the Dirac-vortex laser is topologically robust against variations in the cavity size, and its free spectral range defies the universal inverse scaling law with the cavity size. These lasers will play an important role in CMOS-compatible photonic and optoelectronic systems on a chip.
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Affiliation(s)
- Jingwen Ma
- Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
| | - Taojie Zhou
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
- Department of Electronic and Electrical Engineering, University College London, London, WC1E 7JE, UK
| | - Mingchu Tang
- Department of Electronic and Electrical Engineering, University College London, London, WC1E 7JE, UK
| | - Haochuan Li
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
| | - Zhan Zhang
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China
| | - Xiang Xi
- Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China
| | - Mickael Martin
- Université Grenoble Alpes, CNRS, CEA-LETI, MINATEC, Grenoble INP, LTM, F-38054, Grenoble, France
| | - Thierry Baron
- Université Grenoble Alpes, CNRS, CEA-LETI, MINATEC, Grenoble INP, LTM, F-38054, Grenoble, France
| | - Huiyun Liu
- Department of Electronic and Electrical Engineering, University College London, London, WC1E 7JE, UK
| | - Zhaoyu Zhang
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, 518172, China.
| | - Siming Chen
- Department of Electronic and Electrical Engineering, University College London, London, WC1E 7JE, UK.
| | - Xiankai Sun
- Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China.
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Wei MS, Liao MJ, Wang C, Zhu C, Yang Y, Xu J. Topological laser with higher-order corner states in the 2-dimensional Su-Schrieffer-Heeger model. OPTICS EXPRESS 2023; 31:3427-3440. [PMID: 36785336 DOI: 10.1364/oe.476047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 12/28/2022] [Indexed: 06/18/2023]
Abstract
A nonlinear non-Hermitian topological laser system based on the higher-order corner states of the 2-dimensional (2D) Su-Schrieffer-Heeger (SSH) model is investigated. The topological property of this nonlinear non-Hermitian system described by the quench dynamics is in accordance with that of a normal 2D SSH model. In the topological phase, all sites belonging to the topological corner states begin to emit stable laser light when a pulse is given to any one site of the lattice, while no laser light is emitted when the lattice is in the trivial phase. Furthermore, the next-nearest-neighbor (NNN) couplings are introduced into the strong-coupling unit cells of the 2D SSH model, which open a band gap in the continuous band structure. In the topological phase, similar to the case of 2D SSH model without NNN couplings, the corner sites can emit stable laser light due to the robustness of the higher-order corner states when the NNN couplings are regarded as the perturbation. However, amplitude of the stimulated site does not decay to zero in the trivial phase, because the existence of the NNN couplings in the strong-coupling unit cells make the lattice like one in the tetramer limit, and a weaker laser light is emitted by each corner.
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Zhang H, Zhang Y, Lu C. Topological polarization selection concentrator. OPTICS LETTERS 2022; 47:6121-6124. [PMID: 37219187 DOI: 10.1364/ol.474097] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2022] [Accepted: 10/31/2022] [Indexed: 05/24/2023]
Abstract
Topological polarization selection devices, which can separate topological photonic states of different polarizations into different positions, play a key role in the field of integrated photonics. However, there has been no effective method to realize such devices to date. Here, we have realized a topological polarization selection concentrator based on synthetic dimensions. The topological edge states of double polarization modes are constructed by introducing lattice translation as a synthetic dimension in a completed photonic bandgap photonic crystal with both TE and TM modes. The proposed device can work on multiple frequencies and is robust against disorders. This work provides a new,to the best of our knowledge, scheme to realize topological polarization selection devices, and it will enable practical applications such as topological polarization routers, optical storage, and optical buffers.
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Wei G, Liu Z, Wu H, Wang L, Wang S, Xiao J. Boundary configured chiral edge states in valley topological photonic crystal. OPTICS LETTERS 2022; 47:3007-3010. [PMID: 35709037 DOI: 10.1364/ol.462005] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
Chiral edge states (CESs) have been demonstrated at the external boundary of a valley photonic crystal (VPC), with flexibly tunable group velocity and frequency range by adjusting the boundary structure. In this work, we show parallel and antiparallel CESs located at two opposite VPC-air boundaries, which contain wave components belonging to opposite valleys or the same valley. In addition, we design a meta-structure with four types of air-contacted boundary that support CESs in different frequency ranges. The structure also has an internal interface channel supporting the valley edge state that bridges the top and bottom boundaries. We show that the CESs, while excited at a given port, can be exclusively guided to the other three ports, depending on the operating frequency. Our work provides an alternative way to design compact topological devices for optical waveguides and wave splitters.
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Chen L, Zhao M, Ye H, Hang ZH, Li Y, Cao Z. Efficient light coupling between conventional silicon photonic waveguides and quantum valley-Hall topological interfaces. OPTICS EXPRESS 2022; 30:2517-2527. [PMID: 35209389 DOI: 10.1364/oe.445851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 01/01/2022] [Indexed: 06/14/2023]
Abstract
Robust and efficient light coupling into and out of quantum valley-Hall (QVH) topological interfaces within near-infrared frequencies is demanded in order to be integrated into practical two-dimensional (2D) optical chips. Here, we numerically demonstrate efficient light coupling between a QVH interface and a pair of input/output silicon photonic waveguides in the presence of photonic crystal line defects. When the topological QVH interface is directly end-butt coupled to the silicon waveguides, the input-to-output transmission efficiency is lower than 50% and the exterior boundaries associated with a QVH interface also cause inevitable back-reflections and high-order scatterings, further reducing the transmission efficiency. The transmission efficiency is substantially increased to 95.8% (94.3%) when photonic crystal line defects are introduced between the bridge (zigzag) QVH interface and the waveguides. The buffering line defect mode, with an effective group refractive index between the interface state and the waveguide mode will ease their mode profile conversion. The design we present here brings no fabrication complexity and may be used as a guide for future implementation of on-chip 2D topological photonics.
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Yoshimi H, Yamaguchi T, Katsumi R, Ota Y, Arakawa Y, Iwamoto S. Experimental demonstration of topological slow light waveguides in valley photonic crystals. OPTICS EXPRESS 2021; 29:13441-13450. [PMID: 33985077 DOI: 10.1364/oe.422962] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Accepted: 04/07/2021] [Indexed: 06/12/2023]
Abstract
We experimentally demonstrate topological slow light waveguides in valley photonic crystals (VPhCs). We employed a bearded interface formed between two topologically-distinct VPhCs patterned in an air-bridged silicon slab. The interface supports both topological and non-topological slow light modes below the light line. By means of optical microscopy, we observed light propagation in the topological mode in the slow light regime with a group index ng over 30. Furthermore, we confirmed light transmission via the slow light mode even under the presence of sharp waveguide bends. In comparison between the topological and non-topological modes, we found that the topological mode exhibits much more efficient waveguiding than the trivial one, demonstrating topological protection in the slow light regime. This work paves the way for exploring topological slow-light devices compatible with existing photonics technologies.
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