Robust Fano resonance in the photonic valley Hall states

Chang-Yin Ji, Yongyou Zhang, Bingsuo Zou, and Yugui Yao

Phys. Rev. A 103, 023512 – Published 11 February 2021

Abstract

Rapidly developing photonics brings many interesting resonant optical phenomena, in which the Fano resonance (FR) always intrigues researchers because of its applications in optical switching and sensing. However, its sensitive dependence on environmental conditions makes it hard to implement in experiments. In this work we suggest a robust FR based on the photonic valley Hall insulators, immune to the system impurities. The robust FR is achieved by coupling the valley-dependent edge states with one double-degenerate cavity. The $δ$ -type photonic transport theory we build reveals that this FR dates from the interference of the two transmissions that are attributed to the two cavity modes. We confirm that the induced Fano line shape of the transmission spectra is robust against the bending domain walls and disorders. Our work may provoke exciting frontiers for manipulating the valley transport and pave a way for the valley photonic devices such as optical switches, low-threshold lasers, and ultrasensitive sensors.

Received 17 July 2020
Revised 19 September 2020
Accepted 21 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.023512

Physics Subject Headings (PhySH)

Photonic crystals Topological effects in photonic systems

Atomic, Molecular & Optical

Authors & Affiliations

Chang-Yin Ji^1,2, Yongyou Zhang ^1,*, Bingsuo Zou ³, and Yugui Yao^1,†

¹Key Lab of advanced optoelectronic quantum architecture and measurement (MOE), Beijing Key Lab of Nanophotonics & Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing 100081, China
²China Academy of Engineering physics, Mianyang, Sichuan 621900, China
³Guangxi Key Laboratory of Processing for Non-ferrous Metals and Featured Materials, School of Physical science and Technology, Guangxi University, Nanning 530004, China

^*Author to whom correspondence should be addressed: yyzhang@bit.edu.cn
^†ygyao@bit.edu.cn

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Issue

Vol. 103, Iss. 2 — February 2021

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Images

Figure 1
(a, b) Band structures of two photonic topological valley Hall insulators. Their unit cells A and B are, respectively, given in the insets of panels (a) and (b), both composed of an angle-cut triangle meta-atom embedded in air. Their lattice periods are set to be $a$ with $l = 0.61 a$ and $d = 0.1 a$ . The triangular-like meta-atom is nonmagnetic material with relative dielectric constant $ɛ_{r} = 16$ . (c–f) Distributions of lattice field strength in the first Brillouin zone. Panels (c) and (d) are those of bands 1 for cells A and B, while panels (e) and (f) are those of bands 2 for cells A and B. (g) One-dimensional photonic band diagram of the ribbon-shaped super cell in panel (h). The red and black curves are for the VESs and bulk states, respectively. (h) Magnetic field distribution of the VESs. The attenuated field tells that the VES is localized around the domain wall.
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Figure 2
(a, b) Field distributions of the two degenerate cavity modes with odd and even parities (along the horizontal direction), respectively. (c–e) Transmission spectra of the VESs coupled with the double-degenerate cavity calculated by the finite element method within the COMSOL code. The optical structures are adopted on the right side, whose distance between the cavity and the WG increases from two layers to four layers. The insets are the enlarged views of the Fano profiles and the solid lines are guides for eyes. (f–k) Field distributions whose frequencies of the incident light correspond to the magenta dots marked in panel (c). The positions of the domain walls and cavities are denoted by the green solid lines and dashed ellipses, respectively.
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Figure 3
(a, b) Transmission spectra of the valley-dependent edge states coupled with side cavity with different bending angles for the domain walls. (c) Transmission spectrum of the coupling system under disorder. The corresponding structures and field distributions for the P4/P5 are shown on the right side. The green lines indicate the domain walls and the green dashed ellipses indicate the position of the cavity. The red dashed oval denotes the disordered position.
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Figure 4
(a–d) Transmission spectra of the trivial waveguide coupled with one side cavity. The wave guides are composed of the line defects, on which all the angle-cut triangle meta-atoms are replaced by the cylinder rods with the radius $r = 0.2 a$ . The photonic crystals on the two sides of the interface are both taken as the PVHI described in Fig. 1. In panel (a) the trivial waveguide is straight, in panels (b) and (c) the trivial waveguide is bended, and in panel (d) disorders are introduced along the trivial waveguide and denoted as blue dots.
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Figure 5
(a–c) Theoretical fitting of the transmissivity $T$ (red solid curves) with respect to the numerical data (gray circular dots). (d–f) Transmissivities $T_{O}$ (blue curves) and $T_{E}$ (green curves) corresponding to the transmissivity $T$ in (a–c), respectively. The numerical data in panels (a–c) and (d–f) are identical with those in Figs. 2–2, respectively.
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