Cavity-induced backscattering in a two-dimensional photonic topological system

Open Access

Cavity-induced backscattering in a two-dimensional photonic topological system

Yuhao Kang and Azriel Z. Genack

Phys. Rev. Research 2, 013221 – Published 27 February 2020

Abstract

Topological protection of transmission has been demonstrated in the edge channel in topological insulators in the face of bent paths and on-site randomness in the structure. Microwave measurements and couple-mode theory of a topological medium possessing time-reversal symmetry with a cavity adjacent to the edge channel show that spin is not conserved in scattering from the defect. The transmission time is negative near resonance with the defect.

Received 23 October 2019
Revised 15 January 2020
Accepted 4 February 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.013221

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Metamaterials Quantum spin Hall effect Topological effects in photonic systems

Cavity resonators Coupled mode theory

Polymers & Soft Matter

Authors & Affiliations

Yuhao Kang and Azriel Z. Genack^*

Department of Physics, Queens College and Graduate Center of the City University of New York, Flushing, New York 11367, USA

^*genack@qc.edu

Article Text

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References

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Issue

Vol. 2, Iss. 1 — February - April 2020

Subject Areas

Topological Insulators

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Images

Figure 1
Schematic diagram of the structure. (a) Structure without the upper plate. The red arrow indicates the direction of flow of the incident wave. The blue and orange points are the positions of two detectors located within the cavity and at the output of the sample, respectively. The sample parameters are given in Ref. [7]. They are as follows: The overall dimensions of the sample are $30 \times 40 c m^{2}$ . Lattice constant: 1.0890 cm; spacing between plates: 1.0890 cm; height of collar: 0.3580 cm; diameter of collar: 0.6215 cm; diameter of rod: 0.3175 cm; height of triangular prism: 0.5040 cm; gap between triangular prisms: 0.0810 cm; side length of triangular prism: 0.5020 cm. Within the red border, rods are pushed up so that the attached collars are in contact with the upper plate. The real structure contains 15 layers of triangular prisms and 25 layers of rods. (b) Band structure of edge mode. The bulk band gap extends from 20.3 to 21.3 GHz. (c) Schematic of coupled-resonator model. $K_{1} / K_{2}$ is the coupling coefficient between the cavity mode and the left or right side of the edge channel. $K_{int}$ denotes the internal loss of the cavity.
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Figure 2
Measurement of cavity modes. (a)–(d) Upper panel: The red curve is the measured spectrum; the blue dotted curve is the fit to the data based on the harmonic inversion method. The band gap is indicated by the shaded region. Lower panel: The contribution of each of the quasinormal modes. The distances between the cavity and the boundary line are one, three, five, and seven layers in (a)–(d), respectively. (e) Numerical calculation of the cavity eigenmodes within the bulk of the sample isolated from the edge. From left to right, the modes correspond to the six numeric eigenmodes in Table 1.
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Figure 3
Transmission spectra. Spectra of (a) transmission coefficient and (b) phase at the edge on the output surface. The blue and red curves indicate the measured and analytical results, respectively. (c), (d) Representations in the complex plane of individual modal contributions at the frequencies indicated by arrows $c$ and $d$ in (a). The orange vector indicates the edge channel, while the blue, red, and green vectors correspond to the modes represented by the blue, red, and green dashed lines at around 21 GHz in the lower panel of Fig. 2.
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Figure 4
Reflection induced by cavity. (a) Simulations of the intensity distribution of the wave at 21.02 GHz. The region of cavity is between 0.2 and 0.25 m. (b) The phase change along the boundary. (c) The phase difference between $E_{z}$ and $B_{z}$ along the boundary.
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Figure 5
Transmission through a nonreciprocal system. (a) General complex representation of transmission. (b) Complex representation for three cases with $η = 1, 0.5$ , and 0.3 with phase variation as shown in (c). The arrow represents the direction of increasing $δ$ . (d) Tight-binding simulation following the Haldane model $H = \sum_{i} c_{i}^{†} λ_{i} c_{i} + \sum_{〈 i j 〉} c_{i}^{†} t c_{j} + \sum_{〈 〈 i j 〉 〉} c_{i}^{†} i λ_{SO} ν_{i j} c_{j}$ , for on-site energy $λ_{i} = 4$ , nearest-neighbor hopping $t = - 1$ , and spin-obit coupling strength $λ_{SO} = 0.1$ . Inside the cavity, $λ_{SO} = - 0.1$ . $ν_{i j} = \pm 1$ . The blue line is the phase change of the transmitted field. Two discrete modes are excited. The inset shows the intensity distribution at the two energies indicated by the red dots.
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