Experimental Characterization of the Deterministic Interface States in Two-Dimensional Photonic Crystals

Yuting Yang, Xueqin Huang, and Zhi Hong Hang

Phys. Rev. Applied 5, 034009 – Published 17 March 2016

Abstract

The study of interface and surface states in photonic crystals provides new approaches to control the flow of light. In this work, a type of interface state in two-dimensional photonic crystals is experimentally realized and characterized. The existence of this type of interface state is solely dependent on the reflection properties of the bulk photonic crystals without any surface or interface decorations. Our experimental results are in agreement with numerical simulations, and the propagation properties of these measured interface states indicate that this type of interface state will be a good candidate for future optical waveguiding applications.

Received 17 September 2015

DOI:https://doi.org/10.1103/PhysRevApplied.5.034009

Physics Subject Headings (PhySH)

Photonic crystals

Microwave techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuting Yang¹, Xueqin Huang², and Zhi Hong Hang^1,*

¹College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
²Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

^*zhhang@suda.edu.cn

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Vol. 5, Iss. 3 — March 2016

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Images

Figure 1
(a) Schematic diagram of an interface along the $y$ direction formed by two semi-infinite 2D PCs with square lattice. $a$ is the lattice constant for both PCs. (b) The TM bulk band structures of the PCs constructed by alumina cylinders with radius $R_{1} = 0.170 a$ and relative permittivity $ϵ_{1} = 8.5$ (red squares) and glass cylinders with $R_{2} = 0.352 a$ and $ϵ_{2} = 4.7$ (green squares). (c) The projected band structures for the alumina (red) and glass (green) PCs along the $k_{y}$ direction. The blue triangles represent the simulated band dispersion of the interface states inside the common gap between the two inverted band diagrams. (d) The $E_{z}$ eigenmode distribution of the interface state at frequency $0.636 c / a$ with $k_{y} = 0.05 (2 π / a)$ [magenta star in (c)]. (e) A small perturbation is introduced by adding a thin layer of air gap (with thickness $L = 0.1 a$ ) between the two PCs. The interface state still remains with a tiny change of its dispersion.
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Figure 2
The simulated $E_{z}$ field distributions with normal incident Gaussian beam from the bottom at different frequencies. (a)–(d) show the excited interface states with different wave vectors at the frequencies $0.623 c / a$ , $0.631 c / a$ , $0.634 c / a$ , and $0.635 c / a$ , respectively. At different frequencies, the excited interface states have different “oscillation lengths” along the interface direction, indicating different wave vectors. The left side of the interface is alumina rods with radius $R_{1} = 0.170 a$ and relative permittivity $ϵ_{1} = 8.5$ . Glass rods are on the right side with $R_{2} = 0.352 a$ , $ϵ_{2} = 4.7$ .
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Figure 3
(a), (b) The calculated reflection phase at normal incidence from vacuum for the alumina PC and glass PC inside their common gap. (c), (d) The schematic graphs show the physics of destructive and constructive interferences between incident light and reflected light for different reflection phases. Photographs of the microwave experiment to visualize the reflection-induced interference of the alumina PC and glass PC are shown in (e) and (f), respectively. (g), (h) The microwave experiments confirm our numerical simulations that destructive interference occurs for the alumina PC ( $ϵ_{1} = 8.5$ , $R_{1} = 3.75 mm$ ) while constructive interference occurs for the glass PC ( $ϵ_{2} = 3.5$ , $R_{2} = 7.75 mm$ ) at 9.09 GHz. The lattice constant $a$ for both PCs is 22 mm.
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Figure 4
(a) Photo of experimental setup to observe the deterministic interface states. (b)–(d) Measured field distributions of interface states at different microwave frequencies 8.824, 8.954, and 9.012 GHz, respectively. Strong field confinement can be observed at the interface ( $x = 0 mm$ ).
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Figure 5
The simulated projected bands of the alumina and glass PCs along the $k_{y}$ direction are labeled in orange. The dispersions of the simulated and experimentally measured interface state are indicated by the blue triangles and magenta stars, respectively. The experimental results are achieved from FFT of the spatial field distributions similar to those shown in Fig. 4. Because of the finite-sized experimental sample capable to measure, only discrete values of wave vectors can be obtained.
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Figure 6
Three-dimensional electric field magnitude distribution for the interface state at 9.012 GHz. This mode propagates along the $y$ axis and decays exponentially away from the interface. Negligible loss can be found along the propagation direction for the sample we measure. The electric field magnitude is normalized to the incident microwave intensity.
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