Source: http://aoot.osa.org/oe/abstract.cfm?uri=oe-27-6-7857
Timestamp: 2019-04-26 00:01:01+00:00

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Goos-Hänchen (GH) effect is a fundamental phenomenon in optics. Here we demonstrate theoretically that the surface modes at Parity-time (PT) symmetric interfaces, can induce a giant GH shift at a specific incident angle. It is found that the amplitude of the GH shift can be tuned by adjusting the thickness of the bilayer, and as the thickness grows, its maximum value can go to infinity in theory. The physical mechanism behind this interesting feature is that the surface modes at PT interfaces are quasi-bound states in continuum (BICs), which lead to rapid variation in the phase of the scattered waves. Our work enriches the previous studies about GH effect in PT bilayer structures and provides a way in turn to explore the BICs in non-Hermitian photonic systems.
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Fig. 1 (a) The schematics of a PT-symmetric bilayer structure. A linearly polarized light is incident on the bilayer structure from loss side indicated by the black arrows, or from the gain side marked by the red arrows. Both loss and gain layers with an identical thickness of d meet PT symmetry about z = 0. (b) The parameter space for surface states at PT-symmetric interfaces with infinite thickness. The red dashed line indicates the position where β sw = k 0 . The tiny circle indicate the parameters of ε l =1.5+0.5i and ε g =1.5−0.5i. (c) The dispersion relationship. For a given working frequency ω 0 , a surface mode with β sw < k 0 is in the continuum.
Fig. 2 The bound states at finite PT interfaces. (a) The determinant value for different β and d when γ=0.02. (b) The determinant value for different β and γ when d=0.6λ. (c) The surface states based on Eq. (1) for infinite d. The inset shows the simulated field pattern for a surface state when γ=0.02. Here ε r =0.001 in (a)-(c). The black dashed curves in (a) and (b) denote the solutions of surface states.
Fig. 3 GH-shifts of transmitted wave in PT symmetric bilayers with different loss/gain for TM polarization (a) and TE polarization (b).
Fig. 4 (a) The happening angles θ GH of the giant GH shift for different γ in Fig. 3(a) and the pseudo-Brewster angles θ pB (red hollow circles) in a loss medium ( ε r =0.001+iγ) with a thickness of 1.2λ. (b) The eigenvalues of S-matrix for γ=0.02 and d=0.6λ. (c) The reflection, transmission and transmission phase for γ=0.02 and d=0.6λ. (d) The enlarged drawing for γ=0.02 in Fig. 3(a).
Fig. 5 (a) The giant GH shift vs the thickness d for fixed material parameters. From right to left, the peaks of the giant GH shifts are located at 32.15 ∘ , 29.27 ∘ , 27.83 ∘ and 27.11 ∘ , with corresponding values of L≈3.5λ, 10λ, 25λ and 68λ. (b) The reflectance | r L | 2 vs thickness d and the incident angle. Here ε l =0.001+0.02i and ε g =0.001−0.02i. (c) The reflectance | r L | 2 vs the incident angle for a fixed thickness of d=2.0λ. (d) Transmission phase vs the incident angle for different thickness of d=0.4λ, 0.6λ, 1.0λ, 1.2λand 2.0λ, which are shown by black, red, green, blue, cyan and pink curves, respectively.
Fig. 6 GH effect and BICs in the case of ε l =1.5+0.5i and ε g =1.5−0.5i. (a) The numerically simulated field pattern of the surface modes at the PT-bilayer interface. In simulations, the thickness of each layer is d=3.0λ and the source (see the five star) is mimicked by using a tiny circle with a current of 1A. (b)-(d) are the analytically calculated GH shifts, the reflection | r l | 2 and the transmission phase for different thicknesses. In (b), as d increases, the center point for maximum value goes to θ in = 66.00 ∘ . For d=2.4λ and 3.0λ, the displayed data are real data divided by 5 and 50, respectively.
(3) t L = t G =t= 1 M 22 , r L =− M 21 M 22 , r G = M 12 M 22 .
(4) L r, t =− λ 2π d ϕ r, t d θ in .

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