Optical Degenerate Points Regulation in One‑Dimensional Quaternary Periodic PT Symmetric Structure

Yifei Song; Yetao Shu; peng Tang; ting Wan; Zhaoming Luo

doi:10.3788/CJL221327

Abstract

Objective

Optical parity-time (PT) symmetric systems have attracted significant attention since their inception because of the unique properties possessed by them. Degeneracy in the state space of a dynamical system refers to points where two or more physical eigenstates coalesce into one. Recently, there has been a growing interest in the degeneracy of PT symmetric optical systems. Coherent perfect absorption laser point (CPA-LP) and exceptional point (EP) are two types of optical degenerate points, where special degeneracies of PT symmetric optical systems exist. Some unique optical phenomena, such as bidirectional acoustic negative refraction, giant Goos-H?nchen shift, and the spin Hall effect of light have been discovered at these degenerate points. Manipulating two optical degenerate points has significant application potential and relevance in photonics. Photonic crystals are artificial microstructures of media with different refractive indices that are arranged periodically and are often used to modulate photons. In Refs. [23] and [24], optical degenerate points in composite structures comprising photonic crystal and PT symmetry were manipulated, and unusual scattering features were found. Therefore, the combination of traditional photonic crystals and PT symmetry can provide a new method to manipulate optical degenerate points and explore unique optical phenomena. In this study, we propose a one-dimensional quaternary periodic PT-symmetric structure and investigate the effects of structural parameters on two optical degenerate points.

Methods

The proposed one-dimensional quaternary periodic PT symmetric structure can be denoted as ${(A B C D)}^{N}$ , where $N$ is the period number (Fig. 1). Gain or loss media A, B, C, and $D$ can be prepared by doping quantum dots into common media. In optics, PT symmetry requires a complex refractive index distributed in the form of $n (z) = n^{*} (- z)$ , where $*$ denotes a complex conjugate. Therefore, the refractive indices of media $A$ , $B$ , $C$ , and $D$ are set to n_A=1.8+qi, n_B=1.6-qi, n_C=1.6+qi, and n_D=1.8-qi, respectively, where $q$ is the gain-loss coefficient. This coefficient can be modulated by the doping concentration of the quantum dots. The optical thicknesses of A, B, C, and D are given as $d_{j} = λ / [4 R e (n_{j})]$ with $j = A, B, C, D$ , where $R e (n_{j})$ are the real parts of their complex refractive indices, and $λ$ is the central wavelength of the incident light. When a beam was incident on the one-dimensional quaternary periodic PT symmetric structure, the transfer matrix method was used to solve specific reflection and transmission coefficients. On this basis, the eigenvalues of the scattering matrix were derived further to explore the optical degeneracy of the structure.

Results and Discussions

We investigated the effects of the gain-loss coefficient, incident angle, and period number on the CPA-LP and EP in the proposed one-dimensional quaternary periodic PT-symmetric structure by using numerical simulation. First, we fixed the period number to be N=3, and flexibly adjusted two optical degenerate points under different incident angles by changing the gain-loss coefficient (Fig. 3). Then, we focused on the difference of the reflection characteristics between the EP caused by PT symmetry and the Bragg resonance point related with period, and found that the unidirectional reflectionlessness and the bidirectional transparency appear at the EP and the Bragg resonance point, respectively (Fig.4). To explore the influence of period number on the two optical degenerate points in one-dimensional quaternary periodic PT symmetric structure, we also study the CPA-LP and the EP in the structure with period number N=1,6. The results show that the number of CPA-LP increases in the parameter space as the period number increases, while the number of EP remains unchanged (Figs. 3?5). Finally, we achieved the manipulation of optical phenomena, such as the photonic spin Hall Effect based on the controllable properties of the two optical degenerate points (Fig. 6).

Conclusions

In summary, a one-dimensional quaternary periodic PT-symmetric structure is proposed, and the effects of the gain-loss coefficient, incident angle, and period number on two optical degenerate points in the structure are investigated. At a certain period, two optical degenerate points can be flexibly regulated under different incident angles by adjusting the gain-loss coefficient. The difference in reflection characteristics between the EP, which is attributed to the PT symmetry, and Bragg resonance associated to the periodic structure is analyzed. When the beam is incident along the left and right sides, the reflectance to only one side is zero at the EP, resulting in unidirectional reflectionlessness characteristics, whereas both the reflectance were zero at the Bragg resonance point, resulting in bidirectional reflectionlessness characteristics. The effect of the period number on the two optical degenerate points is investigated further, and the results show that the quantity of CPA-LP increases with the period number, while EP is independent of the period. Finally, the manipulation of optical phenomena such as the photonic spin Hall Effect is done by using the controllable properties of optical degenerate points. These studies can provide a method to manipulate photons for the development of new optoelectronic devices.