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Frontiers of Optoelectronics

ISSN 2095-2759

ISSN 2095-2767(Online)

CN 10-1029/TN

Postal Subscription Code 80-976

Front. Optoelectron.    2021, Vol. 14 Issue (4) : 438-444    https://doi.org/10.1007/s12200-020-0969-3
RESEARCH ARTICLE
Singular PT-symmetry broken point with infinite transmittance and reflectance----a classical analytical demonstration
Yingxin JIANG()
Department of Physics, Jiangsu University, Zhenjiang 212013, China
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Abstract

To demonstrate the existence of singular parity-time symmetry (PT-symmetry) broken point in optics system, we designed a one-dimensional PT symmetric structure including N unit-cell with loss and gain materials in half. We performed an analytical deduction to obtain the transmittance and reflectance of the structure basing on Maxwell’s equations. We found that with the exact structure unit-cell number and the imaginary part of refraction index, the transmittance and reflectance are both close to infinite. Such strict condition is called the singular point in this study. At the singular point position, both the transmission and reflection are direction-independent. Away from the singular point, the transmittance and reflectance become finite. In light of classical wave optics, the single unit and total structure both become the resonance units. The infinite transmittance and reflectance result from the resonance matching of single unit and total structure. In light of quantum theory, the singular point corresponds to the single eigenvalue of electromagnetic scattering matrix. The infinite transmittance and reflectance mean a huge energy transformation from pumping source to light waves. Numerical calculation and software simulation both demonstrate the result.

Keywords parity-time symmetric (PT-symmetric) structure      singular point      transmittance      reflectance     
Corresponding Author(s): Yingxin JIANG   
Online First Date: 11 March 2020    Issue Date: 06 December 2021
 Cite this article:   
Yingxin JIANG. Singular PT-symmetry broken point with infinite transmittance and reflectance----a classical analytical demonstration[J]. Front. Optoelectron., 2021, 14(4): 438-444.
 URL:  
https://academic.hep.com.cn/foe/EN/10.1007/s12200-020-0969-3
https://academic.hep.com.cn/foe/EN/Y2021/V14/I4/438
Fig.1  Schematic diagram of PT symmetric layered structure
Fig.2  (a) Transmittance and (b) reflectance for left incidence as a function of N and ρ
Fig.3  Two eigenvalues of the S matrix with ρ = 0.0158 as a function of N
Fig.4  (a) Ez field distribution inside the PT-symmetric structure at the singular PT-symmetry broken point; (b) localized amplification of (a)
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