Phase diagram of parity-time symmetric photonic heterostructures

Jeng YI Lee^1*

¹Department of Opto-Electronic Engineering, National Dong Hwa University, Hualien, Taiwan

* Presenter:Jeng YI Lee, email:johnnyygod2002@hotmail.com

We study a general property of one dimensional PT photonics with any complex configuration. Parity operators denote spatial \Pi rotation, while time-reversal operators denote not only complex conjugate but also a mapping of incoming ports (outgoing ports) into outgoing ports (incoming ports). The realization of such PT-symmetric photonics would need a balance of gain and loss placed in a spatially symmetric distribution. In the framework of the PT scattering matrix, the corresponding eigenvalues and eigenvectors could be classified into three cases: symmetric phases, exceptional points, and broken phases. The former would lead to the unimodular of the eigenvalues, subject to a general conservation relation, while the latter would form reciprocal pairs in magnitudes. The exception points result in the degeneracy of eigenvalues and eigenvectors, which have applications in ultrasensitive sensors. Compared to unitary lossless systems, the PT system exhibits interesting scattering behaviors, such as coherent perfect absorber-laser, anisotropic transmission resonance, negative refraction, and double refraction.
The mentioned results, however, are due to inferring a specific scattering matrix, without considering global PT construction. In this work, combined with the PT symmetry and reciprocity principle, we develop a general phase diagram for the PT scattering matrix in one dimension, irrespective of any specific structures and material parameters. Based on this space, we can integrate all anomalous scattering states, including the mentioned results. Interestingly, we find that different from the conclusion from PRL 106, 213901 (2011), the PT system not only can support isotropic transmission resonances from both side illumination, but also can achieve the unidirectional invisibility in symmetric phase regime. In addition, we also observe that the PT system can have coherent perfect absorber-lasers occurred at exceptional points. We believe our approach not only can provide a scientific visualization method to reflect the hidden information in complicated systems, but also can be extended to a variety of wave systems subjected to physical symmetries.

Keywords: parity-time symmetry, Transfer matrix , conservation relation