Contrasting Spectral Signatures and Sensitivities of CPA-Lasing in a $\cal PT$-Symmetric Periodic Structure

TL;DR

This paper investigates the spectral signatures of CPA-lasing in $ ext{PT}$-symmetric structures, revealing contrasting sensitivities and spectral widths in eigenvalue and singular value spectra, with implications for sensing and switching.

Contribution

It demonstrates that the singular value spectrum of the scattering matrix shows much wider spectral signatures than the eigenvalue spectrum in $ ext{PT}$-symmetric CPA-lasers, highlighting different sensitivities.

Findings

Singular value spectrum can be orders of magnitude wider than eigenvalue spectrum.

Near perfect absorption and strong amplification occur in the $ ext{PT}$-symmetric phase.

Eigenvalue spectrum is more sensitive to disorder, suitable for sensing; singular value spectrum is more robust, suitable for switching.

Abstract

The CPA-laser is a coexisting state of coherent perfect absorption and lasing that was proposed in parity-time ($\cal PT$) symmetric photonic systems. In this work we show that the spectral signature of a CPA-laser displayed by the singular value spectrum of the scattering matrix ($S$) can be orders of magnitude wider than that displayed by the eigenvalue spectrum of $S$. Since the former reflects how strongly light can be absorbed or amplified and the latter announces the spontaneous symmetry breaking of $S$, these contrasting spectral signatures indicate that near perfect absorption and extremely strong amplification can be achieved even in the $\cal PT$-symmetric phase of $S$, which is known for and defined by its flux-conserving eigenstates. We also show that these contrasting spectral signatures are accompanied by strikingly different sensitivities to disorder and imperfection, suggesting that the eigenvalue spectrum is potentially suitable for sensing and the singular value spectrum for robust switching.