Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials

Abstract

We derive certain identities satisfied by the left/right-reflection and transmission amplitudes, $R^{l/r}(k)$ and $T(k)$, of general $\mathcal{P}\mathcal{T}$-symmetric scattering potentials. We use these identities to give a general proof of the relations, $|T(-k)|=|T(k)|$ and $|R^r(-k)|=|R^l(k)|$, conjectured in [Z. Ahmed, J. Phys. A 45 (2012) 032004], establish the generalized unitarity relation: $R^{l/r}(k)R^{l/r}(-k)+|T(k){|}^2=1$, and show that it is a common property of both real and complex $\mathcal{P}\mathcal{T}$-symmetric potentials. The same holds for $T(-k)=T(k{)}^{\ast }$ and $|R^r(-k)|=|R^l(k)|$.

6 pages

References in corpus (3)

• Coherent Perfect Absorbers: Time-reversed Lasers
• Invisibility and PT-symmetry
• Spectral singularities in PT-symmetric periodic finite-gap systems

Cited by in corpus (8)

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• Non-Hermitian interferometer: Unidirectional amplification without distortion
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• Unitary Scattering Protected by Pseudo-Hermiticity
• A Class of Exactly Solvable Scattering Potentials in Two Dimensions, Entangled State Pair Generation, and a Grazing Angle Resonance Effect
• Broadband and Wide-Angle Invisibility with PT-Symmetric 2D-Weyl Semimetal
• Polar magneto-optic Kerr and Faraday effects in finite periodic \texorpdfstring{$\mathcal{P}\mathcal{T}$}{PT}-symmetric systems