Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution

Abstract

We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians defined in this way are non-Hermitian, but satisfy symmetry properties that have previously been identified in the literature as "pseudo Hermiticity" and "anti-PT symmetry". We show how simple one-channel and two-channel models exhibit transitions between real, imaginary, and complex eigenvalue pairs.

7 pages, 2 figures

References in corpus (5)

• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Exceptional Points in a Non-Hermitian Topological Pump
• Parity-Time Anti-Symmetric Parametric Amplifier
• Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
• Slow light with flat or offset band edges in multi-mode fiber with two gratings

Cited by in corpus (11)

• Non-Hermitian Photonic Lattices: tutorial
• Nonreciprocal slow or fast light in anti-$\mathcal{P}\mathcal{T}$-symmetric optomechanics
• Anti-$\mathcal{P}\mathcal{T}$-symmetric Kerr gyroscope
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Classification of symmetry properties of waveguide modes in presence of gain/losses, anisotropy/bianisotropy, or continuous/discrete rotational symmetry
• Unitary Scattering Protected by Pseudo-Hermiticity
• Generalized coupled mode formalism in reciprocal waveguides with gain/loss, anisotropy or bianisotropy
• Quantum-optical implementation of non-Hermitian potentials for asymmetric scattering
• Parallel numerical method for nonlocal-in-time Schrödinger equation
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Extraction of power transmission parameters from PT-symmetric waveguides