Time-reversal invariant scaling of light propagation in one-dimensional non-Hermitian systems

Abstract

Light propagation through a normal medium is determined not only by the real part of the refractive index but also by its imaginary part, which represents optical gain and loss. Therefore, two media with different gain and loss landscapes can have very different transmission and reflection spectra, even when their real parts of the refractive index are identical. Here we show that while this observation is true for an arbitrary one-dimensional medium with refractive index $n(x)$ and its time-reversed partner with refractive index $n^{\ast }(x)$, there exists a universal scaling that gives identical transmittance and reflectance in these corresponding systems. Interestingly, these scaled transmittance and reflectance reduce to their standard, unscaled forms in a time-reversal invariant system, i.e., one without gain or loss.

arXiv comment6 pages, 4 figures

References in corpus (15)

• Random-Matrix Theory of Quantum Transport
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• PT-symmetric laser-absorber
• Scattering of Massless Particles in Arbitrary Dimension
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Scattering in $\mathcal{P}\mathcal{T}$ and $\mathcal{R}\mathcal{T}$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension
• Extreme Sensitivity of Output Directionality to Boundary Perturbation in Wavelength-Scale Microcavities
• Multimode Coupling by Boundary Wave Scattering
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Constructing the scattering matrix for optical microcavities as a nonlocal boundary value problem

Cited by in corpus (4)

• Linear response theory of open systems with exceptional points
• Giant overreflection of magnetohydrodynamic waves from inhomogeneous plasmas with nonuniform shear flows
• Insight of the Green's function as a defect state in a boundary value problem
• Effects of background periodic flow on MHD fast wave propagation to a coronal loop