SUSY designed broken PT-symmetric optical filters

Abstract

We apply the supersymmetric Darboux transformation to the optical Helmoltz wave equation to generate analytically complex-valued PT-symmetric potentials (physically a graded refractive index dielectric). PT-symmetry is then spontaneously broken controlling the amplitude of the imaginary part of the refractive index distribution. Consequently a resonance is detectable which is related to a singularity of the S matrix, responsible for extraordinary high transmission and reflection peaks in the scattering spectra. We demonstrate how controlling the resonance we can achieve different amplification rates up to four order of magnitude at the exact singular point. Total transmission and very high reflection can be also obtained. All the visible portion of the spectrum can be spanned by enlarging the spatial width of the potential. All these potentials can be unified in a single device with the capability to dynamically control the imaginary part of the refractive index, thus defining a tunable dynamical optical filter behaving as a perfect amplifier, a transparent barrier or a high efficiency mirror.

Broken-SUSY dynamic reflectionless optical amplifier

“…In general, given a fixed incoming wavenumber k sc = ω sc /c (which serves as a spatial scaling factor for the DT i.e. X = k sc x as in [28]), the main action of a DT is to relate the spectral properties of a pair of Schrödinger Hamiltonians through a superpotential σ defined as the logarithmic derivative of a solution of the Schrödinger equation ψ(X, ) for a given potential V (X) for some value of the transformation energy (in units of k 2 sc ) i.e. σ(X, ) = 1 ψ(X, ) dψ(X, ) dX .…”

Using optical potentials with gain-loss to generate structural colors

“…Here the Darboux transformation energy is fixed to ε = 0.00005i (in units of the square of a reference wavenumber used for scaling) and n b = 1 i.e. the optical filter is immersed in air (see [15] for details about the analytical DT). By using the optical potential definition we can calculate the spatial refractive index distribution by n…”