Abstract
In this work, we report the construction of different classes of complex-valued refractive index landscapes, with real spectra, in the framework of the factorization method. The particular case of guiding hyperbolic-type profiles is considered in the PT- and non-PT-symmetric configurations. In both schemes, the imaginary part of the refractive index satisfies the zero-total-area condition indicating that the total transverse optical power is preserved, allowing stable propagating modes to be obtained. The spectra and the guided modal field amplitudes are obtained and their orthogonality relations are established.
Highlights
The task of processing and manipulating light states has been one of the most promising achievements in optical sciences
The quadratic and hyperbolic secant index distributions have deserved a lot of attention due to their focusing and collimating properties and because the corresponding dynamical equations are reduced to exactly solvable differential problems [2,3,4,5,6,7,8,9,10,11,12]
We present a method to construct different classes of exactly solvable guiding refractive index distributions in the gradient index (GRIN) non-Hermitian regime
Summary
The task of processing and manipulating light states has been one of the most promising achievements in optical sciences. Of special interest are non-Hermitian materials, as they allow one to include non-conservative effects in theoretical models These structures are, in general, characterized by complex, GRIN profiles, in which the real part represents the guiding refractive index distribution of the material, while the imaginary one models gain/loss events in the propagation processes [2]. We consider the factorization method for the generation of new classes of exactly solvable, non-homogeneous, balanced gain-and-loss optical structures, by taking full advantage of the equivalence between the Schrödinger and Helmholtz equations in the paraxial approximation.
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