Axisymmetric photonic structures with PT-symmetry

Copyright 2016 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.PT-symmetric structures in photonic crystals, combining refractive index and gain-loss modulations is becoming a research field with increasing interest due to the light directionality induced by these particular potentials. Here, we consider PT-symmetric potentials with axial symmetry to direct light to the crystal central point obtaining a localization effect. The axial and PT-symmetric potential intrinsically generates an exceptional central point in the photonic crystal by the merge of both symmetries. This particular point in the crystal lattice causes field amplitude gradients with exponential slopes around the crystal center. The field localization strongly depends on the phase of the central point and on the complex amplitude of the PT-potential. The presented work analyzes in a first stage 1D linear PT-axisymmetric crystals and the role of the central point phase that determines the defect character, i.e. refractive index defect, gain-loss defect or a combination of both. The interplay of the directional light effect induced by the PT-symmetry and the light localization around the central point through the axial symmetry enhances localization and allows higher field concentration for certain phases. The linearity of the studied crystals introduces an exponential growth of the field that mainly depends on the complex amplitude of the potential. The work is completed by the analysis of 2D PT-axisymmetric potentials showing different spatial slopes and growth rates caused by symmetry reasons.Peer ReviewedPostprint (published version

Self-collimation in 2D Complex P- and PT-symmetric systems

We predict the self-collimation phenomena (or equivalently, dynamical localization) in 2-dimensional P-symmetric and PT-symmetric complex potentials, with periodic modulations of both gain/loss and refractive index. Non diffractive propagation is analytically predicted and further confirmed by numerical integration of a paraxial model. The parameter space is explored to identify the self-collimation regime in crystals with different complex symmetries.Postprint (published version

PT-axisymmetric VCSELs with linear central defect

Semiconductor Lasers and particularly Vertical-Cavity Surface-Emitting Lasers (VCSELs) are important laser sources used for many purposes. However, the applications of these lasers are mainly restricted by their strongly multimode operation given by the lack of an intrinsic transverse mode selection mechanism [1]. The introduction of an axial PT-symmetric potential within this kind of lasers is expected to induce a field enhancement and localization at the symmetry axis, central part of the laser. The required complex potential, combining a modulated refractive index and gain-loss distributions, may be achieved by different configurations with actual fabrication techniques. The Complex Ginzburg-Landau equation is used as a simple VCSELs model, and the numerical results show important localization effects; due to the asymmetric mode coupling energy converges to the center leading to a strong light confinement. The main consequence is a narrow and bright laser emission from the central part of the device. As the system nonlinearities introduce saturation limiting the maximum intensity of the output beam, the inclusion of a central linear defect in the structure allows a larger field concentration.Postprint (published version

Self-collimation in PT -symmetric crystals

We predict the self-collimation phenomena (or equivalently, dynamical localization) in two-dimensional PT-symmetric complex potentials, where the complex modulation is considered in the transverse, longitudinal, or simultaneously in both directions. Nondiffractive propagation is analytically predicted and further confirmed by numerical integration of a paraxial model. The parameter space is explored to identify the self-collimation regime in crystals with different PT symmetries. In addition, we also analyze how the PT-symmetric potentials determine the energy distribution between spatial modes of the self-collimated beams.Peer ReviewedPostprint (published version

Self-collimated beams in 2D complex periodic lattices from P- to PT-symmetry

We analyze self-collimation in two-dimensional periodic complex lattices. We consider P-symmetric and PT-symmetric complex lattices with different geometries, where the periodic modulations of both refractive index and gain-loss are either in-phase, or dephased a quarter of wavelength of the modulation. The non-diffractive propagation of light beams is analytically predicted using coupled mode approach and further confirmed by numerical integration of a paraxial model.Postprint (published version

Non-Hermitian broad aperture semiconductor lasers based on PT-symmetry

In this paper we propose a novel configuration to regularize the complex spatiotemporal dynamics of broad area lasers into bright light beam. It has recently been shown that arbitrary non-Hermitian optical potentials based on local Parity-Time (PT-) symmetry may tailor and control the flow of light, due to the asymmetric mode coupling. We now provide a comprehensive analysis on how this can be applied to stabilize the emission from broad aperture semiconductor lasers. The mechanism relies on a non-Hermitian configuration of the laser potential achieved by simultaneous spatial modulation of the refractive index and gain-loss profiles. This allows concentrating the light into a bright and narrow output beam. We provide a numerical analysis on Vertical Cavity Surface Emitting lasers and Broad Area Semiconductor Lasers. The results indicate a significant intensity enhancement and concentration of the emitted stabilized beam. The proposed mechanism may be technologically achievable, and it is expected to be applicable to regularize the radiation of other broad aperture and microlasers, which typically emit quite random and irregular light patterns. Besides, the reported concentration effect is universal, and could be extended to random and quasi-periodic background potentials.Peer ReviewedPostprint (author's final draft

Inverse-design of non-Hermitian potentials for light management

In this paper, we propose a general inverse-design strategy based on genetic algorithm optimization to achieve ‘on demand’ manipulation of light in one-dimensional (1D) and two-dimensional (2D) non-Hermitian systems. The optimization process faithfully creates non-Hermitian potentials from any given arbitrary real (or imaginary) permittivity distribution for the desired frequency selective and broadband asymmetric response in 1D multilayer structures. As a demonstration in 2D, we design periodic and aperiodic complex permittivity spatial distributions to create "sink-type" concentrators of light around a desired area. The proposed inverse-design approach to generate non-Hermitian potentials represents an alternative to the Hilbert Transform (HT) generalizing the Kramers Kronig relations in space, additionally being selective in spectrum.Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i InfraestructuraPostprint (published version

Restricted Hilbert transform for feasible light management

A feasible restricted Hilbert Transform (HT) is presented to solve the challenging practical realization of non-Hermitian systems, restricting the complex susceptibility within practical limits. Beyond closed-conservative systems, the physics of non-Hermitian systems has become the playground to uncover unusual phenomena. Whilst Kramers Kronig relations break the temporal symmetry leading to causality, we proposed an analogous generalized Hilbert Transform (HT) to engineer complex media holding a nonistrotropic response, thus breaking the spatial symmetry. Applications of such HT range from tailoring the filed flows in arbitrary dimensions with particular application on VCSELS and edge-emitting lasers to cloaking arbitrary objects.Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i InfraestructuraPostprint (published version

Regularization of broad-area lasers by non-Hermitian potentials

It was recently shown that arbitrary non-Hermitian optical potentials based on local Parity-Time (PT-) symmetry may control the flow of light, due to the asymmetric mode coupling. We propose periodic non-Hermitian potentials to efficiently regularize the complex spatial dynamics of broad-area semiconductor (BAS) lasers and Vertical-Cavity Surface-Emitting Lasers (VCSELs). Light generated from the entire active layer is concentrated on the structure axis, confined in an intense central narrow beam opening the path to design compact, bright broad-area lasers.Postprint (published version

Stabilization of Broad Area Semiconductor Laser Sources

We numerically proof the stabilization of broad area semiconductor laser sources by introducing simultaneous in-phase two-dimensional modulations on the refractive index and on the pump (gain). We also examine the interplay between the index and gain modulations and the effect of the slow relaxation of carriers on the stability performance.Peer ReviewedPostprint (published version