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.
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 non-isotropic response, thus breaking the spatial symmetry. Applications of such HT range from tailoring the field flows in arbitrary dimensions with particular application on VCSELS and edge-emitting lasers to cloaking arbitrary objects.
We propose a new approach of optical field management based on a local Hilbert transform, where the non-Hermitian potentials generating arbitrary vector fields of directionality, p→(r→), with desired shapes and topologies are designed. We derive a local Hilbert transform to build systematically such potentials, by modifying background potentials (being either regular or random, extended or localized). In particular, we explore particular directionality fields, for instance in the form of a focus to create sinks for probe fields, to generate vortices in the probe fields, and others. Physically, the proposed directionality fields provide a flexible new mechanism for dynamically shaping and precise control over probe fields leading to novel effects in wave dynamics.
Non-Hermitian potentials, as known since a decade, can favor unidirectionality of the flows in one and two-dimensional systems. Inspired by such counterintuitive property of non-Hermitian potential, we propose a novel concept of PT-vector fields to manipulate the field flows in two- (or higher) dimensional systems. The idea is based on designing complex potentials favoring arbitrary vector fields of directionality 𝑝⃗(𝑟⃗) with desired shapes and topologies. To achieve this, we derive a new mathematical tool referred as local Hilbert transform. We study interesting cases of such vector fields in the form of sink, vortex, and circular channel, constructed from different background patterns using local Hilbert transform. This new concept provides a precise control over the dynamics of the probe fields, which may have potential applications in technological systems.
Broad Area Semiconductor edge-emitting lasers typically display self-focusing nonlinearity due to the refractive index dependence on the population inversion. It induces the homogeneous solution instability, multi-transverse mode operation and filamentation. This behavior strongly deteriorates the beam quality and drastically reduces their applicability. We suppress this instability for semiconductors with small enough linewidth enhancement factors, αH, by the introduction of a single spatial modulation in the transverse and longitudinal directions. For large αH values, optimized multi-frequency spatial modulations are needed. The proposed scheme becomes especially interesting for high nonlinearities that correspond to the normal laser operation.
Optical Parity-Time (PT-) symmetric systems support unusual properties when the symmetric coupling between internal modes is broken. We propose a new class of quasiperiodic PT-axisymmetric systems which lead to a simultaneous extraordinary field enhancement and localization at the symmetry center. The effect is based on the asymmetric radial coupling of outward to inward propagating waves of the complex structure. We explore such optical potentials in 1D and 2D combining gain/loss and index modulations, which could have actual realizations in nanophotonic structures. As a direct application, we show how to render a broad aperture vertical-cavity surface-emitting lasers (VCSEL) into a bright and narrow beam source.
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.
We show that modulation instability (MI) can be suppressed in vertical external cavity surface emitting lasers (VECSELs) by introducing a periodic spatio-temporal modulation of the pump profile which in turn allows a simple flat-mirror configuration. The stability analysis of such pump modulated flat-mirror VECSELs is performed by a modified Floquet method and results are confirmed by full numerical integration of the model equations. It is found that the amplitude of the modulation as well as its spatial and temporal frequencies are crucial parameters for high spatial beam quality emission. We identify regions of complete and partial stabilization in parameter space for VECSELs with different external cavity lengths. The proposed method is shown to efficiently stabilize VECSELs with cavity lengths ranging from millimetres up to centimetres. However, the applicability of this method becomes limited for micro-meter-long cavities due to strong intrinsic relaxation oscillations.
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