Hybrid Patterns and Solitonic Frequency Combs in Non-Hermitian Kerr Cavities.

We unveil a new scenario for the formation of dissipative localized structures in nonlinear systems. Commonly, the formation of such structures arises from the connection of a homogeneous steady state with either another homogeneous solution or a pattern. Both scenarios, typically found in cavities with normal and anomalous dispersion, respectively, exhibit unique fingerprints and particular features that characterize their behavior. However, we show that the introduction of a periodic non-Hermitian modulation in Kerr cavities hybridizes the two established soliton formation mechanisms, embodying the particular fingerprints of both. In the resulting novel scenario, the stationary states acquire a dual behavior, playing the role that was unambiguously attributed to either homogeneous states or patterns. These fundamental findings have profound practical implications for frequency comb generation, introducing unprecedented reversible mechanisms for real-time manipulation.

Non-Hermitian Mode Cleaning in Periodically Modulated Multimode Fibers.

We show that the simultaneous modulation of the propagation constant and of the gain/loss coefficient along the graded index multimode fibers results in unidirectional coupling among the modes, which leads to either the enhancement or the reduction of the excitation of higher order transverse modes, depending on the modulation parameters. In the latter case, effective mode cleaning is predicted, ideally resulting in single-mode spatially coherent output. The effect is semi-analytically predicted on a simplified Gaussian beam approximation and numerically proven by solving the wave propagation equation introducing the non-Hermitian modulated potential.

Inverse-design of non-Hermitian potentials for on-demand asymmetric reflectivity.

We propose a genetic algorithm-assisted inverse design approach to achieve 'on- demand' light transport in periodic and non-periodic planar structures containing dielectric and gain-loss layers. The optimization algorithm efficiently produces non-Hermitian potentials from any arbitrarily given real (or imaginary) permittivity distribution for the desired frequency selective and broadband asymmetric reflectivity. Indeed, we show that the asymmetric response is directly related to the area occupied by the obtained permittivity distribution in the complex plane. In particular, unidirectional light reflection can be designed in such a way that it switches from left to right (or vice versa) depending on the operating frequency. Moreover, such controllable unidirectional reflectivity is realized using a stack of dielectric layers while keeping the refractive index and gain-loss within realistic values. We believe this proposal will benefit the integrated photonics with frequency selective one-way communication.

Regularization of vertical-cavity surface-emitting laser emission by periodic non-Hermitian potentials.

We propose a novel physical mechanism based on periodic non-Hermitian potentials to efficiently control the complex spatial dynamics of broad-area lasers, particularly in vertical-cavity surface-emitting lasers (VCSELs), achieving a stable emission of maximum brightness. A radially dephased periodic refractive index and gain-loss modulations accumulate the generated light from the entire active layer and concentrate it around the structure axis to emit narrow, bright beams. The effect is due to asymmetric inward radial coupling between transverse wave vectors for particular phase differences of the refractive index and gain-loss modulations. Light is confined into a central beam with large intensity, opening the path to design compact, bright, and efficient broad-area light sources. We perform a comprehensive analysis to explore the maximum central intensity enhancement and concentration regimes. This Letter reveals that the optimum schemes are those holding unidirectional inward coupling, but not fulfilling a perfect local PT-symmetry.

Stabilization of broad-area semiconductor laser sources by simultaneous index and pump modulations.

We show that the emission of broad-area semiconductor amplifiers and lasers can be efficiently stabilized by introducing two-dimensional periodic modulations simultaneously on both the refractive index and the pump (gain-loss) profiles in the transverse and longitudinal directions. The interplay between such index and gain-loss modulations efficiently suppresses the pattern-forming instabilities, leading to highly stable and bright narrow output beams from such sources. We also determine the stabilization performance of the device as a function of the pump current and linewidth enhancement factor.

Numerical and experimental demonstration of a wavelength demultiplexer design by point-defect cavity coupled to a tapered photonic crystal waveguide.

We propose and experimentally demonstrate a demultiplexer with point-defect resonators and a reflection feedback mechanism in a photonic crystal waveguide (PCW). A tapered PCW has been chosen as the necessary reflector, which enhances the drop efficiency. Due to the variation of the single-mode waveguide width of the tapered PCW, spatial alteration of the effective refractive index can be achieved. This phenomenon is used to reflect back the forward propagating wave which is then coupled again to the drop channels via the resonators. High transmission efficiency to the dropout channels is numerically predicted by calculations, either in two- and three-dimensional models, and analytically described by a coupled-mode theory. Moreover, an experimental realization in the microwave regime provides confirmation that the targeted wavelengths can be properly transmitted at the drop channels with low crosstalk and relatively high efficiencies.

Unlocked evanescent waves in periodic structures.

We predict the existence of evanescent modes with unlocked phases in two-dimensional (2D) dielectric periodic structures. Contrary to what is known for one-dimensional structures, where evanescent fields lock to the host modulation, we show that in 2D systems a new class of evanescent modes exists with an unlocked real part of the wave vector. Hence, beams constructed from such unlocked evanescent waves can exhibit spatial effects. A significant focalization of a beam propagating within the band gap of a flat photonic crystal slab is also shown. The predicted phenomenon is expected to be generic for spatially modulated materials.

Formation of X-pulses in periodically gain/loss modulated materials.

We propose a versatile and efficient technique for the formation of X-pulses in materials with a periodical gain/loss modulation on the wavelength scale. We show that in such materials the strong wave-vector anisotropy of amplification/attenuation of the Bloch modes enables the shaping of ultra-short light pulses around the edges of the first Brillouin zone. X-pulses generation is numerically demonstrated and the optimum conditions are derived; specific characteristics of X-pulses can be tailored by appropriate selection of the geometry and modulation depth.

Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures.

We study the second-harmonic (SH) parametric processes in unpoled crystals of Strontium Barium Niobate (SBN) with disordered structures of ferroelectric domains. Such crystals allow for the simultaneous phase matching of several second-order nonlinear processes. We analyze the polarization properties of these parametric processes using two types of generation schemes: quasi-collinear SH generation and transverse SH generation. From our experimental data we determine the ratio of d(32) and d(33) components of the second order susceptibility tensor and also the statistical properties of the random structure of the SBN crystal.

Nondiffractive propagation of light in photonic crystals.

We investigate nondiffractive propagation of electromagnetic radiation, including visible light, through materials with a periodic space modulation of the refraction index, i.e., through photonic crystals. We calculate analytically and numerically the regimes where the dominating order of diffraction vanishes, i.e., the light beams of arbitrary width propagate without diffractive broadening and, equivalently, arbitrary light patterns can propagate without diffractive "smearing." We investigate the subdiffractive light propagation, where the propagation is governed by the higher (fourth) diffraction order, when the dominating order of diffraction vanishes.

Subdiffractive band-edge solitons in Bose-Einstein condensates in periodic potentials.

A type of matter wave diffraction management is presented that leads to subdiffractive solitonlike structures. The proposed management technique uses two counter-moving, identical periodic potentials (e.g., optical lattices). For suitable lattice parameters, a different type of atomic bandgap structure appears in which the effective atomic mass becomes infinite at the lowest edge of an energy band. This way, normal matter-wave diffraction (proportional to the square of the atomic momentum) is replaced by fourth-order diffraction, and hence the evolution of the system becomes subdiffractive.

Efficient parametric amplification of narrow beams in photonic crystals.

We theoretically predict and numerically demonstrate that narrow beams (of the width of few wavelengths) can be efficiently parametrically amplified in nonlinear photonic crystal (with chi((2)) nonlinearity) tuned to sub-diffractive (self-collimating) regimes. We derive relations and give analytic estimations for the efficiency of amplification.