The work unveils a hybrid scenario of dissipative localised structures combining two independent types of soliton solutions in extended nonlinear systems. We show the hybridisation of these two well established soliton formation mechanisms in Kerr cavities with periodic non-Hermitian modulations, resulting in a novel scenario that embodies the properties of both formation mechanisms. The hybridisation blends the properties of anomalous and normal dispersion regimes in a normal dispersive cavity and allows the stabilisation of new families of frequency combs associated to stable solitons, molecules and patterns. Moreover, it introduces unexpected mechanisms for real-time and reversible manipulation of frequency combs.
We propose an all-optical control of the mode dynamics in GRaded INdex (GRIN) multimode waveguides, by a Non-Hermitian potential (simultaneous modulation of the refractive index and of the gain/loss coefficient). Such potential induces a unidirectional mode-coupling. Depending on the modulation parameters it yields to the enhancement/ reduction of the excitation of higher order transverse modes. In the latter case, this leads to an all-optical mode-cleaning. The proposal is supported by analytical predictions based on a coupled mode theory for 1D waveguides, which is numerically proven solving the wave propagation equation. The proposal is generalized to the more involved case of 2D waveguides for different geometries controlling the unidirectional mode-coupling and final beam shape.
Non-Hermitian Physics has emerged as a fertile ground for a smart control of waves. Here, we present direct and inverse-design strategies to achieve ‘on demand’ dynamical manipulation of light by non-Hermitian potentials. The direct approach is based on our recently proposed generalized Hilbert Transform relating the real and imaginary distributions of the complex permittivity to induce spatial symmetry breaking to control scattering, widening the concept Kramers Kronig relations in space. A recipe to design complex potentials to tailor the propagation of light following any vector field, or to generate invisible potentials where light propagates as in free space. The procedure may be applied on any given arbitrary background permittivity distribution being regular or random, extended or localized. Moreover, it is possible to keep the design parameters within realistic limits, even avoiding gain. Beyond this fundamental approach, we also we also present supervised and unsupervised learning techniques for knowledge acquisition in non-Hermitian systems which accelerate the inverse the “on demand” design process. The different proposals may have direct applications to control the wave dynamics in semiconductor lasers or other linear and nonlinear physical systems including cloaking sensors and arbitrary shaped objects.
We investigate the effect of dynamic non-Hermitian potentials on the control of turbulence in nonlinear systems. The proposed mechanism consists on the introduction of a complex modulation both in space and time. The non-Hermitian potential is intended to asymmetrically affect the excitation cascade responsible of turbulence. We show how the system effectively promotes or opposes to the excitation cascade through wavenumbers depending on the interplay between the real and the imaginary parts of the temporal modulation. The proposal is proved on the universal Complex Ginzburg Landau Equation and its fractional counterpart.
Vertical-cavity semiconductor lasers as well as single units or arrays of Edge Emitting Lasers suffer from dynamical spatiotemporal instabilities leading to temporally unstable and low spatial beam quality. We propose a feasible stabilization mechanism for microlasers based on periodic non-Hermitian potentials, i.e. simultaneous modulations of refractive index and gain-loss. The proposed spatiotemporal modulations can be introduced by a potential directly acting on the field or by carrier modulations. The stabilization effect is based either on the suppression of the modulation instability or on asymmetric couplings in the transverse direction to localize and stabilize the field.
We propose a new light management mechanism in graded index (GRIN) multimode fibers (MMFs) that allow to control the spectral mode distribution of the propagated beam. The effect is achieved through longitudinal non-Hermitian modulations of the complex refractive index, i.e. the refraction index (for instance, a modulation of the core radius) and a periodic gain/loss profile. The applied potential holding a longitudinal spatial period close to the intermodal beat frequency of the parabolic index profile, to strongly influence the transverse mode dynamics. The non-Hermitian potential introduces a unidirectional and controllable coupling between the transverse modes. In turn, the spatial shift between the real and imaginary components of the modulation controls the unidirectional coupling either to higher or lower order modes. The effect is simultaneously demonstrated by solving a (2+1) D Linear Schrodinger Equation (two transverse plus one longitudinal spatial coordinates) as well as it is predicted by a simplified model for an oscillating Gaussian beam ansatz, leading to a system of ordinary differential equations. We demonstrate, both analytically and numerically, a mode cleaning effect, i.e. the improvement of the spatial structure of light in its propagation along the modulated MMFs; in an ideal case resulting in single-mode spatially coherent output. On the contrary, when inducing the coupling towards higher order modes, pulsing is enhanced, which may eventually contribute to super-continuum generation. The proposed scheme could lead to actual applications as it could be experimentally realized within the current nanofabrication technologies.
KEYWORDS: Acoustics, Radio propagation, Scattering, Resonators, Physics, Electromagnetism, Solar concentrators, Metamaterials, Electromagnetic scattering, Control systems
Non-Hermitian physics is an emerging field that for the unconventional management and control of wave fields. PT-symmetric metamaterials or dipoles have already been proposed as a flexible platform to redirect electromagnetic fields. Acoustic PT-dipoles have also been recently studied for sound guidance, showing an asymmetric scattering response. Therefore, we experimentally propose pairs of identical Helmholtz resonators with different losses distributed in the plane to create such dipoles (as electromagnetic analogues) and either concentrate the field, redirect it or even silence predefined areas. The experimental results confirm that the two-dimensional sound pressure field can be successfully modified on the bases of non-Hermitian physics.
We show that a non-Hermitian modulation of the potential along the nonlinear multimode fibers controls dynamics of propagating radiation. Specifically we consider simultaneous modulation of the refraction index and gain/loss profile. We predict and observe that the non-Hermitian modulation introduces a unidirectional and controllable coupling towards the lower/higher order transverse modes, depending on the potential parameters. Such effect may enhance the beam self-cleaning phenomena, i.e. improve the spatial structure of light in propagation. On the contrary, coupling towards higher order modes may enhance pulsing, turbulence and, eventually help in super-continuum generation.
Asymmetries arising from time-symmetry breaking in non-Hermitian potentials are shown to be an effective mechanism to control turbulence in nonlinear systems. The scheme is based on the introduction of a spatiotemporal non-Hermitian potential to control the excitation cascade mechanism responsible for the turbulence. We show the proposal on the complex Ginzburg Landau equation, that covers the universal phenomenon of turbulence in a wide range of disciplines, in particular a fundamental model for laser-like systems. Energy effectively condensates by reducing the energy transfer between transverse modes to high harmonics. The study is performed in one and two-spatial dimensions plus time, both numerically and analytically. The analysis of the turbulent spectrum distributions and the level of condensation of energy into the lower order mode show a crucial dependency on the phase shift between the two quadratures of the complex modulation. The desired turbulence reduction is numerically found for phases close to the ones predicted from the theoretical analysis. Depending on the phase, we are able to either enhance or reduce the spatial instability by breaking the energy cascading symmetry through wave vectors. Therefore, we are able to tailor and control turbulence in the complex Ginzburg Laudau equation and expect these results to have applications in different fields; most straightforward in optics where a non-Hermitian potential may be achieved by manipulating the complex permittivity (representing gain and refractive index).
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.
We propose and explore a stabilization mechanism of a semiconductor laser array based on asymmetric coupling between neighboring lasers. The stabilization scheme takes advantage of the symmetry breaking of non-Hermitian potentials. We perform a comprehensive numerical analysis in terms of the design parameters, namely the distance between lasers and spatial shift between the individual laser stripe and corresponding electrode. In turn, a mirror symmetric architecture is intended to lead to a light redistribution within the array which is expected to facilitate direct coupling efficiency to optical fibers.
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 introduce a new method to affect the energy cascade through wavevectors accountable for the turbulence. By the introduction of a spatiotemporal non-Hermitian potential we have been able to tilt or promote the energy cascade to reduce or increase turbulence in the universal Complez Ginzburg Landau equation. This is possible thanks to the asymmetric properties of these type of potentials. We show that the most efficient management of the turbulence happens for a phase shift between the real and imaginary part of the modulation different from the one arising from a conventional PT-symmetric theory for transverse potentials. We have been able to physically and analiticaly understand this difference.
The new physics of open-dissipative, non-Hermitian systems have become a fruitful playground to uncover novel physical phenomena, even in exotic or counterintuitive ways, especially in optics and, more recently, also in acoustics. In this work, we propose a non-Hermitian metasystem in acoustics for the control of the sound field in two dimensions. The building blocks, or meta-atoms composing the arrangements, are pairs of identical Helmholtz resonators with different gain or loss functions. Such Helmholtz resonator dipoles may be designed to hold asymmetric scattering, as was theoretically analyzed and experimentally confirmed. Furthermore, aiming to create a complicated directivity, we explored different ensembles of Helmholtz resonator dipoles and numerically demonstrated a sound concentration with various configurations. The proposed non-Hermitian parity-time- symmetric dipoles made of a pair of Helmholtz resonators may be a potential artificial element for the creation of complex sound fields.
We propose a compact solution to spatially regularize and temporally stabilize edge emitting (broad area) semiconductor lasers. The scheme relays on the local asymmetries generated by a non-Hermitian potential with a central symmetry axis to manage the flow of light, which stabilizes the radiation while enhancing and localizing the generated laser beam. We introduce a harmonic modulation on the pump with a central symmetry axis, and a complex refractive index modulation that generates a local PT-symmetry within the laser. The local PT-symmetry creates an inward mode coupling that concentrates the light generated in the active layer on axis. We perform a comprehensive analysis of all the modulation parameters and find regimes of simultaneous temporal stability and light concentration. The present approach produces two in one: light localization into a narrow beam emission and the control over the spatiotemporal dynamics, improving the laser performance.
The paper demonstrates spatial filtering in reflection based on meta-mirrors, composed of periodic subwavelength gratings. The periodic modulation of the refraction index on the sub-micron scale exhibits optical beam shaping with transverse invariance. The paper starts with a theoretical model for the proposed metamirrors based on multiple scattering theory. The results from the proposed analytical model coincide with the that from FDTD simulations. The analytical studies in the paper show that the filtering performance is enhanced by structured cavities where Mie resonances occur. Observations of different Mie resonances for varying units of the meta-mirrors are also presented in this paper. The metamirror may serve as a versatile tool for narrowing beam with high efficiency and transverse invariance.
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.
With the development of various recent tools to control electromagnetic wave propagation, such as transformation optics, the long-sought dream of rendering objects invisible has become a matter of practical implementation. However, the required index profile derived with such techniques leads to material properties that are not readily available in nature and, hence, various experimental simplifications and performance scarifications are inevitable. Therefore, it has been a widespread belief that perfect cloaking cannot be achieved with conventional materials. Here, we follow a different direction and provide a unique method based on scattering cancellation rather than conventional coordinate transformations, and show that perfect invisibility can be indeed achieved for any specified angular range and operational bandwidth by employing merely all-dielectric materials. The presented method is based on our recently proposed generalized Hilbert-like transform [1] that is able to eliminate the undesired scattered waves for any type of object, regardless of its shape/size, by directly tailoring the object’s scattering potential. In this direction, we show that the impinging wave on an object can be perfectly restored owing to the effective cancellation of the scattered waves emanating from the object and the surrounding index profile. We demonstrate this effect by experimental analyses conducted at the gigahertz regime. The proposed method represents an important step towards the ultimate goal of cloaking arbitrarily large objects at various wavelength regimes and may have profound implications especially in noninvasive near-field probing applications, where conventional transformation optics based cloaks fail to provide the interaction of the wave with the object.
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.
We simulate and analyze how beam quality improves while being amplified in edge emitting broad area semiconductor amplifiers with a periodic structuring of the electrical contacts, in both longitudinal and lateral directions. A spatio-temporal traveling wave model is used for simulations of the dynamics and nonlinear interactions of the optical fields, induced polarizations and carrier density. In the case of small beam amplification, the optical field can be expanded into few Bloch modes, so that the system is described by a set of ODEs for the evolution of the mode amplitudes. The analysis of such model provides a deep understanding of the impact of the different parameters on amplification and on spatial (angular) filtering of the beam. It is shown that under realistic parameters the two-dimensional modulation of the current can lead not only to a significant reduction of the emission divergence, but also to an additional amplification of the emitted field.
We show that periodic distributions of gain or losses on the wavelength scale allow managing spatial diffraction of light beams, with no index contrast. It has been recently predicted that such artificial periodic structures, analogous to Photonic Crystals (PhCs), would also hold the novel spatial beam propagation effects reported for PhCs such as subdiffraction propagation, self-collimation, spatial filtering or beam focusing by a lens with flat interfaces. In particular, we consider an ideal periodic 2-dimensional (2D) arrangement of lossy cylinders embedded in air. We analytically show that this loss distribution affects diffraction. Indeed, a significant focusing behind a thin flat-flat crystal slab is observed, following the estimation of anomalous spatial dispersion for specific frequency ranges. Besides, close to the edges of the first Brillouin Zone, the light intensity map of a Gaussian beam exiting the lossy structure exhibits a high transmission windows instead of the transmission stop band expected for PhCs. This results from the strong anisotropic attenuation provided by the loss periodicity. Finally, we also consider a more realistic system with combined modulations of refractive index and losses: a 2D metallic photonic crystal (MPhC). We demonstrate that MPhCs also support selfcollimation and focusing, being such effects associated to zero and negative diffraction respectively. Finally, due to the anisotropic attenuation of light, the structure is also able to spatially filter noisy beams.
Broad area semiconductors lasers and amplifiers are of technological relevance because of their high conversion
efficiency and high output power, in a wide range of wavelengths. However, due to their specific waveguiding planar
geometry, which is unique to this kind of heterostructures, the beam is usually of low spatial and temporal quality.
Therefore, the beam quality restricts their potential use. We propose to improve the beam quality of semiconductors
lasers and amplifiers using a two-dimensional spatial modulation of both the refractive index and the optical gain/loss, on
the scale of the wavelength. The modulation of the refractive index and gain/loss function on a small scale modifies the
spatial dispersion and introduces anisotropic gain on a large scale. As a result, the modified dispersion gives rise to
interesting and technologically useful effects, such as spatial filtering or focalization behind the amplifier. We show that
such effects can be achieved considering a modulated injection current which imposes a periodic spatial modulation of
the active layer of the semiconductor.
We perform a theoretical study on the group velocity for finite thin artificial opal slabs made of a reduced number of
layers in the spectral range where the light wavelength is on the order of the lattice parameter. The vector KKR method
including extinction allows us to evaluate the finite-size effects on light propagation in the ΓL and ΓX directions of fcc
close-packed opal films made of dielectric spheres. The group is index determined from the phase delay introduced by
the structure to the forwardly transmitted electric field. We show that for certain frequencies, light propagation can either
be superluminal -positive or negative- or approach zero depending on the crystal size and absorption. Such
anomalous behavior can be attributed to the finite character of the structure and provides confirmation of recently
emerged experimental results.
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