Wiktor Walasik

Phase transition in multimode nonlinear parity-time-symmetric waveguide couplers

Parity-time-symmetric (-symmetric) optical waveguide couplers offer new possibilities for fast, ultracompact, configurable, all-optical signal processing. Here, we study nonlinear properties of finite-size multimode -symmetric couplers and predict the nonlinear oscillatory dynamics that can be controlled by three parameters: input light intensity, gain and loss amplitude, and input beam profile. Moreover, we show that this dynamics is driven by a transition triggered by nonlinearity in these structures, and we demonstrate that with the increase of the number of dimers in the system, the transition threshold decreases and converges to the value corresponding to an infinite array. Finally, we present a variety of periodic intensity patterns that can be formed in these couplers depending on the initial excitation.

Dynamics of Large Femtosecond Filament Arrays: Possibilities, Limitations, and Trade-Offs

Stable propagation of large, multifilament arrays over long distances in air paves new ways for microwave-radiation manipulation. Although, the dynamics of a single or a few filaments was discussed in some of the previous studies, we show that the stability of large plasma filament arrays is significantly more complicated and is constrained by several trade-offs. Here, we analyze the stability properties of rectangular arrays as a function of four parameters: relative phase of the generating beams, number of filaments, separation between them, and initial power. We find that arrays with alternating phase of filaments are more stable than similar arrays with all beams in phase. Additionally, we show that increasing the size of an array increases its stability, and that a proper choice of the beam separation and the initial power has to be made in order to obtain a dense and regular array of filaments.

Reconfigurable topological photonic crystal

Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically protected from scattering due to structural defects and disorders. Recently, it was shown that photonic crystals can serve as a platform for realizing a scatter-free propagation of light waves. In conventional photonic crystals, imperfections, structural disorders, and surface roughness lead to significant losses. The breakthrough in overcoming these problems is likely to come from the synergy of the topological photonic crystals and silicon-based photonics technology that enables high integration density, lossless propagation, and immunity to fabrication imperfections. For many applications, reconfigurability and capability to control the propagation of these non-trivial photonic edge states is essential. One way to facilitate such dynamic control is to use liquid crystals, which allow to modify the refractive index with external electric field. Here, we demonstrate dynamic control of topological edge states by modifying the refractive index of a liquid crystal background medium. Background index is changed depending on the orientation of a liquid crystal, while preserving the topological order of the system. This results in a change of the spectral position of the photonic bandgap and the topologically protected edge states. The proposed concept might be implemented using conventional semiconductor technology, and can be used for robust energy transport in integrated photonic devices, all-optical circuity, and optical communication systems.

Modulation instability of structured-light beams in negative-index metamaterials

One of the most fundamental properties of isotropic negative-index metamaterials, namely opposite directionality of the Poynting vector and the wavevector, enable many novel linear and nonlinear regimes of light-matter interactions. Here, we predict distinct characteristics of azimuthal modulation instability of optical vortices with different topological charges in negative-index metamaterials with Kerr-type and saturable nonlinearity. We derive an analytical expression for the spatial modulation-instability gain for the Kerr-nonlinearity case and show that a specific condition relating the diffraction and the nonlinear lengths must be fulfilled for the azimuthal modulation instability to occur. Finally, we investigate the rotation of the necklace beams due to the transfer of orbital angular momentum of the generating vortex on the movement of solitary necklace beams. We show that the direction of rotation is opposite in positive- and negative-index materials.

Nanoscale orbital angular momentum beam instabilities in engineered nonlinear colloidal media

Colloidal media with well-defined optical properties have been widely used as model systems in many fundamental and applied studies of light-matter interactions in complex media. Recent progress in the field of engineered nanoscale optical materials with fundamentally new physical properties opens new opportunities for tailoring the properties of colloids. In this work, we experimentally demonstrate the evolution of the optical vortex beams of different topological charges propagating in engineered nano-colloidal suspension of negative polarizability with saturable nonlinearities. Due to the high power of the incident beam, the modulation instability leads to an exponential growth of weak perturbations and thus splits the original vortex beam into a necklace beam consisting of several bright spots. At a fixed power, the number of observed bright spots is intrinsically determined by the topological charge of the incident beam and agrees well with the predictions of our linear stability analysis and numerical simulations. Besides contributing to the fundamental science of light-matter interactions in engineered soft-matter media, this work opens new opportunities for dynamic optical manipulation and transmission of light through scattering media as well as formation of complex optical patterns and light filamentation in naturally existing colloids such as fog and clouds.

Experimental demonstration of silicon-based topological photonic crystal slab at near infrared frequencies and its dynamic tunability (Conference Presentation)

Topological insulators are materials that behave as insulators in their interior but support boundary conducting states due the non-trivial topological order. These edge states are robust to defects and imperfections, allowing lossless energy transport along the surface. Topological insulators were first discovered in field of electronics, but recently photonic analogues of these systems were realized. Most of experimentally demonstrated photonic topological insulators to date are bulky, incompatible with current semiconductor fabrication process or operate in microwave frequency range. In this work, we show silicon photonic-crystal-based Valley-Hall topological insulator operating at telecommunication wavelengths. Light propagation along the trapezoidally-shaped path with four 120 degrees turns is demonstrated and compared with propagation along the straight line. Nearly the same transmittance values for both cases confirm robust light transport in such Valley-Hall topological photonic crystal. In the second part of this talk, we discuss the possibility of dynamic tuning of the proposed topological insulator by modulation of the refractive index of silicon. The modulation is facilitated by shining focused ultraviolet pulsed light onto silicon photonic crystal slab. Ultraviolet light illumination causes formation of electron-hole pairs, excitation of free-carriers and results into decrease of refractive index with estimated modulation on the order of 0.1. Due to the index change, spectral position of the bandgap and the edge states shift allowing their dynamic control. Proposed concept can find applications in communication field for fast all-optical switching and control over light propagation.

Supersymmetry-based mode selection and optimization in coupled systems (Conference Presentation)

The concept of supersymmetry originated in the fields of particle physics and enabled treatment for bosons and fermions on equal footing. Supersymmetry has rapidly expanded to other fields such as quantum mechanics, where it provided a way of generating pairs and families of potentials with similar properties, e.g. different reflection-less potentials; and optics where it can be used to design (de)multiplexing arrays of waveguides. In the first part of the talk, we show that for parity-time symmetric structures supersymmetric transformation is isospectral only locally (at a specific amplitude of gain and loss). Moreover we show that depending on whether a passive mode (with real propagation constant) or an active mode (with gain or loss) is removed, the parity-time symmetry of the system is preserved or broken as a function of gain/loss amplitude. In the second part of the talk we investigate the influence of supersymmetric transformation on the scattering spectrum of reflection-less structures and systems with epsilon-near-zero materials. We show that the transmission/reflection properties of a structure containing an epsilon-near-zero material can be mimicked using materials with refractive index values above unity, which are more easily accessible and introduce smaller losses to the system. The relation between these two systems is governed by supersymmetry. We conduct a quantitative performance analysis of realistic structure in which the continuous variation of the refractive index is replaced by the step-wise profile corresponding to a realistic layered structure. Our studies pave the way towards achieving remarkable properties of the epsilon-near-zero materials with the use of much more accessible materials compatible with the state-of-the-art integrated optics fabrication.

All-dielectric, nonlinear, reconfigurable metasurface-enabled optical beam converter (Conference Presentation)

Optical beams with a phase term proportional to the azimuthal angle possess a singularity at the beam center and carry an orbital angular momentum (OAM). The OAM beams find important applications including the trapping and rotation of microscopic objects, atom-light interactions and optical communications. The OAM beams can be generated by spiral phase plates or spatial light modulators which are bulky. Recently, planar optical components including q-plates, arrays of nano-antennas and all-dielectric metasurfaces, have attracted significant attention. However, they lack reconfigurability, which means that once the components are fabricated, their functionality cannot be changed. In this work, we experimentally demonstrate a nonlinear metasurface-based beam converter which is designed to transform a Hermite-Gaussian beam to a vortex beam with an OAM in a transmission mode. The proposed converter is built of an array of nano-cubes made of chalcogenide(As2S3) glass. Chalcogenides offer several advantages for designing all-dielectric, nonlinear metasurfaces, including high linear refractive index at near-infrared wavelengths, low losses, and relatively high third-order nonlinear coefficient. In particular, reconfigurability is enabled by the intensity-dependent refractive index or Kerr nonlinearity. Input Hermite-Gaussian beam at low intensity transmitting through the metasurface acquired an OAM, while at high intensity, remained its original intensity and phase profile. The parameters of the reconfigurable metasurface were optimized and its functionality was verified using numerical simulation and in laboratory experiments. Compared to conventional metasurfaces, their nonlinear counterparts are likely to enable a number of novel devices for all-optical switching and integrated circuits applications.

Necklace beams in engineered nonlinear media (Conference Presentation)

Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. Previous studies of Gaussian beams propagation in various colloidal suspensions predicted in a number of remarkable optical phenomena and applications, including initiation and regulation of chemical reactions, sorting different species of nanoparticles and imaging through highly scattering media. As compared to the conventionally used Gaussian beams, optical vortices that are characterized by the doughnut-shaped intensity profile and a helical phase front offer even more degrees of freedom for, in particular, optical trapping or imaging applications. In our earlier work, we predicted, using the linear stability analysis and numerical simulations, that the perturbations with an orbital angular momentum of a particular charge will be amplified and lead to the formation of a necklace beam with a particular number of peaks, or “beads.” Here, we performed detailed experimental studies of such necklace beam formation that show an excellent agreement with the analytical and numerical predictions. This work might bring about new possibilities for dynamic optical manipulation and transmission of light through scattering media as well as formation of complex optical patters in colloids.

Harnessing Optical Loss for Unique Microlaser Functionality

By harnessing optical losses designed at an exceptional point, we demonstrate a microring laser with new functionality of producing OAM vortex lasing and the ability to precisely define the topological charge of the OAM mode.