Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons as described by the Kerr nonlinear Maxwell system. Using a model of the nonlinear polarization, which does not generate higher harmonics, we obtain a closed curl-curl problem for the fundamental harmonic of the gap soliton. For gap solitons with frequencies inside spectral gaps and in an asymptotic vicinity of a gap edge we use a slowly varying envelope approximation based on the linear Bloch waves at the edge and slowly varying envelopes. We carry out a systematic derivation of the coupled mode equations (CMEs) which govern the envelopes. This derivation needs to be carried out in Bloch variables. The CMEs are a system of coupled nonlinear stationary Schrödinger equations with an additional cross derivative term. Examples of gap soliton approximations are numerically computed for a photonic crystal with a hexagonal periodicity cell and an annulus material structure in the cell.
We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range where the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.
We report the existence of transversely stable soliton trains in optics. These stable soliton trains are found in two-dimensional square photonic lattices when they bifurcate from X-symmetry points with saddle-shaped diffraction inside the first Bloch band and their amplitudes are above a certain threshold. We also show that soliton trains with low amplitudes or bifurcated from edges of the first Bloch band (Gamma and M points) still suffer transverse instability. These results are obtained in the continuous lattice model and further corroborated by the discrete model.
We introduce a scheme of a photonic coupler built of two parallel topological-insulator slab waveguides with the intrinsic Kerr nonlinearity, separated by a gap. Josephson oscillations (JO) of a single edge soliton created in one slab, and of a pair of solitons created in two slabs, are considered. The single soliton jumping between the slabs is subject to quick radiative decay. On the other hand, the JO of the copropagating soliton pair may be essentially more robust, as one soliton can absorb dispersive waves emitted by the other. The most robust JO regime is featured by the pair of solitons…
We predict that a photonic crystal fiber whose strands are filled with a defocusing nonlinear medium can support stable bright and also vortex solitons if the strength of the defocusing nonlinearity grows toward the periphery of the fiber. The domains of soliton existence depend on the transverse growth rate of the filling nonlinearity and nonlinearity of the core. Remarkably, solitons exist even when the core material is linear.
Gas-filled hollow-core photonic crystal fibers offer unprecedented opportunities to observe novel nonlinear phenomena. The various properties of gases that can be used to fill these fibers give additional degrees of freedom for investigating nonlinear pulse propagation in a wide range of different media. In this review, we will consider some of the the new nonlinear interactions that have been discovered in recent years, in particular those which are based on soliton dynamics.
We show that solitons undergo a strong blue shift in fibers with a dispersion landscape that varies along the direction of propagation. The experiments are based on a small-core photonic crystal fiber, tapered to have a core diameter that varies continuously along its length, resulting in a zero-dispersion wavelength that moves from 731 nm to 640 nm over the transition. The central wavelength of a soliton translates over 400 nm towards shorter wavelength. This accompanied by strong emission of radiation into the UV and IR spectral region. The experimental results are confirmed by numerical sim…
Nonlinearities in lattices with topological band structures can induce topological interfaces in the bulk of structures and give rise to bulk solitons in the topological bandgaps. Here we study a photonic Chern insulator with saturable nonlinearity and show the existence of topological bulk solitons. The fundamental bulk solitons exhibit as semi-vortex solitons, where only one pseudospin component has a nonzero vorticity. The bulk solitons have equal angular momentum at different valleys. This phenomenon is a direct outcome of the topology of the linear host lattice and the angular momentum ca…
We theoretically study the properties of one-dimensional nonlinear saturable photonic lattices exhibiting multiple mobility windows for stationary solutions. The effective energy barrier decreases to a minimum in those power regions where a new intermediate stationary solution appears. As an application, we investigate the dynamics of high-power gaussian-like beams finding several regions where the light transport is enhanced.
We report on the existence of a novel kind of squeezing in photonic crystal fibers which is conceptually intermediate between the four-wave mixing induced squeezing, in which all the participant waves are monochromatic waves, and the self-phase modulation induced squeezing for a single pulse in a coherent state. This hybrid squeezing occurs when an arbitrary short soliton emits quasi-monochromatic resonant radiation near a zero group velocity dispersion point of the fiber. Photons around the resonant frequency become strongly correlated due to the presence of the classical soliton, and a reduc…
We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability i…
We study two-component solitons and their symmetry-breaking bifurcations (SBBs) in linearly coupled photonic systems with a spatially inhomogeneous strength of the coupling. One system models an inverted virtual photonic crystal, built by periodically doping the host medium with atoms implementing the electromagnetically induced transparency (EIT). In this system, two soliton-forming probe beams with different carrier frequencies are mutually coupled by the EIT-induced effective linear interconversion. The system is described by coupled nonlinear Schrödinger (NLS) equations for the probes, wit…
An optical trapping scheme is proposed by which ultrashort low-amplitude radiations, co-propagating with a continuous train of temporal pulses in a hollow-core photonic crystal fiber filled with Raman-inactive noble gases, can be trapped and reshaped into optical soliton trains by means of cross-phase modulation interactions. The scheme complements and extends a recently proposed idea that a single-pulse soliton could trap an ultrashort small-amplitude radiation in a symmetric hollow-core photonic crystal fiber filled with a noble gas, thus preventing its dispersion [M. F. Saleh and F. Biancal…
We predict that photonic moiré patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media allow the formation of parametric solitons under conditions that are strongly impacted by the geometry of the pattern. The question addressed here is how the geometry affects the joint trapping of multiple parametrically-coupled waves into a single soliton state. We show that above the localization-delocalization transition the threshold power for soliton excitation is drastically reduced relative to uniform media. Also, the geometry of the moiré pattern shifts the conditio…
Exceptional points are a ubiquitous concept widely present in driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. It is characterized by the degeneracy of the Hamiltonian's eigenvalues and coalescence of corresponding eigenvectors. Recent developments demonstrated that exceptional points can play an important role in photonics. However, to date, exceptional points have been extensively examined in the systems supporting only a few optical modes, thereby leaving the observation of collective (multimode) effects outside of the scope of study. In the present paper, we ana…
We show theoretically that the photoionization process in a hollow-core photonic crystal fiber filled with a Raman-inactive noble gas leads to a constant acceleration of solitons in the time domain with a continuous shift to higher frequencies, limited only by ionization loss. This phenomenon is opposite to the well-known Raman self-frequency red-shift of solitons in solid-core glass fibers. We also predict the existence of unconventional long-range non-local soliton interactions leading to spectral and temporal soliton clustering. Furthermore, if the core is filled with a Raman-active molecul…
We analyze localization of light in honeycomb photonic lattices restricted in one dimension which can be regarded as an optical analog of (``armchair'' and ``zigzag'') graphene nanoribbons. We find the conditions for the existence of spatially localized states and discuss the effect of lattice topology on the properties of discrete solitons excited inside the lattice and at its edges. In particular, we discover a novel type of soliton bistability, the so-called geometry-induced bistability, in the lattices of a finite extent.
We demonstrate that spatial solitons undergo two consecutive spontaneous symmetry breakings (SSBs), with the increase of the total power, in nonlinear photonic crystals (PhCs) built as arrays of alternating linear and nonlinear stripes, in the case when maxima of the effective refractive index coincide with minima of the self-focusing coefficient, and vice versa, i.e.,the corresponding linear and nonlinear periodic potentials are in competition. This setting may be induced, as a virtual PhC, by means of the EIT (electromagnetically-induced-transparency) technique, in a uniform optical medium. …
The nonlinear propagation of light pulses in liquid-filled photonic crystal fibers is considered. Due to the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagating inside such structures can be approximated, for pulse durations much shorter than the molecular relaxation time, by temporally highly-nonlocal solitons, analytical solutions of a linear Schroedinger equation. The physical relevance of these novel solitary structures, which may have a broad range of applications, is discussed and supported by detailed numerical simulations.
We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations…
Quantization and Biphoton Statistics of k-Gap Solitons in Nonlinear Photonic Time Crystals
State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology and Center for Transformative Science, ShanghaiTech University（上海科技大学量子功能材料国家重点实验室、物理科学与技术学院和变革科学中心）
Many physical systems display quantized energy states. In optics, interacting resonant cavities show a transmission spectrum with split eigenfrequencies, similar to the split energy levels that result from interacting states in bonded multi-atomic, i.e. molecular, systems. Here, we study the nonlinear dynamics of photonic diatomic molecules in linearly coupled microresonators and demonstrate that the system supports the formation of self-enforcing solitary waves when a laser is tuned across a split energy level. The output corresponds to a frequency comb (microcomb) whose characteristics in te…
We study the properties of two-color nonlinear localized modes which may exist at the interfaces separating two different periodic photonic lattices in quadratic media, focussing on the impact of phase mismatch of the photonic lattices on the properties, stability, and threshold power requirements for the generation of interface localized modes. We employ both an effective discrete model and continuum model with periodic potential and find good qualitative agreement between both models. Dynamics excitation of interface modes shows that, a two-color interface twisted mode splits into two beams …
One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for…
Complex systems are a proving ground for fundamental interactions between components and their collective emergent phenomena. Through intricate design, integrated photonics offers intriguing nonlinear interactions that create new patterns of light. In particular, the canonical Kerr-nonlinear resonator becomes unstable with a sufficiently intense traveling-wave excitation, yielding instead a Turing pattern composed of a few interfering waves. These resonators also support the localized soliton pulse as a separate nonlinear stationary state. Kerr solitons are remarkably versatile for application…
Topological photonics has emerged recently as a novel approach for realizing robust optical circuitry, and the study of nonlinear effects in topological photonics is expected to open the door for tunability of photonic structures with topological properties. Here, we study the topological edge states and topological gap solitons which reside in the same bandgaps described by the nonlinear Dirac model, in both one- and two-dimensions. We reveal strong nonlinear interaction between those dissimilar topological modes manifested in the excitation of the topological edge states by scattered gap sol…
A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are considered. Time-reversal symmetry is broken by varying/rotating the waveguides, longitudinally, along the direction of propagation. Different sublattice rotation and structure are allowed. Linear Floquet bands are constructed for intricate sublattice rotation patterns such as counter rotation, phase offset rotation, as well as different lattice sizes and frequencies. An asymptotic analysis of the edge modes, valid in…
Exploration of the impact of synthetic material landscapes featuring tunable geometrical properties on physical processes is a research direction that is currently of great interest because of the outstanding phenomena that are continually being uncovered. Twistronics and the properties of wave excitations in moiré lattices are salient examples. Moiré patterns bridge the gap between aperiodic structures and perfect crystals, thus opening the door to the exploration of effects accompanying the transition from commensurate to incommensurate phases. Moiré patterns have revealed profound effects i…
Time domain Stokes mechanism of pair correlated k gap solitons in nonlinear photonic time crystal slabs
State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology and Center for Transformative Science, ShanghaiTech University（上海科技大学物理科学与技术学院量子功能材料国家重点实验室与变革科学中心）
The generation of high-intensity optical fields from harmonic-wave photons, interacting via a cross-phase modulation with dark solitons both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time-entangled dark-soliton patterns, forming a periodic waveguide along the path of the harmonic-wave probe. It is shown that an increase of the strength of cross-phase modulation respective to the self-phase modulation, favors soliton-mode proliferation in the bound-state spectrum of the trapped harmonic-wave probe. The induced soliton modes, which display the stru…
