Parametric amplification of soliton steering in optical lattices

Azimuthons induced by degenerate linear eigenmodes and their conversions under nonlinear modulation

A method for generating azimuthons in a nonlinear Kerr medium is presented. The findings indicate that azimuthons can be represented as a combination of two co-rotational azimuthally modulated degenerate linear eigenmodes, along with an additional shift in the propagation constant. Moreover, the conversions between azimuthons are showcased using longitudinal nonlinear modulation. The results reveal that, under the resonance condition, direct conversion between neighboring azimuthons is possible, leading to the emergence of Rabi oscillation. However, for non-neighboring azimuthons, direct conversion is less effective, requiring cascaded modulation for their conversion.

Propagation of Gaussian Schell-model beams in modulated graded-index media

The evolution of partially coherent beams in longitudinally modulated graded-index media is studied. The special cases of Gaussian Schell-model beams and parametric modulation, when the modulation period is half the fiber self-imaging period, are examined in detail. We show that the widths of the intensity and coherence of Gaussian Schell-model beams undergo amplification in parametrically modulated parabolic graded-index media. The process is an analog of quantum mechanical parametric amplification and generation of squeezed states. Our work may find application in spatial and temporal imaging of partially coherent beams in fiber-based imaging systems.

Soliton dynamics in a PT-symmetric optical lattice with a longitudinal potential barrier

We present dynamics of spatial solitons propagating through a PT symmetric optical lattice with a longitudinal potential barrier. We find that a spatial soliton evolves a transverse drift motion after transmitting through the lattice barrier. The gain/loss coefficient of the PT symmetric potential barrier plays an essential role on such soliton dynamics. The bending angle of solitons depends on the lattice parameters including the modulation frequency, incident position, potential depth and the barrier length. Besides, solitons tend to gain a certain amount of energy from the barrier, which can also be tuned by barrier parameters.

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrödinger equation

By using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrödinger equation (NLSE) with cubic and quintic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) coefficients. We obtain a class of wide localized exact solutions of NLSE in the presence of a number of non-Hermitian parity-time (PT)-symmetric external potentials, which are constituted by a mixing of external potentials and source or drain terms. The exact solutions found here can be applied to theoretical studies of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. We show that, even in the presence of gain or loss terms, stable solutions can be found and that the PT symmetry is an important feature to guarantee the conservation of the average energy of the system.

Switching management in couplers with biharmonic longitudinal modulation of refractive index

We address light propagation in couplers with longitudinal biharmonic modulation of refractive index in neighboring channels. While simplest single-frequency out-of-phase modulation allows suppression of coupling for a strictly defined set of resonant frequencies, the addition of modulation on multiple frequencies dramatically modifies the structure of resonances. Thus, additional modulation on a double frequency may suppress the primary resonance, while modulation on a triple frequency causes fusion of primary and secondary resonances.

Light tunneling inhibition and anisotropic diffraction engineering in two-dimensional waveguide arrays

We address two-dimensional (2D) waveguide arrays where light tunneling into neighboring waveguides may be effectively suppressed by an out-of-phase harmonic modulation of the refractive index in neighboring waveguides at suitable frequencies. Genuine 2D features, such as anisotropic diffraction engineering, diffraction-free propagation along selected directions in the transverse plane, and tunneling inhibition for multichannel vortices, are shown to occur.

Nonlinearity-induced broadening of resonances in dynamically modulated couplers

We report the observation of nonlinearity-induced broadening of resonances in dynamically modulated directional couplers. When the refractive index of the guiding channels in the coupler is harmonically modulated along the propagation direction and is out-of-phase in two channels, coupling can be completely inhibited at resonant modulation frequencies. We observe that nonlinearity broadens such resonances and that localization can be achieved even in detuned systems at power levels well below those required in unmodulated couplers.

Parametric amplification of random lattice soliton swinging

We consider the propagation of solitons in media with an imprinted transverse periodic or parabolic refractive index modulation when the modulation depth fluctuates slightly along the propagation direction. We find that, under suitable spectral resonance conditions, small transverse soliton oscillations may get parametrically amplified.

Interlaced linear-nonlinear optical waveguide arrays

The system of coupled discrete equations describing a two-component superlattice with interlaced linear and nonlinear constituents is studied as a basis for investigating binary waveguide arrays, such as ribbed AlGaAs structures, among others. Compared to the single nonlinear lattice, the interlaced system exhibits an extra band-gap controlled by the, suitably chosen by design, relative detuning. In more general physics settings, this system represents a discretization scheme for the single-equation-based continuous models in media with transversely modulated linear and nonlinear properties. Continuous wave solutions and the associated modulational instability are fully analytically investigated and numerically tested for focusing and defocusing nonlinearity. The propagation dynamics and the stability of periodic modes are also analytically investigated for the case of zero Bloch momentum. In the band-gaps a variety of stable discrete solitary modes, dipole or otherwise, in-phase or of staggered type are found and discussed.

Spatial soliton tunneling, compression and splitting

We numerically investigate the tunneling of spatial solitons through a focusing Kerr nonlinear optical lattice with longitudinal potential barrier, and find that the position of input beams apparently affects the tunneling behaviors of spatial solitons, which exhibit compression or splitting when passing through the barrier, and that the transverse modulation frequency of lattice and the intensity of input beams strongly affect the ability of tunneling. Based on these properties, we present a scheme for compressing soliton and splitting soliton into stable twin beams. The obtained results may have promising applications in all-optical devices based on spatial solitons.

Chaotic soliton walk in periodically modulated media

We show that a weak transverse spatial modulation in (2+1) nonlinear Schrödinger-type equation can result in nontrivial dynamics of a radially symmetric soliton. We provide examples of chaotic soliton motion in periodic media both for conservative and dissipative cases. We show that complex dynamics can persist even for soliton sizes greater than the modulation period.

Resonant mode oscillations in modulated waveguiding structures

We put forward the concept of resonant, Rabi-like oscillatons and adiabatic transitions between confined light modes in properly modulated multimode waveguides. The phenomenon is shown to take place in both the linear and the nonlinear regimes. In addition, we find that the mode transitions occur not only in simple geometries, but also in complex confining multimode structures. The phenomenon is analogous to the familiar stimulated state transitions that occur in multilevel quantum systems.

Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model

A novel method for obtaining analytical solitary wave solutions of the nonlinear Kronig-Penney model in periodic photonic structures with self-defocusing nonlinearity is applied for providing generic families of solutions corresponding to the gaps of the linear band structure. Characteristic cases are shown to be quite robust under propagation.

Soliton control in fading optical lattices

We predict new phenomena, such as soliton steering and soliton fission, in optical lattices that fade away exponentially along the propagation direction. Such lattices, featuring tunable decay rates, arise in photorefractive crystals in the wavelength range 360-400 nm. We show that the predicted phenomena offer different opportunities for soliton control.

Topological dragging of solitons

We put forward properties of solitons supported by optical lattices featuring topological dislocations and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.

Anderson localization of solitons in optical lattices with random frequency modulation

We report on the phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with the growth of the frequency fluctuation level. The localization process is strongly sensitive to the lattice depth since in shallow lattices walking solitons experience random refraction and/or multiple scattering in contrast to relatively deep lattices, where solitons are typically immobilized in the vicinity of local minimums of modulation frequency.

Soliton dragging by dynamic optical lattices

We report on the phenomenon of controllable soliton dragging by dynamic optical lattices induced by three imbalanced interfering plane waves. Because of such an imbalance, the transverse momentum of the lattice does not vanish, and thus the dynamic lattice can cause soliton dragging. The dragging rate is shown to depend on the amplitude and on the angle of incidence of the third plane wave making the optical lattice.

Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices

We consider parametric amplification of two-dimensional spatial soliton oscillations in longitudinally modulated harmonic and Bessel lattices in Kerr-type saturable medium. We show that soliton center oscillations along different axes in two-dimensional lattices are coupled, which gives rise to a number of interesting propagation scenarios including periodic damping and excitation of soliton oscillations along perpendicular axes, selective amplification of soliton oscillations along one transverse axis, and enhancement of soliton spiraling.

Stable ring-profile vortex solitons in bessel optical lattices

Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.

Multicolor vortex solitons in two-dimensional photonic lattices

We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable almost in the entire domain of their existence, and that the instability domain decreases with the increase of the lattice depth. We also show the generation of the solitons, and the feasibility of the concept of lattice soliton algebra.

Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices

We address azimuthally modulated Bessel optical lattices imprinted in focusing cubic Kerr-type nonlinear media, and reveal that such lattices support different types of stable solitons whose complexity increases with the growth of lattice order. We reveal that the azimuthally modulated lattices cause single solitons launched tangentially to the guiding rings to jump along consecutive sites of the optical lattice. The position of the output channel can be varied by small changes of the launching angle.

Stabilization of vector solitons in optical lattices

We address the properties and dynamical stability of one-dimensional vector lattice solitons in a Kerr-type cubic medium with harmonic transverse modulation of the refractive index. We discovered that unstable families of scalar lattice solitons can be stabilized via cross-phase modulation (XPM) in the vector case. It was found that multihumped vector solitons that are unstable in uniform media where the XPM strength is higher than that of self-phase modulation can also be stabilized by the lattice.

Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice

We investigate the existence and stability of three-dimensional spatiotemporal solitons in self-focusing cubic Kerr-type optical media with an imprinted two-dimensional harmonic transverse modulation of the refractive index. We demonstrate that two-dimensional photonic Kerr-type nonlinear lattices can support stable one-parameter families of three-dimensional spatiotemporal solitons provided that their energy is within a certain interval and the strength of the lattice potential, which is proportional to the refractive index modulation depth, is above a certain threshold value.

Tunable soliton self-bending in optical lattices with nonlocal nonlinearity

We address the phenomenon of soliton self-bending in Kerr-type nonlocal nonlinear media with an imprinted transverse periodic modulation of the linear refractive index. We show that the imprinted optical lattice makes possible to control the mobility of soliton by varying the depth and the frequency of the linear refractive index modulation.

Soliton eigenvalue control in optical lattices

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.

Rotary solitons in bessel optical lattices

We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media. We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, in addition to the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.

Stable soliton complexes in two-dimensional photonic lattices

We show that two-dimensional photonic Kerr nonlinear lattices can support stable soliton complexes composed of several solitons packed together with appropriately engineered phases. This may open up new prospects for encoding pixellike images made of robust discrete or lattice solitons.

Resonant phenomena in nonlinearly managed lattice solitons

The formation of nonlinearly managed spatial solitons in Kerr-type nonlinear media with transverse periodic modulation of the refractive index is considered. The phenomenon of resonant enhancement of lattice soliton amplitude oscillations is reported. We show how the tunable discreteness and competition between such characteristic scales as the beam width and the lattice period influence propagation dynamics and properties of breathing lattice solitons.

Packing, unpacking, and steering of multicolor solitons in optical lattices

We discuss potential applications of multicolor solitons supported by periodic lattices imprinted in quadratic nonlinear media. Such lattice solitons can be packed together with appropriate relative phases to form stable soliton trains that can be treated as bit sequences. We describe controllable splitting of the trains into their soliton constituents and the angle- and power-controlled steering and trapping of solitons moving across the lattice into the desired guiding channel.

Multicolor lattice solitons

We report on the existence of multicolor solitons supported by periodic lattices made from quadratic nonlinear media. Such lattice solitons bridge the gap between continuous solitons in uniform media and discrete solitons in strongly localized systems and exhibit a wealth of new features. We discovered that, in contrast to uniform media, multipeaked lattice solitons are stable. Thus they open new opportunities for all-optical switching based on soliton packets.