Resonant mode oscillations in modulated waveguiding structures

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.

Spin-orbit Rabi oscillations in optically synthesized magnetic fields

Rabi oscillation has been proven to be one of the cornerstones of quantum mechanics, triggering substantial investigations in different disciplines and various important applications both in the classical and quantum regimes. So far, two independent classes of wave states in the Rabi oscillations have been revealed as spin waves and orbital waves, while a Rabi wave state simultaneously merging the spin and orbital angular momentum has remained elusive. Here we report on the experimental and theoretical observation and control of spin-orbit-coupled Rabi oscillations in the higher-order regime of light. We constitute a pseudo spin-1/2 formalism and optically synthesize a magnetization vector through light-crystal interaction. We observe simultaneous oscillations of these ingredients in weak and strong coupling regimes, which are effectively controlled by a beam-dependent synthetic magnetic field. We introduce an electrically tunable platform, allowing fine control of transition between different oscillatory modes, resulting in an emission of orbital-angular-momentum beams with tunable topological structures. Our results constitute a general framework to explore spin-orbit couplings in the higher-order regime, offering routes to manipulating the spin and orbital angular momentum in three and four dimensions. The close analogy with the Pauli equation in quantum mechanics, nonlinear optics, etc., implies that the demonstrated concept can be readily generalized to different disciplines.

Soliton transformation between different potential wells

This paper presents a novel, to the best of our knowledge, method for realizing soliton transformation between different potential wells by gradually manipulating their depths in the propagation direction. The only requirements for such a transformation are that the gradient of the manipulated depth is smooth enough and the solitons in different potential wells are both in the regions of stability. The comparison of transformed solitons with the iterative ones obtained by the accelerated imaginary-time evolution method proves that our method is efficient and reliable. An interesting consequence is that in some complex potential wells in which it is difficult to find solitons by iterative numerical methods, stable solitons can be obtained by the transformation method. The controllable soliton transformation provides an excellent opportunity for all-optical switching, optical information processing, and other applications.

A Pair of Coupled Waveguides as a Classical Analogue for a Solid-State Qubit

We have determined conditions when a pair of coupled waveguides, a common element for integrated room-temperature photonics, can act as a qubit based on a system with a double-well potential. Moreover, we have used slow-varying amplitude approximation (SVA) for the "classical" wave equation to study the propagation of electromagnetic beams in a couple of dielectric waveguides both analytically and numerically. As a part of an extension of the optical-mechanical analogy, we have considered examples of "quantum operations" on the electromagnetic wave state in a pair of waveguides. Furthermore, we have provided examples of "quantum-mechanical" calculations of nonlinear transfer functions for the implementation of the considered element in optical neural networks.

Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices

We investigate the discrete Talbot self-imaging effect in Floquet superlattices based on a mesh of directional couplers with periodically varying separation between waveguides, both theoretically and numerically. The modulated discreteness of the lattices sets strong constraints to ensure the Talbot effect generation. We show that discrete Talbot effect occurs only if the incident periods are N = 1, 2, and 4 in dispersive regimes of the Hermitian superlattices. In both dynamic localized and rectification regimes, self-imaging effect can occur for arbitrary input period N. For the rectification case, Talbot distance equals the input period. In the regime of dynamical localization, the Talbot distance remains unchanged irrespective of the pattern period. For non-Hermitian Floquet superlattices, due to the non-zero imaginary part of quasi-energy spectrum arising at the center of the Brillouin zone, where the mode degeneracy occurs, Talbot revival is not preserved when the input period is an even number, and exists only as N = 1 in the dispersive regime. The theoretical calculations and numerical simulations verify each other completely.

Geometric control of vector vortex light beams via a linear coupling system

We demonstrate a novel theoretical platform to realize geometric control of vector vortex states in an optical coupling system. These complex states are characterized by spatially varying polarizations and coupled with vortex phase profiles. It can be mapped uniquely as a point on a higher-order Poincaré sphere. The geometric theory clearly reveals how a tailored phase mismatch profile, together with a suitable coupling, supports state conversion between these higher-order complex light fields, in analogous to the processes appearing in two-level quantum system as well as three-wave mixing process in nonlinear optics. Specifically, in the phase matching condition, it is shown that these complex states carried by an envelope field exhibit periodic oscillations in the course of state evolution; whereas in the phase mismatching condition the oscillations become detuned, leading to noncyclic state evolution. Intriguingly, when using an adiabatic technique for the phase mismatch, robust state conversion between two arbitrary vector vortex light fields can be realized. Our demonstrations provide a fully control over the vector vortex states on the sphere, and we suggest that it would benefit various potential applications both in the classical and the quantum optics.

Talbot effect in arrays of helical waveguides

We demonstrate that periodic self-imaging of light patterns with certain input periods can be effectively realized in one-dimensional and two-dimensional helical waveguide arrays. The band structure is drastically dependent on the helix radius and period, and the complete collapse of quasi-energy bands occurs for a certain helix radius and period, which strongly affects the intensity carpet and the Talbot length of the Talbot self-imaging effect. Talbot length would extend to infinity, as the helix radius and period approach the corresponding critical values corresponding to the band collapse, where the inversion of intensity distribution between even and odd waveguides is observed for the binary input pattern with π/2 phase shift between the adjacent waveguides.

Generation of Coherent and Spatially Squeezed States of an Electromagnetic Beam in a Planar Inhomogeneous Dielectric Waveguide

We use slow-varying amplitude approximation (SVA) for the wave equation to study both analytically and numerically propagation of an electromagnetic beam in the waveguide structure with parabolic susceptibility spatial dependence. Such a structure is similar to the harmonic oscillator in quantum mechanics. We analyze this structure as a single mode guide and introduce the notion of number of “photons” in the mode. In particular, we pay special attention to the possibility of effective build-up of the coherent and spatially squeezed vacuum states of the mode that can be of interest for a number of practical applications. The way to provide these types of mode excitation is suggested. Several applications for controlling the mode composition of an electromagnetic wave in the parabolic index-gradient waveguide for various frequency ranges are considered.

Rabi-like oscillation of photonic topological valley Hall edge states

We investigate Rabi-like oscillations of topological valley Hall edge states by introducing two zigzag domain walls in an inversion-symmetry-breaking honeycomb photonic lattice. Such resonant oscillations are stimulated by weak periodic modulation of the lattice depth along the propagation direction that does not affect the overall symmetry and the band topology of the lattice. Oscillations are accompanied by periodic switching between edge states with the same Bloch momentum but located at different domain walls. Switching period and efficiency are the non-monotonic functions of the Bloch momentum in the Brillouin zone. We discuss how the efficiency of this resonant process depends on the detuning of modulation frequency from the resonant value. Switching of nonlinear edge states is also briefly discussed. Our work brings about an effective approach to accomplish resonant oscillations of the valley Hall edge states in time-reversal-invariant topological insulators.

Generation and probing of 3D helical lattices with tunable helix pitch and interface

We propose a method for generation of tunable three-dimensional (3D) helical lattices with varying helix pitch. In order to change only the lattice helix pitch, a periodically varying phase along the propagation direction is added to the central beam - one of the interference beams for lattice construction. The phase periodicity determines the helix pitch, which can be reconfigured at ease. Furthermore, a helical lattice structure with an interface (domain wall) is also achieved by changing the phase structure of the lateral beams, leading to opposite rotating direction (helicity) on different sides of the interface. When a Gaussian beam is used to probe the bulk lattice, it can evolve into a spiral beam with its helicity varying in accordance with that of the lattice. Probing along the interface with two dipole-like optical beams leads to unusual propagation dynamics, depending on the phase and size of the two beams. This approach could be further explored for studies of nonlinear interface solitons and topological interface states. In addition, the helical lattices may find applications in dynamical multi-beam optical tweezers.

Dynamics of Gaussian beam modeled by fractional Schrödinger equation with a variable coefficient

In the paper, we investigate the propagation dynamics of the Gaussian beam modeled by the fractional Schrödinger equation (FSE) with a variable coefficient. In the absence of the beam's chirp, for smaller Lévy index, the Gaussian beam firstly splits into two beams, however under the action of the longitudinal periodic modulation, they exhibit a periodically oscillating behaviour. And with the increasing of the Lévy index, the splitting behaviour gradually diminishes. Until the Lévy index equals to 2, the splitting behaviour is completely replaced by a periodic diffraction behaviour. In the presence of the beam's chirp, one of the splitting beams is gradually suppressed with the increasing of the chirp, while another beam on the opposite direction becomes stronger and exhibits a periodically oscillating behaviour. Also, the oscillating amplitude and period are investigated and the results show that the former is dependent on the modulation frequency, the Lévy index and the beam's chirp, the latter depends only on the modulation frequency. Thus, the evolution of the Gaussian beam can be well manipulated to achieve the beam management in the framework of the FSE by controlling the system parameters and the chirp parameter.

Beam propagation management in a fractional Schrödinger equation

Generalization of Fractional Schrödinger equation (FSE) into optics is fundamentally important, since optics usually provides a fertile ground where FSE-related phenomena can be effectively observed. Beam propagation management is a topic of considerable interest in the field of optics. Here, we put forward a simple scheme for the realization of propagation management of light beams by introducing a double-barrier potential into the FSE. Transmission, partial transmission/reflection, and total reflection of light fields can be controlled by varying the potential depth. Oblique input beams with arbitrary distributions obey the same propagation dynamics. Some unique properties, including strong self-healing ability, high capacity of resisting disturbance, beam reshaping, and Goos-Hänchen-like shift are revealed. Theoretical analysis results are qualitatively in agreements with the numerical findings. This work opens up new possibilities for beam management and can be generalized into other fields involving fractional effects.

Rabi oscillations of surface plasmon polaritons in graphene-pair arrays

We investigate the Bloch mode conversion of surface plasmon polaritons in a periodic array of graphene pairs with each consisting of two separated parallel graphene sheets. The employment of graphene pair as a unit cell in the array yields two Bloch modes belonging to different bands. By periodically modulating the permittivity of dielectrics between graphene along the propagation direction, the interband transitions occur and the modes will alternatively couple to each other, similar to traditional Rabi oscillations in quantum systems. The indirect Rabi oscillations can also be observed through introducing transverse modulation momentum. The period of Rabi oscillations can be optimized by taking advantage of the flexible tunability of graphene. The study suggests that the structure have applications in optical switches and mode converters operating on deep-subwavelength scale.

Efficient mode conversion in guiding structures with longitudinal modulation of nonlinearity

We describe power-dependent dynamics of conversion of the guided modes of various guiding structures due to nearly resonant longitudinal modulation of the nonlinear coefficient of the medium. It is shown that the control of the energy exchange integrals, as well as of the input weights of the interacting modes, is especially crucial for efficient mode conversion in the setting considered here. Complex dynamics of conversion incorporates various scenarios, including nonharmonic oscillations of the energy weights, which mimics Jacoby elliptical functions.

Rabi oscillations and stimulated mode conversion on the subwavelength scale

We study stimulated mode conversion and dynamics of Rabi-like oscillations of weights of guided modes in deeply subwavelength guiding structures, whose dielectric permittivity changes periodically in the direction of light propagation. We show that despite strong localization of the fields of eigenmodes on the scales below the wavelength of light, even weak longitudinal modulation couples modes of selected parity and causes periodic energy exchange between them, thereby opening the way for controllable transformation of the internal structure of subwavelength beams. The effect is reminiscent of Rabi oscillations in multilevel quantum systems subjected to the action of periodic external fields. By using rigorous numerical solution of the full set of the Maxwell's equations, we show that the effect takes place not only in purely dielectric, but also in metallic-dielectric structures, despite the energy dissipation inherent to the plasmonic waveguides. The stimulated conversion of subwavelength light modes is possible in both linear and nonlinear regimes.

Resonant mode conversion in the waveguides with unbroken and broken PT symmetry

We study resonant mode conversion in parity time (PT)-symmetric multimode waveguides, where symmetry breaking manifests itself in the sequential destabilization (i.e., the appearance of complex eigenvalues) of the pairs of adjacent guided modes. We show that efficient mode conversion is possible even in the presence of the resonant longitudinal modulation of the complex refractive index. The distinguishing feature of the resonant mode conversion in the PT-symmetric structure is a drastic growth of the width of the resonance curve when the gain/losses coefficient approaches a critical value, at which symmetry breaking occurs. We found that in the system with broken symmetry, the resonant coupling between the exponentially growing mode and the stable higher-order one effectively stabilizes dynamically coupled pairs of modes and remarkably diminishes the average rate of the total power growth.

Resonant Bloch-wave beatings

We introduce Bloch-wave beatings in arrays of multimode periodically bent waveguides with a transverse refractive index gradient. The new phenomenon manifests itself in the periodic drastic increase of the amplitude of the Bloch oscillations that accompanies resonant conversion of modes guided by the individual waveguides. The Bloch-wave beatings are found to be most pronounced when the length of the resonant mode conversion substantially exceeds the longitudinal period of the Bloch oscillations. The beating frequency decreases when the amplitude of waveguide bending decreases, while the beating amplitude is restricted by the amplitude of the Bloch oscillations that emerge from the second allowed band of the Floquet-Bloch lattice spectrum.

Enhancement and inhibition of light tunneling mediated by resonant mode conversion

We show that the rate at which light tunnels between neighboring multimode waveguides can be drastically increased or reduced by the presence of small longitudinal periodic modulations of the waveguide properties that stimulate resonant conversion between the eigenmodes of each waveguide. Such a conversion, available only in multimode guiding structures, leads to periodic power transfer into higher-order modes, whose tails may considerably overlap with neighboring waveguides. As a result, the effective coupling constant for neighboring waveguides may change by several orders of magnitude upon small variations in the longitudinal modulation parameters.

Dynamics of topological light states in spiraling structures

We expose a mechanism for the dynamical generation and control of light states with diverse topologies in spiraling guiding structures. Specifically, we show that spiraling shallow refractive index landscapes induce coupling and periodic energy exchange between states with different topological charges. Such a resonant effect enables excitation of optical vortices by vortex-free inputs and allows the output topological charge of the beam to be controlled. The presence of nonlinearity results in a strong asymmetrization of the resonant curves and a shift of the resonant frequencies. Resonant vortex dynamic generation, including revivals, is shown to be possible not only in waveguides mediated by total internal reflection but also in Bragg-guiding hollow-core geometries.

Dynamic diffraction and interband transitions in two-dimensional photonic lattices

We reveal a direct link between two fundamental wave phenomena in periodic media, Pendellösung oscillations and resonant coupling between spectral bands. We experimentally measure the power transfer between laser beams associated with the high-symmetry points in periodic and biased hexagonal photonic lattices. As a result, we demonstrate that Pendellösung oscillations dominate the dynamics of resonant interband transitions on a short propagation scale.

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.

Quasi-BLOCH oscillations in curved coupled optical waveguides

We report the observation of quasi-Bloch oscillations, a recently proposed, new type of dynamic localization in the spatial evolution of light in a curved coupled optical waveguide array. By spatially resolving the optical intensity at various propagation distances, we show the delocalization and final relocalization of the beam in the waveguide array. Through comparisons with other structures, we show that this dynamic localization is robust beyond the nearest-neighbor tight-binding approximation and exhibits a wavelength dependence different from conventional dynamic localization.

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.

Experimental observation of Rabi oscillations in photonic lattices

We demonstrate spatial Rabi oscillations in optical waveguide arrays. Adiabatic transitions between extended Floquet-Bloch modes associated with different bands are stimulated by periodic modulation of the photonic lattice in the propagation direction. When the stimulating modulation also carries transverse momentum, the transition becomes indirect, equivalent to phonon-assisted Rabi oscillations. In solid state physics such indirect Rabi oscillations necessitate coherent phonons and hence they have never been observed. Our experiments suggest that phonon-assisted Rabi oscillations are observable also with Bose-Einstein condensates, as well as with other wave systems-where coherence can be maintained for at least one period of the Rabi oscillation.