Rabi oscillations and stimulated mode conversion on the subwavelength scale

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.

Nonlinear Thouless Pumping: Solitons and Transport Breakdown

One-dimensional topological pumping of matter waves in two overlaid optical lattices moving with respect to each other is considered in the presence of attractive nonlinearity. It is shown that there exists a threshold nonlinearity level above which the matter transfer is completely arrested. Below this threshold, the transfer of both dispersive wave packets and solitons occurs in accordance with the predictions of the linear theory; i.e., it is quantized and determined by the linear dynamical Chern numbers of the lowest bands. The breakdown of the transport is also explained by nontrivial topology of the bands. In that case, the nonlinearity induces Rabi oscillations of atoms between two (or more) lowest bands. If the sum of the dynamical Chern numbers of the populated bands is zero, the oscillatory dynamics of a matter soliton in space occurs, which corresponds to the transport breakdown. Otherwise, the sum of the Chern numbers of the nonlinearity-excited bands determines the direction and magnitude of the average velocity of matter solitons that remain quantized and admit fractional values. Thus, even in the strongly nonlinear regime the topology of the linear bands is responsible for the evolution of solitons. The transition between different dynamical regimes is accurately described by the perturbation theory for solitons.

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 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.