Dejan V. Timotijević

Spatiotemporal effects in double phase conjugation

Spatial and temporal effects arising in photorefractive crystals during the process of double phase conjugation are analyzed numerically with a novel beam-propagation method. Slowly varying envelope wave equations in the paraxial approximation are solved under the appropriate boundary conditions. Our analysis includes dynamical effects caused by the buildup of diffraction gratings in the crystal and the turn-on of phase-conjugate beams as well as spatial effects caused by the finite transverse spread of beams and by the propagation directions of the beams. Various phenomena are observed, such as self-bending of phase-conjugate beams, convective flow of energy out of the interaction region, mode oscillations, critical slowing down at the oscillation threshold, and irregular spatial pattern formation. For a real beam-coupling constant and constructive interaction of interference fringes in the crystal we find steady or periodic behavior. For a complex coupling constant and/or induced phase mismatch in the grating a transition to spatiotemporal chaos is observed. We believe that under stable operating conditions the transverse double phase-conjugate mirror in the paraxial approximation is a convective oscillator, rather than an amplifier. Improved agreement with experimental results is obtained.

Spatiotemporal optical instabilities in nematic solitons

We investigate numerically the propagation of self-trapped optical beams in nematic liquid crystals. Our analysis includes both spatial and temporal behavior. We display the formation of stable solitons in a narrow threshold region of beam intensities for fixed birefringence, and depict their spatiotemporal instabilities as the input intensity and the birefringence are increased. We demonstrate the breathing and filamentation of solitons above the threshold with increasing input intensity, and discover a convective instability with increasing birefringence. We consider the propagation of complex beam structures in nematic liquid crystals, such as dipoles, beam arrays, and vortices.

Soliton formation by decelerating interacting Airy beams

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction between the Airy beams decelerates their bending and enables the formation of straight propagating solitary states. Our experimental results represent an intriguing combination of two fundamental effects, accelerated optical beams and nonlinearity, together enable novel mechanisms of soliton formation that will find applications in all-optical light localization and switching architectures. Our experimental results are supported by corresponding numerical simulations.

Exact solution to photorefractive two-wave mixing with arbitrary modulation depth

We obtain analytical solution to the slowly varying envelope wave equations describing two-wave mixing in photorefractive crystals with arbitrary dependence of the gain and absorption on the two-wave fringe modulation depth. We introduce a novel form of the correction function for the space charge field that offers an improved agreement with the experiment.

Breathing solitons in nematic liquid crystals

Dynamical and steady-state behavior of beams propagating in nematic liquid crystals (NLCs) is analyzed. A well-known model for the beam propagation and the director reorientation angle in a NLC cell is treated numerically in space and time. The formation of steady-state soliton breathers in a threshold region of beam intensities is displayed. Below the region the beams diffract, above the region spatiotemporal instabilities develop, as the input intensity and the material parameters are varied. Curiously, the only kind of solitons we could demonstrate in our numerical studies was the breathers. Despite repeated efforts, we could not find the solitons with a steady profile propagating in the NLC model at hand.

Extension of the stability criterion for dissipative optical soliton solutions of a two-dimensional Ginzburg–Landau system generated from asymmetric inputs

The evolution and stability of dissipative optical spatial solitons generated from an input asymmetric with respect to two transverse coordinates x and y are studied. The variational approach used to investigate steady state solutions of a cubic–quintic Ginzburg–Landau equation is extended in order to consider initial conditions without radial symmetry. The stability criterion is generalized to the asymmetric case. A domain of dissipative parameters for stable solitonic solutions is determined. Following numerical simulations, an asymmetric input laser beam with dissipative parameters from this domain will always give a stable dissipative spatial soliton.

Counterpropagating beams in nematic liquid crystals.

The behavior of counterpropagating self-trapped optical beam structures in nematic liquid crystals is investigated. A time-dependent model for the beam propagation and the director reorientation in a nematic liquid crystal is numerically treated in three spatial dimensions and time. We find that the stable vector solitons can only exist in a narrow threshold region of control parameters. Below this region the beams diffract, above they self-focus into a series of focal spots. Spatiotemporal instabilities are observed as the input intensity, the propagation distance, and the birefringence are increased. We demonstrate undulation, filamentation, and convective dynamical instabilities of counterpropagating beams. Qualitatively similar behavior as of the copropagating beams is observed, except that it happens at lower values of control parameters.

Transverse effects in double phase conjugation

Abstract Spatial and dynamical effects in double phase conjugate mirrors are investigated analytically and numerically. A variety of spatial and temporal effects are observed, such as beam-bending, self-defocusing, mode oscillations and irregular pattern formation. We conclude that in more than one spatial dimension the double phase conjugate mirror is a convective oscillator. For strong beam couplings and strong diffraction we find that the oscillation threshold is not well defined, and that the double phase conjugate mirror becomes unstable. An improved agreement with experimental results is obtained.

Two- and four-wave mixing with saturable absorption and gain

An exact solution to a model of two- and four-wave mixing in photorefractive media with saturable gain and absorption is presented. Pump depletion effects are accounted for, and the procedure for matching two-point boundary conditions is given. Possibilities of multistable solutions are investigated, and procedures on how to deal with such situations are outlined. It is found that the energy transfer between waves is less effective in the nonsaturated regime as compared to the saturated regime. It is also established that the nonsaturated system is more stable than the saturated under the same conditions. >

Exact solution to four-wave mixing with complex couplings: reflection geometry

An exact solution to photorefractive four-wave mixing equations with complex couplings in ref lection geometry is obtained. It is shown that the efficiency of the process of phase conjugation can be enhanced by introduction of a frequency shift between the pumps and the signal, similar to the case of transmission geometry. However, to obtain an improved agreement with experiment, the inclusion of transverse effects is found to be necessary.