Phase dependent forward three wave amplification in photorefractive BSO

The results of three wave mixing experiments in photorefractive Bi12SiO20 are presented. The results confirm theoretical predictions that amplification by three wave mixing is strongly dependent on the phase relationship between the three beams at the input to the medium.

Solitons: permanent waves

Communications engineers are learning to create an electromagnet wave at will, to transmit information. This wave, the optical soliton, is the subject of astounding recent developments in nonlinear optics and lasers. The author describes the principles behind the use of solitons in optical communications and shows that in the context of such communications the most important property of solitons is that they are extremely stable. Not only do they not disperse, but an encounter with a perturbation (e.g. a joint in optical fibre) will usually leave the soliton unaltered.

Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling

Using a new experimental geometry, we have proved for the first time that the generation of spatial subharmonic gratings in photorefractive crystals is not dependent on optical nonlinearity. We present results which confirm that the subharmonic gratings result from a parametric excitation of ultra low-frequency eigenmodes of a crystal by a time modulated fundamental grating.

Verification of the standard model of the photorefractive nonlinearity in BSO crystals

On the basis of the standard model for the photorefractive nonlinearity we investigate whether a systematic description of the dependence of two-beam energy exchange on beam polarization and grating vector K is possible. Our result is that there is good agreement between theory and experiment with respect to the polarization properties and semi-quantitative agreement with respect to the K-dependence of the energy exchange.

Low frequency peculiarities of the photorefractive response in sillenites

We investigate experimentally and theoretically the dependence of the amplitude of the spatial fundamental grating, created by a pair of coherent light beams while using the running grating technique [M.P. Petrov, S.I. Stepanov and A.V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Springer Series in Optical Sciences (Springer, 1991); P. Refregier, L. Solymar, H. Rajbenbach and J.P. Huignard, J. Appl. Phys. 58 (1985) 45], as a function of detuning frequency and beam ratio ß in photorefractive Bi12SiO20. It is shown that for ß > 0.05, in addition to the main peak in the frequency dependence of the amplitude, there is an additional peak of lower frequency which, as a rule, dominates the main peak. The position of the main peak depends on ß. The experimental results are in good agreement with the theoretical analysis and the general ideas about excitation and nonlinear interaction of weakly damped space-charge waves.

Optical activity in photorefractive Bi12TiO20

The influence of optical activity on two-wave mixing (TWM) in photorefractive BTO and BSO crystals in the absence of an applied field is studied both theoretically and experimentally. For the conventinal orientations of the grating vector, K [001] and K[001], the piezoelectric and photoelastic effects are either zero or negligible. This makes an analytical treatment of the TWM problem possible. We obtain an analytical solution for the coupled wave equations of TWM valid for arbitrary optical activity. This result is of special importance for BTO crystals. In these crystals under the condition of maximum energy transfer (|K|rD=1, where rD is the Debye radius) neither the approximation of small optical activity nor the one of dominating optical activity is applicable and our analytical solution becomes essential. Our experimental setup uses beams with a trapezoidal overlap that allows us to study the thickness-dependence of the gain in a single measurement. Experimental and theoretical results for a BTO crystal are compared with those for a BSO crystal and are explained in the framework of the model used.

Excitation of higher harmonic gratings in AC-field biased photorefractive crystals

We analyze the nonlinear excitation of holographic gratings in a photorefractive crystal being subject to an alternating electric field and a stationary light interference pattern. The influence of the higher harmonics on the fundamental grating is illustrated for the case where a crystal of Bi12SiO20 is the recording medium. We analyze both the steady state and the transient consequences of the higher harmonic excitation.

Longitudinal parametric oscillation in photorefractive sillenites: comparison between theory and experiment

By using an alternative setup for photorefractive parametric oscillation in which wave mixing between the recording beams is avoided it has become possible to make more detailed comparisons with the space-charge wave theory. In the present paper we compare the experimental features of longitudinal parametric oscillation observed in a crystal of Bi12SiO20 with the theoretical predictions.

A perturbative analysis of dispersion-managed solitons

We study soliton solutions of the path-averaged propagation equation governing the transmission of dispersion-managed (DM) optical pulses in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. In the case of small dispersion map strengths, the averaged pulse dynamics is governed by a perturbed form of the nonlinear Schrödinger equation; applying a perturbation theory – elsewhere developed – based on inverse scattering theory, we derive an analytic expression for the envelope of the DM soliton. This expression correctly predicts the power enhancement arising from the dispersion management. Theoretical results are verified by direct numerical simulations.

Dispersion-managed solitons in fibre systems and lasers

Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a variety of physical problems and engineering applications. The mathematical concept of dispersion managed solitons already has made an impact on the development of fibre communications, optical signal processing and laser science. We overview here the field of the dispersion managed solitons starting from mathematical theories of Hamiltonian and dissipative systems and then discuss recent advances in practical implementation of this concept in fibre-optics and lasers.

Statistics of three interacting optical solitons

We examine the statistics of three interacting optical solitons under the effects of amplifier noise and filtering. We derive rigorously the Fokker-Planck equation that governs the probability distribution of soliton parameters.