Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Anisotropic diffraction of stratified volume holographic grating in photorefractive media

We have studied the anisotropic diffraction properties of the stratified volume holographic gratings recorded in photorefractive media using the anisotropic coupled wave theory. It is shown that the diffraction efficiency of such system exhibit the uniform periodic Bragg selectivity properties. In addition the dependence of the stratified volume holographic optical elements (SVHOEs) diffraction properties on the buffer-layer thickness, grating-layer thickness, number of modulation layers, and total thickness of system are discussed in detail. (c) 2005 Elsevier GrnbH. All rights reserved.

One-dimensional incoherently coupled grey solitons in two-photon photorefractive media

We show that grey solitons, grey-grey soliton pairs, and multi-component grey solitons can be realized in two-photon photorefractive media. The results for soliton pairs and multi-component solitons are derived under the assumption that the carrier beams share the same polarization, wavelength, and are mutually incoherent.

Theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of a sharp steplike initial discontinuity in a beam with one-dimensional striplike geometry. This approach is confirmed by numerical simulations, which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.

High-efficiency volume hologram recording with a pulsed signal beam

We present an efficient photorefractive volume hologram recording technique with a pulsed signal beam and continuous reference-beam illumination. The grating envelope can be simply controlled by manipulation of the duty cycle of the signal beam. Thus, for any grating coupling strength and different initial reference-signal intensity ratios, the diffraction efficiency can be maximized with this technique and can be greatly increased in comparison with that of the conventional recording technique. (C) 1998 Optical Society of America.

Optical data encryption using time-dependent dynamics of refractive index changes in LiNbO3

We present a method for optical encryption of information, based on the time-dependent dynamics of writing and erasure of refractive index changes in a bulk lithium niobate medium. Information is written into the photorefractive crystal with a spatially amplitude modulated laser beam which when overexposed significantly degrades the stored data making it unrecognizable. We show that the degradation can be reversed and that a one-to-one relationship exists between the degradation and recovery rates. It is shown that this simple relationship can be used to determine the erasure time required for decrypting the scrambled index patterns. In addition, this method could be used as a straightforward general technique for determining characteristic writing and erasure rates in photorefractive media.

Characteristics of recording and thermal fixing in lithium niobate

We present a theoretical model in which the band-transport equations and the coupled-wave equations are considered to study the two thermal-fixing methods (simultaneous fixing and postfixing) in Fe:LiNbO3. We found that, in simultaneous fixing, the existing ionic-grating affects the writing of the electronic grating by reduction of the coupling gain, and the grating envelope of the fixed-index grating is quite uniform inside the photorefractive crystal in comparison with the method of postfixing. The resulting diffraction efficiency of the fixed-volume grating is dependent mainly on the initial intensity modulation of the two writing beams. A set of experiments is also presented. (C) 1998 Optical Society of America.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

High performance numerical modeling of ultra-short laser pulse propagation based on multithreaded parallel hardware

The focus of this study is development of parallelised version of severely sequential and iterative numerical algorithms based on multi-threaded parallel platform such as a graphics processing unit. This requires design and development of a platform-specific numerical solution that can benefit from the parallel capabilities of the chosen platform. Graphics processing unit was chosen as a parallel platform for design and development of a numerical solution for a specific physical model in non-linear optics. This problem appears in describing ultra-short pulse propagation in bulk transparent media that has recently been subject to several theoretical and numerical studies. The mathematical model describing this phenomenon is a challenging and complex problem and its numerical modeling limited on current modern workstations. Numerical modeling of this problem requires a parallelisation of an essentially serial algorithms and elimination of numerical bottlenecks. The main challenge to overcome is parallelisation of the globally non-local mathematical model. This thesis presents a numerical solution for elimination of numerical bottleneck associated with the non-local nature of the mathematical model. The accuracy and performance of the parallel code is identified by back-to-back testing with a similar serial version.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.