Investigation of two-wave mixing in arbitrary oriented sillenite crystals

A generalized systematic description of the Two-Wave Mixing (TWM) process in sillenite crystals allowing for arbitrary orientation of the grating vector is presented. An analytical expression for the TWM gain is obtained for the special case of plane waves in a thin crystal (|g|d«1) with large optical activity (|g|/?«1, g is the coupling constant, ? the rotatory power, d the crystal thickness). Using a two-dimensional formulation the scope of the nonlinear equations describing TWM can be extended to finite beams in arbitrary geometries and to any crystal parameters. Two promising applications of this formulation are proposed. The polarization dependence of the TWM gain is used for the flattening of Gaussian beam profiles without expanding them. The dependence of the TWM gain on the interaction length is used for the determination of the crystal orientation. Experiments carried out on Bi12GeO20 crystals of a non-standard cut are in good agreement with the results of modelling.

Resonant two-wave mixing in photorefractive materials with the aid of dc and ac fields

A recently predicted resonant effect for the enhancement of two-wave mixing in photorefractive materials is investigated. The resonance occurs when the frequency of the applied ac field agrees with the eigenfrequency of the excited space-charge wave. Experimentally a clear resonance is found, as predicted by the theory, for high dc electric fields, but the resonance is smeared out for lower fields. A modified theory, taking into account the second temporal harmonic of the space-charge wave, shows good agreement with the experimental results.

Observations of diffraction and self diffraction effects during two wave mixing in a nematic liquid crystal

We report observations of the diffraction pattern resulting when a nematic liquid crystal is illuminated with two equal power, high intensity beams of light from an Ar+ laser. The time evolution of the pattern is followed from the initial production of higher diffraction orders to a final striking display arising as a result of the self-diffraction of the two incident beams. The experimental results are described with good approximation by a model assuming a phase distribution at the output plane of the liquid crystal in the form of the sum of a gaussian and a sinusoid.

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.

Two-wave mixing in BTO in the presence of detuning

The gain of a weak signal beam is measured in the usual two-wave mixing configuration in a photorefractive BTO crystal by varying a set of parameters, namely the applied electric field, the detuning, the beam ratio and the input intensity of the pump beam. All the experimental results are shown to be in good agreement with a theory based on that of Kukhtarev et al.

Amplification of temporally modulated signal beams via two-wave mixing in Bi12SiO20

A theoretical analysis of two-wave mixing in a BSO crystal is developed in the undepleted-pump approximation for a modulated signal beam. It is shown that, for a modulation of high enough frequency, significant ac amplification is possible at three distinct values of pump-beam detuning. A signal beam that is amplitude modulated by a square wave is analyzed by means of the theory, and experimental results are presented in confirmation of the analysis. Finally, it is shown that in the presence of absorption the optimum detunings for dc and ac amplification are different.

Observations of Spatial Subharmonics arising during Two-Wave Mixing in BSO

During two-wave mixing experiments in BSO, output beams have been observed which result from diffraction of the pump beams from subharmonics of the grating vector recorded within the crystal. The subharmonic beams are characterised as a function of pump beam detuning and electric field, and our observations are contrasted with those reported earlier.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Band-limited airy pulses for invariant propagation in single mode fibers

By spectral analysis, and using joint time-frequency representations, we present the theoretical basis to design invariant band-limited Airy pulses with an arbitrary degree of robustness, and an arbitrary range of single mode fiber chromatic dispersion. The numerically simulated examples confirm the theoretically predicted pulse partial invariance in the propagation of the pulse in the fiber.

The throughput order of multicast traffics with physical-layer network coding in random wireless ad hoc networks

This paper attempts to address the effectiveness of physical-layer network coding (PNC) on the throughput improvement for multi-hop multicast in random wireless ad hoc networks (WAHNs). We prove that the per session throughput order with PNC is tightly bounded as T((nvmR (n))-1) if m = O(R-2 (n)), where n is the total number of nodes, R(n) is the communication range, and m is the number of destinations for each multicast session. We also show that per-session throughput order with PNC is tight bounded as T(n-1), when m = O(R-2(n)). The results of this paper imply that PNC cannot improve the throughput order of multicast in random WAHNs, which is different from the intuition that PNC may improve the throughput order as it allows simultaneous signal access and combination.

Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA

Simultaneous conversion of the two orthogonal phase components of an optical input to different output frequencies has been demonstrated by simulation and experiment. A single stage of four-wave mixing between the input signal and four pumps derived from a frequency comb was employed. The nonlinear device was a semiconductor optical amplifier, which provided overall signal gain and sufficient contrast for phase sensitive signal processing. The decomposition of a quadrature phase-shift keyed signal into a pair of binary phase-shift keyed outputs at different frequencies was also demonstrated by simulation.

Nonlinear soliton propagation in a few mode optical fibre

We experimentally demonstrate adiabatic soliton propagation in the fundamental mode of a few mode optical fibre and more complex behaviour in a higher order mode, indicating that the impact of nonlinearities differs for each mode.