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A study is conducted to numerically analyze the possibility of achieving nanosecond delays, near the band edges of two-dimensional (2-D) photonic crystal waveguides. The results indicated that solution propagation in photonic crystal waveguides might open a new pathway to obtain compact optical delay lines and nonlinear elements in integrated form.

The model studies the soliton-based optical delay lines and derives a continuous wave propagation. It is seen that the delay line can achieve nanosecond delay at a propagation length.

A detailed derivation of the evolution equation of the amplitude of a cavity mode, coupled to a waveguide, starting from Maxwell's equations, is provided by using the reciprocity relations. Results confirm that detuning is estimated in the case of photonic crystal cavity, coupled to a photonic crystal waveguide, showing that it is significant especially, if the structure is used for filtering applications.

The tight binding formalism is applied in the analysis of finite chains of coupled optical cavities of arbitrary length. The analytic results are compared with the numerical results of the plane wave expansion method in the case of a finite two-dimensional photonic crystal chain of coupled resonators and an excellent agreement is observed.

The implication of the variation of the size of the rods is studied by applying coupled mode theory (CMT). CMT can provide a useful insight in the effect of size variations, and unlike other numerical methods such as the finite difference time domain, it neither does nor require excessive computational time.

Fiber nonlinearities can degrade the performance of a wavelength-division multiplexing optical network. For high input power, a low chromatic dispersion coefficient, or low channel spacing, the most severe penalties are due to four-wave mixing (FWM). To compute the bit-error rate that is due to FWM noise, one must evaluate accurately the probability-density functions (pdf) of both the space and the mark states. An accurate evaluation of the pdf of the FWM noise in the space state is given, for the first time to the authors' knowledge, by use of Monte Carlo simulations. Additionally, it is shown that the pdf in the mark state is not symmetric as had been assumed in previous studies. Diagrams are presented that permit estimation of the pdf, given the number of channels in the system. The accuracy of the previous models is also investigated, and finally the results of this study are used to estimate the power limits of a wavelength-division multiplexing system. OCIS codes: 060.4230, 190.4380.

In this work, we consider nearest neighbour q-random walks on Zd for d = 1,2,3, with transition probabilities q-varying by the number of steps, 0 < q < 1, and we study under which conditions these q-random walks are transient or recurrent. Also, we define the relative continuous time q-random walks on the integers and on the two dimensional integer lattices. Moreover, we present a q-Brownian motion as a continuous analogue of the q-random walk on the integers and we study the maxima and first hitting time of this q-Brownian motion. Furthermore, we present simulations, using R statistical computing environment, of the considered stochastic processes on Zd for d = 1,2 and of the q-Brownian motion, indicating first hitting times to the origin. [ABSTRACT FROM AUTHOR]