An efficient technique for the design of an arrayed-waveguide grating with flat spectral response

The spectral response of the arrayed-waveguide grating (AWG) plays an important role in optical networks. Ideally, the grating should have a rectangular transfer function to reduce the need for accurate wavelength control and achieve low crosstalk. In this paper, a new technique for designing an AWG with flat spectral response is presented. The problem of the optimization of the transfer function is reduced to that of adjusting the arrayed waveguide lengths and their relative positions on the edge of the free propagating regions in order to minimize a certain error function. As a result, the waveguide lengths and their positions are determined using a rigorous mathematical procedure. The resultant transfer function is flat with low sidelobes

Numerical study of the fabrication tolerance of conventional and MMI-flattened AWGs

In this letter, the fabrication tolerance of conventional and multimode interference (MMI)-flattened arrayed waveguide gratings (AWGs) is compared. It is shown that the crosstalk of an MMI-flattened AWG is approximately equal to that of a conventional AWG with the same 3-dB bandwidth. However, the dispersion of the MMI-flattened AWG is greater than that of the conventional one and this poses limitations in the maximum bit rate in a cascade of MMI-flattened AWGs. © 2004 IEEE

A new formulation of coupled propagation equations in periodic nanophotonic waveguides for the treatment of Kerr-induced nonlinearities

Nonlinear phenomena could be used to implement important signal processing functionalities in future nanophotonic integrated optical devices. In this paper, a semi-analytical model incorporating the influence of Kerr-induced nonlinearity in the propagation of an optical signal inside a periodic nanophotonic waveguide is derived. The approach consists of a system of nonlinear coupled mode propagation equations and is applicable to both single and multimode waveguides. The influence of the mode group velocity on the value of the self-phase modulation coefficient gamma is analyzed and the impact of higher order nonlinear terms is also investigated both at the middle and edge of the guided band. The model is also applied to estimate the nonlinear coupling coefficients of a photonic crystal waveguide coupler and provides an efficient method to analyze the influence of nonlinear phenomena in periodic nanophotonic waveguide devices. © 2007 IEEE

Performance analysis of differential-phase-shift-keying optical receivers in the presence of in-band crosstalk noise

In-band crosstalk can pose important limitations in an all-optical wavelength-division-multiplexed (WDM) network. Recent studies have demonstrated that differential phase shift keying (DPSK), can tolerate higher in-band crosstalk-noise levels compared to amplitude shift keying (ASK). In this paper, the performance of a DPSK receiver, limited by in-band crosstalk noise, is studied theoretically. The model takes into account both the in-band crosstalk noise as well as the amplified-spontaneous-emission (ASE) noise of the optical amplifiers. The model is based on the evaluation of the moment-generating function (MGF) of the decision variable through which, the error probability (EP) can be calculated by applying the saddle point approximation. This provides a rigorous model for the evaluation of the EP of a DPSK receiver in the presence of ASE and in-band crosstalk noises. In the absence of the ASE noise, a closed-form formula for the EP is also given that is useful for estimating the error floor set by the in-band crosstalk noise

A population dependent diffusion model with a stochastic extension

Diffusion modeling is rather broad in nature, and is important in the areas of estimation and forecasting. Conventional models do not incorporate parameters that explicitly take into account the size of the population, or, equivalently, the size of the potential market. As a consequence, the models often fail to provide accurate forecasts, especially when the diffusion process is in the take-off stage. Furthermore, since diffusion is not a strictly deterministic process, forecasts should provide a measure of the underlying uncertainty of the process by incorporating a stochastic process into the formulation of the models. The aim of the present work is to fill this gap by proposing an aggregate diffusion model, the "population" diffusion model (PDM), which incorporates the potentially varying market size as a function of the corresponding population. This model realization provides more accurate estimations and future forecasts of the diffusion process, especially when compared to the conventional aggregate diffusion models. © 2012

Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using coupled mode theory

Photonic crystals (PCs) are a promising technology for the realization of high-density optical integrated circuits. PC-based couplers have been proposed as a compact means of achieving wavelength multiplexing and demultiplexing. However, the performance of such devices can be limited by fabrication imperfections such as rod size nonuniformities. In this paper, coupled mode theory (CMT) is applied in order to study the implication of the variation of the size of the rods. 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 does not require excessive computational time. Using CMT, the relation between the size nonuniformities and the coupler's insertion loss and extinction ratio is analyzed. It is shown that even a small size variation of the order of 2%-3% can degrade the performance of the device. © 2005 IEEE

Frequency dependence of the coupling coefficients and resonant frequency detuning in a nanophotonic waveguide-cavity system

Waveguide-cavity interactions may find important applications in future nanophotonic devices. This paper provides a detailed derivation of the evolution equation of the amplitude of a cavity mode coupled to a waveguide, starting from Maxwell's equations and using the reciprocity relations. The analysis applies to both constant cross-section and periodic waveguides as well. Unlike previous studies, the analysis enables the estimation of the frequency dependence of the coupling coefficients. It is also confirmed that the waveguide-cavity coupling causes a detuning of the resonant frequency of the cavity mode. The detuning is estimated in the case of a photonic crystal waveguide-cavity system and it is shown that it can be significant especially if the structure is intended for filtering applications. The analysis is generalized to the case of a multimode or multiple cavities and provides a useful tool in the analysis of devices based on coupled cavities. © 2006 IEEE