Nonlinear slow light propagation in photonic crystal slab waveguides: theory and practical issues

In this paper, we consider the propagation of slow light optical pulses inside photonic crystal slab waveguides (PCSW) both from a theoretical and an application point-of-view. The numerical model used relies on a nonlinear envelope propagation equation that includes the effects of second and third order dispersion, optical losses and self phase modulation. Pulse propagation is examined both in the linear and nonlinear regime. It is numerically shown that for rates of 10Gb/s, the order of nanosecond delays can be achieved through the PCSW defect modes without excessive pulse broadening in the nonlinear regime. In the nonlinear case, it is shown that soliton pulses exhibit less broadening than pulses in the linear case. In comparing the linear and the non-linear case we consider launching pulses with the same initial full width at half maximum or the same RMS width. The influence of optical losses on the soliton pulse broadening factor is also incorporated and discussed providing a more practical perspective. The results demonstrate the potential of implementing a variety of linear and nonlinear signal processing applications in PCSWs, such as optical buffering

Approximate expressions for the estimation of the four-wave mixing efficiency in slow light photonic crystal waveguides

We present approximate analytical expressions for the estimation of the degenerate four-wave mixing conversion efficiency in slow light photonic crystal waveguides. The derived formulas incorporate the different effective modal areas and the frequency-dependent linear and nonlinear parameters of the pump, signal and idler waves. The influence of linear loss, two-photon absorption and free-carrier generation is also accounted for. Numerical solution of the coupled propagation equations is used to verify the validity of the proposed expressions under different values of the linear and nonlinear parameters of the waveguide. It is shown that the derived expressions provide an accurate estimation of the conversion efficiency and are thus expected to be very useful in the design of photonic crystal waveguides for nonlinear signal processing applications

Optimization of the storage capacity of slow light photonic crystal waveguides

The storage capacity of slow light photonic crystal waveguides is maximized using a systematic procedure based on the optimization of various parameters of the structure. Both optical loss and dispersion-induced broadening are incorporated into the model. The results indicate that this procedure can provide up to a threefold increase in storage capacity

Systematic optimization of the storage capacity of slow light photonic crystal waveguides

A systematic design process of slow light photonic crystal slab waveguides is presented with the aim of maximizing the storage capacity. Dispersion effects and propagation losses characteristics are included in order to increase the design accuracy. Our procedure allows the optimization of the structure at the same time by varying as many as ten design parameters. We show that storage capacities of almost 32bits at 40Gb/s and 65bits at 100Gb/s can be obtained

An Efficient Technique for the Design of an Arrayed Waveguide Grating with Flat Spectral Response

Abstract-The spectral response of the Arrayed Waveguide Grating 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 a

Designing slow-light photonic crystal waveguides for four-wave mixing applications

We discuss the optimization of photonic crystal waveguides for four-wave mixing applications, taking into account linear loss and free-carrier effects. Suitable figures-of-merits are introduced in order to guide us through the choice of practical, high efficiency designs requiring relatively low pump power and small waveguide length. In order to realistically perform the waveguide optimization process, we propose and validate an approximate expression for the four-wave mixing efficiency, which significantly alleviates our numerical calculations. Promising waveguide designs are identified by means of exhaustive search, altering some structural parameters. Our approach aims at optimizing the waveguides for nonlinear signalprocessing applications based on the four-wave mixing

Nonlinear slow light propagation in photonic crystal slab waveguides: theory and practical issues

In this paper, we consider the propagation of slow light optical pulses inside photonic crystal slab waveguides (PCSW) both from a theoretical and an application point-of-view. The numerical model used relies on a nonlinear envelope propagation equation that includes the effects of second and third order dispersion, optical losses and self phase modulation. Pulse propagation is examined both in the linear and nonlinear regime. It is numerically shown that for rates of 10Gb/s, the order of nanosecond delays can be achieved through the PCSW defect modes without excessive pulse broadening in the nonlinear regime. In the nonlinear case, it is shown that soliton pulses exhibit less broadening than pulses in the linear case. In comparing the linear and the non-linear case we consider launching pulses with the same initial full width at half maximum or the same RMS width. The influence of optical losses on the soliton pulse broadening factor is also incorporated and discussed providing a more practical perspective. The results demonstrate the potential of implementing a variety of linear and nonlinear signal processing applications in PCSWs, such as optical buffering

Accuracy of the tight binding approximation for the description of the photonic crystal coupled cavities

Coupled optical cavities are constantly attracting increased attention in telecommunication applications. For an infinite chain of optical cavities, also known as the coupled resonator optical waveguide (CROW), the tight binding approximation has been used in order to evaluate its dispersion characteristics and the modal fields. In this paper, the accuracy of the tight binding formalism is investigated for a finite chain of optical cavities of arbitrary length. This approximation allows the derivation of simple analytical formulas for the resonant frequencies and the corresponding modal fields, which involve only the resonant frequency of the isolated cavity and the coupling coefficients between two consecutive coupled cavities. The equations for the modal fields involve an expansion in terms of displaced versions of the field distribution of the mode of the isolated cavity and simple trigonometric functions. These analytical results are compared with the numerical results of the plane wave expansion method in the case of a finite photonic crystal chain of coupled resonators and an excellent agreement is observed even if the cavities are placed close together. The results clearly indicate the usefulness and accuracy of the tight binding formalism for the description of coupled optical resonators