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In this Chapter, a complete design cycle of phased array lasers based on photonic crystals processed in dielectric membranes has been given. First, full-wave electromagnetic computations with the FDTD method allow us to determine a photonic bandgap of the selected passive photonic crystal lattices processed in a dielectric membrane. Second, a single- either multi-channel waveguide array is introduced into the lattice and dispersive properties of the modes within the corresponding photonic bandgap are computed. The goal is to evaluate the spectrum, where a single-mode propagation of the supermodes is possible along the channels. Third, for given geometry settings and the mode's wavelength spectrum, the above-threshold laser small-signal gain characteristic is computed with the non-orthogonal coupled mode theory. Gain computations are two-fold. In the first approach, numerical computations of an electric field envelope within a passive structure are executed with the aid of the FDTD method, while the second method is based on an equivalent effective waveguide structure. Both methods provide similar values of the optimum reflection coefficient of the

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**8** 

*Iran* 

**Employing Optical** 

**Nonlinearity in Photonic Crystals:** 

*Photonics Research Lab., Amirkabir University of Technology* 

Mohammad Danaie and Hassan Kaatuzian

**A Step Towards All-Optical Logic Gates** 

Employing nonlinear elements in photonic crystals (PCs) opens up lots of new design opportunities. In comparison to ordinary linear PC structures, using optically nonlinear elements in PCs leads to the observation of many interesting phenomena that can be utilized to design all-optical devices. Optical bistability in PCs is among the mentioned observations, which due to its many applications has attracted the researchers' attention. Many optical devices such as limiters, switches, memories can be implemented when nonlinear elements are embedded in PCs. Kerr type nonlinearity is mostly used for this purpose. In this chapter we are going to discuss the benefits of using nonlinearity in photonic crystal devices. Since most of nonlinear optical devices are either based on directional couplers (DCs) or coupled cavity waveguides (CCWs), we have focused on these two groups to provide a better insight

The first practical case of employing nonlinearity in PCs was for optical switches. Scholz and his colleagues were among the first ones to use optical Kerr nonlinearity in PCs (Scholz et al., 1998). They designed an all-optical switch using a one dimensional photonic crystal which was placed inside two cross waveguides. In their switch, a strong pump signal lateral to the PC layers made the crystal nonlinear and slightly shifted the position of the bandgap. The data signal wavelength was chosen on the bandgap edge such that it could not be placed in the shifted bandgap region (when the probe signal was present). Therefore; when no probe signal existed, the data signal could not pass through the PC layers, while when the probe was present, the shifted photonic bandgap would allow its transmission. Later the optical bistability in two dimensional nonlinear photonic crystal waveguides coupled to a micro-cavity was discussed in (Centeno & Felbacq, 2000) and it was suggested that the mentioned phenomena could be use to design all-optical switches. Mingaleev and Kivshar placed nonlinear elements in waveguides and bends to obtain optical limiters (Mingaleev & Kivshar, 2002). Meanwhile other structures were suggested by (Soljacic´ et al., 2002) and (Fan, 2002) for optical switching. Later in 2004 (Locatelli et al., 2004) and (Cuesta-Soto et al, 2004) suggested optical switches using directional couplers. Thereafter, some logic components were reported in literature such as: An optical AND gate by (Zhu et al., 2006), an all-optical PC on-chip memory implemented in (Shinya et. al., 2008), a PC half-adder

**1. Introduction** 

into their future prospects.

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Mohammad Danaie and Hassan Kaatuzian *Photonics Research Lab., Amirkabir University of Technology Iran* 
