**1. Introduction**

210 Optical Communications Systems

Voges, E. and Peteramann, K., (2002), *Optische Kommunikationstechnik - Handbuch für* 

Venghaus, H., (2006), *Wavelength Filters in Fibre Optics,* Springer, Berlin.

*Wissenschaft un Industrie* Springer-Verlag, Berlin.

Recently, photonic crystals (PCs) have attracted great interests due to their potential ability of controlling light propagation with the existence of photonic bandgap (PBG), and the possibilities of implementing compact nanophotonic integrated circuits. Some of the most successful structures are based on planar PCs. In such structures, the optical field is confined, horizontally, by a PBG provided by the PC and, vertically, by total internal reflection due to refractive index differences. Various PC components, such as, waveguides, bends, Y splitters, directional couplers, low crosstalk intersections and all-optical switches have already been realized. These basic building blocks can be combined to realize complete circuits with various optical functions within an extremely small area. One of the most important fields for ultra-dense integrated circuits is optical communications. A key component in modern optical communications systems is a wavelength division multiplexer (WDM). This component is needed to divide and combine different wavelength channels each carrying an optical data signal. Traditionally, WDM components are realized using thin-film filters, fiber Bragg gratings (FBG), or arrayed waveguide gratings. However, such devices are not convenient for ultra-dense integration. Various concepts for realizing a WDM component utilizing the extraordinary properties of PCs have recently been proposed. These ideas include optical micro-cavities, multimode self-imaging waveguides, and superprisms, but we focus on the components which are based on the interaction of the PC micro-cavities with the waveguides.

The chapter is organized as follows: In Section 2, the hybrid waveguides are introduced and analyzed using coupled-mode theory (CMT) and the finite-difference time-domain (FDTD) methods. First, the resonance frequencies and the field distribution of the resonance modes have been analyzed, then the hybrid waveguides are introduced and analyzed using FDTD and CMT methods, and the conditions which lead to quasi-flat and Lorentzian transmission spectrum will be presented. Finally, the Fundamental approach to low cross-talk and wideband intersections design which is based on the orthogonal hybrid waveguides is presented and analyzed using CMT and FDTD methods. It will be shown that when the phase-shift of the electromagnetic waves traveling between two adjacent PC coupled cavities is approximately equal to ( 1/2) , *k* the best performance for the intersection can be achieved. In addition it will be shown that simultaneous crossing of ultra-short pulses is

Design and Modeling of WDM Integrated Devices Based on Photonic Crystals 213

hexagonal lattice of dielectric rods in air. The rods have lattice constant *a*, radius *r a* 0.20 , and refractive index 3.4. *nrod* This structure prohibits propagation of TM light

PBG regions of the PC structure, the MIT Photonic-Bands package (http://abinitio.mit.edu/mpb) is used. In order to couple energy into the cavity, it is necessary to transfer energy through the walls of the PC. Incident light can transfer energy to the resonant mode by the evanescent field across the array of rods. The setup is shown in Fig. 1. To compute the resonant frequencies, we consider a finite-sized 13 21 PC in which a single rod has been removed. We send a wide-spectrum plane wave pulse with TM polarization at the incident angle of around 15 respect to the z-axis. On the other side of the PC, the field amplitude is monitored at a short length, marked as ''Monitor''. This configuration facilitates identifying of the resonance peaks of transmission spectrum, especially in some degenerate states. In this configuration the excitation has a Gaussian profile centered at

*c a* which extends beyond the edges of the

*c a* To determine the

(in-plane magnetic field) in the frequency range 0.280 to 0.452 (2 / ).

 0.6 (2 / ) 

PBG. The resonant frequencies of the cavities are plotted as a function of the cavity radius in Fig. 2. This figure shows that as the radius of the cavity is reduced to 0.15 , *a* due to the increasing perturbation, a resonant cavity mode appears at the bottom of the PBG (Villeneuve et al., 1996). As the cavity radius is further reduced, since the cavity involves removing dielectric material in the PC, based on perturbation theorem, a higher frequency resonant mode is obtained (Joannopoulos et al., 2008), and eventually reaches

( *Ey* ) distributions of the resonant mode is shown in Fig. 3-(d) for the case 0.1 . *dr a* We name this state as "monopole", because it has no nodal lines in the central (cavity) rod. By increasing the cavity radius to 0.25 , *a* three triply-degenerate dipole states appears at the top

Fig. 1. The used set up for determining the resonance frequency of the cavity states in PC of

of the PBG (the field distributions are shown in Fig. 3-(a) for the case 0.3 *dr a* ).

*c a* when the rod is completely removed. The corresponding electric-field

 0.37 (2 / ) 

 0.3953 (2 / ) 

hexagonal lattice.

*c a* and a width of

possible. In Section 3, a three-port high efficient CDF with a coupled cavity-based wavelength-selective reflector is introduced and analyzed. According to the theoretical theory using CMT in time, the performance of the proposed CDF will be investigated and the conditions which lead to 100% drop efficiency will be extracted. The performance of the designed filter will also be calculated using the 2D-FDTD method. The simulation results show that the designed CDF has a line-width of 0.78*nm* at the center wavelength 1550 , *nm* and also a multi-channel CDF with channel spacing around 10*nm* (1 ) *nm* with inter-channel crosstalk below 30*dB* ( 15 ) *dB* is possible. These characteristics make the proposed CDF suitable for use in WDM optical communication systems.
