**6. Conclusion**

Thus all the logic gates functions are implemented in non-channel photonic crystal. Selfcollimation, bending and splitting effects are used to realize logic gates. The Finite Difference Time Domain method (FDTD) gives fairly accurate results in line with the theoretically predicted concepts. The proposed design exhibits an on-off contrast ratio around 3 dB and a device size of 10x10 μm2 operating at the optical communication wavelength 1550 nm. The main advantages of all-optical logic gates are small dimensions, simple structure and high speed. These devices may turn out to be good candidate for optical computing and photonic integrated circuits.

### **7. References**

78 Photonic Crystals – Introduction, Applications and Theory

The designing of the beam splitter and the mirror requires high precision of fabrication. Any small deviation from the design of the beam splitters leads to a decay of the optical performance. For instance, a beam splitter would present a wrong phase shift, optical loss, unequal splitting or even mirror like operation if its narrow veins are unintentionally narrower or removed. The Silicon rods must be uniform, smooth and vertical at the side wall in order to maintain the collimation effect throughout the device. The optical path length of the interfering signals should be maintained equal otherwise it will lead to

Thus all the logic gates functions are implemented in non-channel photonic crystal. Selfcollimation, bending and splitting effects are used to realize logic gates. The Finite Difference Time Domain method (FDTD) gives fairly accurate results in line with the theoretically predicted concepts. The proposed design exhibits an on-off contrast ratio around 3 dB and a device size of 10x10 μm2 operating at the optical communication wavelength 1550 nm. The main advantages of all-optical logic gates are small dimensions, simple structure and high speed. These devices may turn out to be good candidate for

Fig. 12. Integrated photonic crystal based devices

optical computing and photonic integrated circuits.

**5. Challenges in fabrication** 

additional phase shift.

**6. Conclusion** 


**5** 

*France* 

**MEMS Based Deep 1D Photonic Crystal** 

Since the Bragg layers, also referred as to 1D photonic crystal, lie at the core of many optical devices, this chapter is devoted to the study of the theory underlying the design of multilayered structures [Macleod 2001]. The corresponding analytical model is explained in details in section 2 followed in the next sections, by various design examples for the shake of

Of special interest are the Silicon-Air Bragg mirrors obtained by DRIE micromachining. They are considered as an important building block leading to a wide variety of applications. First, we elaborate on the use of this building block in resonant cavities and in interferometers (section 3). Then, we apply the multilayered stack theory to a case of study for a special structure: The mode selector, covered in section 3.7). Finally, we conclude this work by highlighting about an advanced architecture of 1D photonic crystals based on

Under specific conditions, a stack of multilayered structure gives rise to nearly perfect optical reflectance, approaching 100 %, as compared to the reflectance from a single interface. This is the main characteristic that makes the interest in such structures, called Bragg reflectors or Bragg mirrors. This phenomenon of enhanced reflectivity might be explained by the fact that the presence of two (or more) interfaces means that a number of light beams will be produced by successive reflections, that may interfere constructively (or destructively, when considering anti-reflective surfaces), and the properties of the multilayered film will be determined by the summation of these beams. This might be the case in thin film assemblies. In thick assemblies however, the later phenomenon does not take place. Before going into the analytical details, we differentiate between thin and thick films. We say that the film is thin when interference effects can be detected in the reflected or transmitted light, that is, when the path difference between the beams is less than the coherence length of the light, and thick when the path difference is greater than the coherence length. Note that no interference can be observed when effects of light absorption dominate within the film, even in the case of thin films. The same film can appear thin or thick depending entirely on the illumination conditions. The thick case can be shown to be identical with the thin case integrated over a sufficiently wide wavelength range or a sufficiently large range of angles of incidence. Normally, we will find that the films on the

**1. Introduction**

illustration.

curved Bragg mirrors.

**2. Theory and modeling of Bragg reflectors** 

Maurine Malak and Tarik Bourouina

*Université Paris-Est, ESIEE Paris* 

gates based in two- and three-modes nonlinear optical fiber couplers, *Optical and Quantum Electronics*, Vol. 39, No. 14, pp. 1191-1206

