**Dynamic All Optical Slow Light Tunability by Using Nonlinear One Dimensional Coupled Cavity Waveguides**

Alireza Bananej1, S. Morteza Zahedi1,

S. M. Hamidi2, Amir Hassanpour3 and S. Amiri4

*1Laser and Optics Research School, NSTRI* 

*2Laser and Plasma research Institute, Shahid Beheshti University, Evin, Tehran 3Department of physics, K. N. Toosi University of Technology, Tehran 4Institute for Research in Fundamental Sciences, Tehran I. R. Iran* 

#### **1. Introduction**

30 Photonic Crystals – Innovative Systems, Lasers and Waveguides

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, IEEE

D.S. Song, Y.J. Lee, H.W. Choi, Y.H. Lee, Appl. Phys. Lett. 82 (2003) 3182.

Photon. Technol. Lett. 10 (1998) 6.

Light propagation at slow speed, delaying light, has a tremendous role in a wide range of advanced technology from peta-bit optical networks to even laser fusion technology [1,2]. Recently, it was realized that delaying of an optical signal is useful for a number of applications such as optical buffering, signal processing, optical sensing and enhancement of optical nonlinearity in materials [3]. Also, as a consequence of important role of fiber lasers in laser fusion technology, coherent beam combining of several fiber lasers for achieving high power output is a crucial problem in future fusion technology. This task can be overcome by using proper engineered photonic components for achieving specific group delay time [2].

Generally, the speed of light is related to the refractive index of the propagation medium. From the basic definition of group velocity, <sup>g</sup> d v dk , It can be shown that group velocity of light in a medium can be derived as [4]:

$$\mathbf{v}\_{\&} = \frac{\mathbf{d}\,\rho\mathbf{o}}{\mathbf{d}\mathbf{k}} = \frac{\mathbf{c}}{\mathbf{n} + \rho(\frac{\mathbf{d}\mathbf{n}}{\mathbf{d}\,\rho})}$$

Where, is the light frequency, *c* is the speed of light in vacuum, *n* is the refractive index of the medium and *k* is the propagation constant. Evidently, as a reason of limited optical materials and hence, limited refractive indices, it is not possible to slow down the speed of light sufficiently or adjust it to a specific desired value. However, it is obvious that by controlling the rate of refractive index changing, dn d , the speed of light can be controlled and

in a special case when dn <sup>1</sup> d , slow down the speed of light can be obtained sufficiently.

Dynamic All Optical Slow Light Tunability

be tuned to any desired values.

The basic structure for 1D-NCCW is as:

**2. Theory** 

structure.

index material.

by Using Nonlinear One Dimensional Coupled Cavity Waveguides 33

In the following chapter we will investigate the optical properties of the resonance modes such as, group delay, group velocity and bandwidth-delay product (BDP), in nonlinear one dimensional CCWs (1D-NCCWs) which defect mediums consist of intensity dependentrefractive index material. It can be seen by tuning the input optical intensity, the interested parameters such as, group velocity, delay time and specially delay-bandwidth product can

1D-NCCW is formed by placing optical resonator in a linear array, to guide light through whole of the structure by photon hopping between adjacent resonators. As a result of overlapping the evanescent field in the defect medium, cavity zone, electric field enhancement in this region can be obtained. Tight binding (TB) approximation (like using it in solid state physics) is used to describe the mechanism of waveguiding of the

NNN n (HL) HD(HL) HD(HL) H Glass 0

Where, *H* and *L* denotes for high index (TiO2) and low index (SiO2) materials as *nH*=2.33 and *nL*=1.45, respectively for construction the basic resonators. Also, *N* is number of the repetition for the basic structure. It can be shown that by increasing *N,* light confinement in

As an example, defect layer, *D* is consist of CdSe which is an intensity dependent refractive

The input pulse comes from left hand and during passing through whole of the 1D-NCCW, experiences delay time. This phenomenon is as a reason of reduction the speed of light propagation and confinement in the defect layer. It can be seen the enhancement of the

Nonlinear refraction is commonly defined either in terms of the optical field intensity *I* as [23]:

nn I d d0 

(1)

defect layer will be increased. Fig.1. Shows the basic structure of 1D-NCCW.

Fig. 1. Schematic illustration of 1D-NCCW with two defects.

electric field component of the incident light in the defect layer [21].

During recent years different approaches have been done by scientists for generating of slow light. Electromagnetically induced transparency (EIT) is the first technique for achieving group delay and slow light in vapor mediums [5-9]. The group delay of incident pulses in an EIT system was studied first by Kasapi *etal* in lead vapor. Also, in 1999 Hau *etal* showed 7.05 s delay in an EIT system which consists of condensed cloud of sodium atoms [10].

As a reason of complicated situation for slow light generation in EIT systems, it is important for real applications that these phenomena could be occurred in room temperature and in compact and solid materials.

Therefore, Spectral holes due to coherence population oscillation (CPO) in room temperature and in solids, can be considered as one of the interesting methods for slow light generation [11]. Slow light generation based on CPO has been studied in various material systems. So, ultraslow light, 57.5m/s, in ruby crystal has been studied by Boyd's group at Rochester [12].

On the other hand, during recent years a new kind of optical waveguides have been considerable attracted both theoretical and experimental attention due to their intense applications not only in data transferring but also in optical data processing [13]. Coupled cavity optical waveguides (CCWs) can be considered as the latest proposal mechanism for optical waveguiding which have been introduced by Yariv *etal* at Caltech [14]. This new kind of waveguides is based on the periodic dielectric structures as photonic crystals, which is separated by the high quality factor cavities that are coupled to each of the nearest neighbor in multiple spatial dimensions [15]. Due to existence of the cavities along the structure and as a result of the overlapping of the evanescent fields, light can be propagated through the CCWs [16]. Actually, it was investigated theoretically and experimentally that CCWs exhibit more advantages over conventional optical waveguides. One of the most important features of CCW is that due to strong optical confinement in defect medium, and high slope of transmission at resonance wavelengths, group velocity at the edge of each resonance modes can be reduced considerably [17]. Slow light generation in CCWs offers several practical advantageous like, design freedom, direct integration with other optoelectronics devices and ability to slow down light in a desired region of wavelengths at room temperature [18].

On the other hand, it should be noticed that the CCWs structures for stopping light suffer a fundamental trade off between the transmission and the optical delay bandwidth [19,20]. Therefore, in the field of slow light technology, delay-bandwidth product is an important parameter which should be considered greatly.

Furthermore, from system points of view, in future photonic circuits, adjustability of the optical properties of components is a great and important bottleneck which many scientists have been proposed special methods. In CCWs, the optical properties such as group velocity, dispersion and its higher order can be modulated through different mechanism such as electro optic effect, free-carrier injection and thermo optic effect [21]. As a consequence of necessity for all optical networks in future, dynamic all optical processing, controlling light by light, can be considered as one of the crucial bottlenecks for future all optical systems [22].

In the following chapter we will investigate the optical properties of the resonance modes such as, group delay, group velocity and bandwidth-delay product (BDP), in nonlinear one dimensional CCWs (1D-NCCWs) which defect mediums consist of intensity dependentrefractive index material. It can be seen by tuning the input optical intensity, the interested parameters such as, group velocity, delay time and specially delay-bandwidth product can be tuned to any desired values.
