Aug 21, 2009 - some optical communication devices incorporating photonic crystals, such as thresholdless laser diodes (LDs), low-loss and sharp bend ...
PIERS Proceedings, Moscow, Russia, August 18–21, 2009
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An All Optical Switch Based on Nonlinear Photonic Crystal Microcavities N. Nozhat, A. Taher Rahmati, and N. Granpayeh Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
Abstract— In this paper, the performance of an all optical switch based on two dimensional (2-D) nonlinear photonic crystal (PC) microcavities has been demonstrated. We have used an effective numerical method based on the finite-difference time-domain (FDTD) method. It has been shown that by increasing the input signal power the refractive indices of the rods besides the waveguide are changed, due to the nonlinear Kerr effect. Therefore, the resonant frequency of the cavity shifts to a lower value, compared to that of the linear case. The performance of the switch in linear and nonlinear states for various radii of the microcavity and different distances from the waveguide have been simulated and analyzed. The distributions of the electromagnetic fields have been illustrated. The nonlinear resonant frequency of the cavity and the refractive index variations of the rods due to the Kerr nonlinearity have been derived. 1. INTRODUCTION
Recently, photonic crystals, either two or three dimensional periodic structures, have attracted many researchers’ attentions. These structures have a photonic band gap (PBG), the range of frequency that the light cannot be propagated in them. Because of their attractive properties, some optical communication devices incorporating photonic crystals, such as thresholdless laser diodes (LDs), low-loss and sharp bend waveguides, endlessly single mode fibers and Mach-Zehnder interferometers have been proposed and fabricated [1–6]. Among various devices, channel adddrop filters, which select one wavelength from the input spectrum and leaving the others, have been applicable to wavelength division multiplexing (WDM) systems. In recent years, some all optical switches based on linear photonic crystals have been proposed and fabricated. For example, tunability of the photonic band-gap (PBG) has been obtained by modulating the PC’s refractive index by electro-optic or thermo-optic effect [7–9]. Also, nonlinear photonic crystals have remarkable properties for using in the all optical information processing. For example, the bistability of the nonlinear PCs have been utilized to design optical switches, transistors, logical gates, and optical memories [10–12]. Therefore, the other useful approach for ultra-fast switching is to use nonlinear photonic crystals. In this paper, the performance of a switch in linear and nonlinear states for various radii of the microcavity and different distances from the waveguide have been simulated and analyzed by the FDTD method. The distributions of the electromagnetic fields have been demonstrated. The nonlinear resonant frequency of the cavity and the refractive index variations of the rods due to the Kerr nonlinearity have been derived. 2. NUMERICAL RESULTS AND DISCUSSION
The proposed structure, as shown in Fig. 1, consists of one waveguide and one resonant microcavity adjacent to it. The structure composed of a 15 × 15 square lattice of AlGaAs rods with linear refractive index of n0 = 3.4 and nonlinear-index coefficient of n2 = 1.5 × 10−17 m2 /W at 1550 nm wavelength. The rods are located in air with radii of r = 0.2a, where a is the lattice constant. The structure has a large bandgap for transverse magnetic (TM) fields between frequencies of 0.29(c/a) and 0.42(c/a), where c is the speed of light in vacuum. In the linear state, when the frequency of the input signal is the same as the resonant frequency of the cavity, that is f = 0.3816(c/a), the input lightwave couples to the cavity and there is no output power at port 2, as demonstrated in Fig. 2(a). By increasing the power of the input signal, the refractive indices of the rods and the resonant frequency of the cavity change, because of the nonlinearity of the rods. So, the input lightwave transmits through the waveguide, without coupling to the cavity, and there is an output power at port 2, as shown in Fig. 2(b). The normalized nonlinear frequency is 0.38. Since the defect involves removing dielectric material of the crystal, the effective refractive index of the cavity decreases and the mode moves towards the higher edge of the gap [13, 14].
Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 18–21, 2009 1579
(a)
Figure 1: Schematic of proposed nonlinear photonic crystal switch with one waveguide and one cavity besides it.
(b)
Figure 2: Electric field distribution of the photonic crystal switch at normalized resonant frequency of 0.3816 in (a) linear and (b) nonlinear states.
In linear state, by increasing the refractive index of all rods of the structure to 3.54, similar to nonlinear state, the incident light cannot couple to the cavity at f = 0.3816(c/a). This has simulated the effect of the refractive index variations of the rods by the Kerr nonlinearity. We have also investigated the effect of variation of the radius and the distance of the microcavity from the waveguide to the resonant frequency of the switch. If the cavity distance from the waveguide is decreased to 2a, the resonant frequency increases to f = 0.3832(c/a), which is due to the slight decrease in the effective refractive index of the cavity. Also, the coupling loss increases [12]. The transmittance spectrum of the structure in drop state is shown in Fig. 3. So, when we have launched a sinusoidal wave with frequency of f = 0.3832(c/a) to port 1 of the waveguide, there is no output power at port 2. By increasing the input power, the resonant frequency of the cavity decreases to f = 0.382(c/a), due to the Kerr nonlinear effect; so the input power transmits through the waveguide and exits from port 2. In this situation, the amount of increase in the refractive index of the rods is 0.1. The normalized resonant frequencies of the cavity in linear and nonlinear states for cavity distances of 3a and 2a, have been demonstrated in Fig. 4. In both cases, the resonant frequencies in the nonlinear states have been shifted to lower frequencies. Now instead of removing one rod, the radius of it is increased, which result in decreasing of the resonant frequency. By increasing the rod radius, its effective refractive index of it increases and hence the resonant frequency decreases. Therefore, the microcavity resonant frequency can be tuned by modifying the size the cavity [4]. For the cavity rod radius of r = 0.1a, the linear resonant frequency of the cavity is f = 0.3286(c/a). When we increase the input power, the photonic crystal shows its nonlinearity and the resonant frequency of the cavity decreases to f = 0.3272(c/a). Also, by increasing the refractive index of the rods to 3.6 in linear state, we can see the similar results of nonlinearity. The normalized frequencies of the cavity with r = 0.1a in linear and nonlinear states have been depicted in Fig. 5.
Transmittance (a. u.)
1 0.8 0.6 0.4 0.2 0
0.38
0.385
0.39
0.395
0.4
0.405
0.41
Normalized Frequency (c/a)
Figure 3: Transmittance spectrum of the photonic crystal switch at normalized frequency of 0.3832. The microcavity distance from the waveguide is 2a.
PIERS Proceedings, Moscow, Russia, August 18–21, 2009 1.2
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Transmittance (a. u.)
Transmittance (a. u.)
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0.8 0.6 0.4
0.8 0.6 0.4
0.2
0.2
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0.376 0.378 0.38 0.382 0.384 0.386 0.388 0.39 Normalized Frequency (c/a)
0.376 0.378 0.38 0.382 0.384 0.386 0.388 0.39 Normalized Frequency (c/a)
(a)
(b)
Figure 4: Spectrum of the resonant frequency of the microcavity at the distances of (a) 3a and (b) 2a from the waveguide. The solid and dashed lines show the resonant frequency in linear and nonlinear states, respectively. 1.2
Transmittance (a. u.)
1 0.8 0.6 0.4 0.2 0 0.32 0.322 0.324 0.326 0.328 0.33 0.332 0.334 0.336
Normalized Frequency (c/a)
Figure 5: Spectrum of the resonant frequency of the microcavity with r = 0.1a and 2a distance from the waveguide. The solid and dashed lines show the resonant frequency in linear and nonlinear states, respectively. 3. CONCLUSION
In this paper, the performance of a nonlinear photonic crystal switch has been investigated. The linear and nonlinear resonant frequencies of the microcavity for various radii of the cavity and different distances from the waveguide have been calculated. It has been shown that if the input lightwave signal frequency is the same as the resonant frequency of the cavity, there is no power at port 2. By increasing the input signal power the resonant frequency of the cavity changes, due to the Kerr nonlinear effect and hence the wave transmits through the waveguide and exits from port 2. For every case, the nonlinear resonant frequency of the cavity has been obtained. The refractive index variations of the rods due to the Kerr nonlinearity have been calculated. REFERENCES
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