Realization of All-Optical Digital Amplification in Coupled Nonlinear Photonic Crystal Waveguides

Abstract

Abstract-In this conceptual study, all-optical amplification of the light pulses in two weakly coupled nonlinear photonic crystal waveguides (PCWs) is proposed. We consider two adjacent PCWs, which consist of line defects in a 2D square lattice of periodically distributed circular rods made from dielectric material with Kerr-type nonlinearity. Dispersion diagrams of the PCW's symmetric and antisymmetric modes are analyzed using a recently developed analytical formulation. The operating frequency is properly chosen to be located at the edge of the PCW's dispersion diagram (i.e., adjacent to the photonic crystals low-energy band edge), where in the linear case no propagation modes are excited. However, in case of a nonlinear medium when the amplitude of the injected signal is above some threshold value, solitons are formed propagating inside the coupled nonlinear PCWs. The near field distributions of the propagating light pulse inside the coupled nonlinear PCWs and the output power of the received signal are numerically studied in a detail. A very good agreement between the analytic soliton solution based on the nonlinear Schrödinger equation and numerical result is obtained. Amplification coefficients are calculated for the various amplitudes of the input signals. The results vividly demonstrate the effectiveness of the weakly coupled nonlinear PCWs as an all-optical digital amplifier.

Realization of true all-optical AND logic gate based on nonlinear coupled air-hole type photonic crystal waveguides

“…Other two modes are not propagating. The threshold amplitude could be calculated from the relation [12,21]:…”

“…Its enhancement is accounted for by multiplying (3) with the square of the slowdown factor -in our case slowdown factor is equal to 16. The coe cient  takes into account the weakening of the nonlinearity due to the existence of air holes in the planar background material [21]. If we x , E y ) of the three C-PCWs as shown in Fig.…”

“…This means that, when operating frequency of the CW signal launched in Port 2 is located su ciently close to the photonic band edge, the weak signals injected into Port 1 and/or Port 3 are becoming capable to overcome the amplitude threshold and a soliton can be generated with amplitude and shape that is completely defined by the CW signal injected into Port 2. In other words, the weak input pulse just triggers the creation of a stable soliton with predefined amplitude yielding a complete regeneration of the input signal pulse prior (and during) the proposed optical digital signal processing [21,30,31]. Note that within the context of the aforementioned "digitalization" Port 2 can be viewed as an "enable pin" of the proposed logic gate where the CW signal will act as the "enable signal" common in digital electronics.…”

“…PhC guarantee a good confinement of the light in the slow light regime, which is a necessary condition for the enhancement of the nonlinear e ects [18]. The idea of band-gap transmission was already successfully applied within earlier conceptual studies where we proposed an amplification e ect of the signal in both, subwavelength metallic waveguides [19] and coupled PhC waveguides (C-PCWs) [20,21].…”

Flat-band localization and self-collimation of light in photonic crystals

“…Similar to electronic bands in solids, photonic bands exhibit band gaps where photonic states are prohibited, resulting in the prohibition of light propagation in a certain frequency range. Owing to the existence of photonic band gaps, PCs have been widely exploited as waveguides, [1][2][3][4][5][6] solar cells, [7][8][9][10][11][12] lasesr 13-20 etc. In particular, one intriguing aspect of PCs is a localization of light, where a primary approach is to introduce a defect or imperfection to a PC that leads to localized modes at the defect, regarded as analogous to microcavity modes.…”