ECE 4332 ELECTR OOPTIC DEVICES AND SYSTEMS Assignment

ECE 4332 ELECTR OOPTIC DEVICES AND SYSTEMS - Assignment Example Accompanying the evolution from copper wire or wireless connection to lightwave networks is the proliferation of new optical devices. Discoveries in optical transmitters, amplifiers, frequency converters, filters and multiplexers enable ways to generate, condition, and detect light. The study of wave interactions with periodic structures has yielded convenient methods of analysis and the results have been extended to gratings in wavelengths such as those in distributed feedback lasers, acousto-optic modulators and filters, and other diffracted waveguide devices. The fiber Bragg gratings is readily analyzed by coupled mode and transfer matrixes analysis. the two modes of the waveguide Bragg grating are the counter propagating waves in the fiber which are coupled through the grating reflection. In the absence of the grating, the spatial dependence of the polarization currents for the forward wave are proportional to. Perturbations by a grating having spatial period Ù ¨ create new sidebands that result in wave coupling i.e. exp( jÃŽ ²z)cos(2Ï€z/Ù ¨) = Â ½{exp[j(ÃŽ ²-2Ï€/Ù ¨)z]+exp[j(ÃŽ ²+2Ï€/Ù ¨)z]} and mode coupling to the backward coupling wave. Exp[-jÃŽ ²z] described by the first term on the right-hand side, occurs when -ÃŽ ²~(ÃŽ ²-2Ï€/Ù ¨). T hen the forward propagating wave is reflected (coupled) into the backward propagating wave. Coupled mode equations are readily derived upon substitution by the grating refractive index function into the wave equation +[]2E(Ù ¤)=0 where Ù ¤=koz is the normalized axial dimension and n(Ù ¤)/no=1+ÏÆ'(Ù ¤)+2h(Ù ¤)cos[2Ù ¤+2Ç ¿(Ù ¤)]. Here, no is the effective index of the propagating waves, and k0=Ù ¤onok is the nominal Bragg wave number, for constant Ç ¿, the Bragg wavelength is ÃŽ »bragg=2Ï€n0/k0. Change in the local average refractive index is defined by ÏÆ', the peak-to-peak index variation is 4h and corresponds to grating