Theoretical Study Of Long-Period Grating In Slab Waveguides

The relevant theories for long-period waveguide grating (LPWG) are demonstrated that include planar wavguide theory, coupled-mode theory, waveguide grating theory, perturbation analysis and transmission line method. On the basis of these theories, the coupled-mode equation and phase-matching condition suitable for LPWG are derived.To demonstrate the effect of different materials on the LPWG, two kind of polymers: Bis-benzo-cyclobutene (BCB) and Epoxy-novolak-resin (ENR) are selected as both guiding layer and grating materials, with the polymethyl-methacrylate (PMMA) as the cladding material and with the silicon dioxide on silicon (SiO2/Si) as the substrate. The principle of designing an optimized LPWG is demonstrated in detail and the effect of the LPWG parameters on the power transmission spectrum is also described from the role of the application of LPWG as a gain flattening device for erbium-doped filter amplifier (EDFA).Our results cover both TE and TM modes. Using C program and MATLAB language, single mode condition of LPWG with two kinds of key materials is obtained. The dependence of grating period on the waveguide layer thickness and the dependence of the maximum attenuation (dip) on the grating period in transmission spectrum i. e. the so-called phase-matching curve, were calculated. The effect of the grating period, the waveguide thickness, the grating height and length on the dip and FWHM are discussed. In addition, the dual-resonance and over-coupling phenomenon are also explained.