Investigation of the 1D symmetrical linear graded superconductor-dielectric photonic crystals and its potential applications as an optimized low temperature sensors

Based on the Transfer Matrix Method (TMM) and the two fluid model for a superconductor and by taking account of the thermal expansion effect and thermo optical effects, we theoretically investigates the transmittance spectra of a one dimensional superconductor -dielectric photonic crystal (PC) designed as ((HLS)5/(SLH)5) made up of a BiGeO12(H), SiO2(L) and YaBO2CuO7 (S). The transmittance spectra shows that the system realizes a tunable filter which depends on a nonlinear relation with temperature. It's found that the symmetrical application of a linear deformation d(m) = d0+(m-1).δd(m) where d0 is the initial thickness of the layer m, δd(m) is the elementary added thickness at each layer. This linear gradation of the thickness permits to improve the temperature sensitivity of the system which acts as an optimized low temperature sensor.