Thermal Behavior of Waveguide Gratings

We investigate the design of binary grating structures, e.g. resonance waveguide filters (RWFs), with subwavelength feature sizes, taking the temperature dependence of different material parameters into account. Our final goal is to demonstrate devices with athermal operation. We design the binary grating structures to be made in polymer substrates, such as polycarbonate (PC), due to their potential for low cost, mass fabrication. The high thermal expansion coefficient (TEC) of polymers, compared to inorganic optical materials, enhances the thermal sensitivity of the grating structures. The gratings are designed using Fourier Model Method (FMM) by considering both thermal expansion and thermo-optic effects on the resonance wavelength shift. The fabrication of RWF structures is proposed by e-beam lithography, creating a master stamp and copying the structures into a polymer substrate by some replication techniques, followed by an ALD deposition of TiO2. When the resonance waveguide grating RWG is designed for nearly room temperature operation at a peak wavelength of 633 nm with a full width half maximum FWHM of 3 nm (TM mode reflectance), the peak wavelength shifts 0.2 nm /5C when only the TEC is taken into account. However, taking into account also the thermo-optic coefficients TOCs of PC and TiO2, the peak position shifts to 0.4 nm/ 5C on the opposite side of spectral central wavelength. Thus the overall shift reduces to 0.2 nm /5 C, illustrating partial athermalization. It was also observed that thermo-optic coefficient TOC contributed more significantly than TEC effect. The wavelengths shift was almost linear with respect to temperature for both effects and showed slopes of 0.0673, 0.0422 and 0.02352 for TOC, TEC and combined effects, respectively.