Modal analysis of spatial pattern formation in fused silica under ultraviolet irradiation

Focused laser light is used as part of the photolithography process. Finer-resolution applications demand smaller-wavelength light, but this higher-energy light causes compaction of the lens glass. This changes its index of refraction, eventually rendering the lens unusable. The underlying model requires the use of Maxwell’s equations with a varying index of refraction coupled to a nonlinear constitutive compaction law. By modeling the light wave in the paraxial limit, one obtains a nonlocal partial integrodifferential equation for the amplitude. Stability analysis is performed in the steady and quasi-steady cases, and the results show how the instability depends on physical parameters in the problem. The results compare favorably with experimental analyses of the failure length and time scales and provide simple laws connecting the relevant failure scales.