Impact of modulational instability of partially coherent light in photosensitive optical polymers on the fabrication of optical microstructures
Photo-curable optical polymers have established for a wide range of micro-optical applications due to the great flexibility of their processing. Photolithographic patterning of these materials is often the basis for the fabrication of complex micro-optical elements and 3D microstructures. But, in the past, the optical functionality of "thick" microstructures (50 µm) fabricated by UV-lithography was often limited due to an inhomogeneous internal refractive index distribution. Experiments showed that a homogeneous exposure of an UV-sensitive polymer will not lead to a homogeneous degree of polymerization, but to waveguide-like filament patterns. For photo-initiated polymerization processes a saturable and integrating non-linear refractive index change during the exposure process is characteristic. We present a general analytic analysis which shows that this non-linear material response leads to a modulational instability (MI) of the exposure light, if a certain degree of spatial coherence is exceeded. Then, perturbations of the incident wave are growing during propagation and the wave decays into filaments with well-defined spatial modulation frequency. It will be shown that these effects are characteristic for photosensitive polymers and different from the conventional MI, e.g. in Kerr-like media. Besides MI, the geometry of the resulting 3D patterns strongly depends on the initial intensity and phase distribution. If the degree of spatial coherence is below the threshold value, initial perturbations are not amplified. Therefore, it will be shown that the choice of suitable coherence properties or the specific modification of the spatial coherence of the effective light source within the lithographic patterning is a capable method to improve the homogeneity of optical microstructures. All theoretical results could be proven successfully within experiments.