Nanolithography considerations for multi-passband grating filters

The placement accuracy and resolution of direct-write patterning tools, in particular the atomic force microscope (AFM), is considered for application to fabricating multi-passband integrated optical filters. Because of its simpler fabrication a grating structure is proposed that consists of identical stripes that are non-periodically spaced. The recently developed pseudorandom encoding method from the field of computer generated holography is modified to effectively assign analog reflectances at each point along the grating by selective withdrawal and offsetting of the stripes from a periodic spacing. An example filter designed by this method has two 1.5 nm bandwidth passbands and -23 dB of rejection for lightly coupled stripes. As with single band filters, the passbands broaden as the coupling increases. A calculation of the coupling coefficient of stripes on a fundamental mode, slab waveguide indicate that stripes on the order of 100 nm in depth and width support low insertion loss, multipassband filtering applications at visible wavelengths. Lines of these dimensions patterned with an AFM on (110) silicon indicates the feasibility of fabricating these filters. These conclusions are specific to current AFM's that are limited to writing fields of 100 mu m. Increased rejection and decreased passband widths will result from incorporating precise field-stitching into future AFM's.