Theoretical investigation of adjustable period sub-wavelength grating inscribed by TE0 waveguide modes interference lithography

Abstract

Sub-wavelength grating is a critical element in micro and nano-photonics. So its fabrication and application have attracted a great deal of research attention. While the existing lithography technologies of sub-wavelength grating fabrication have some insufficient points, such as high cost, low output, technical complexity, or difficult to change the period of the sub-wavelength grating. In this paper, an adjustable period and large area sub-wavelength grating with low cost and maskless is proposed and theoretically realized. The sub-wavelength grating is inscribed by the interference between two TE0 waveguide modes, where the TE0 waveguide mode is existent in an asymmetric metal-cladding dielectric waveguide structure excited by the prism coupling method. The dispersion curve of TE0 waveguide mode, the relationship between the period of the sub-wavelength grating and the exciting light source, the refractive index of the prism and the photoresist, especially the thickness of the photoresist are theoretically analyzed in detail. The distribution of the interference optical field of TE0 waveguide mode in the multilayer structure including metal film, photoresist and air layer is numerically simulated using the finite element method. The shorter the exciting light wavelength with the identical photoresist condition, the smaller the period of sub-wavelength grating inscribed by TE0 waveguide modes interference lithography is. For further studying the influences of refractive index and thickness of photoresist and the refractive index of the prism on the period of sub-wavelength grating, the exciting light with 442 nm wavelength and the Ag matel film are used. The period of sub-wavelength grating is smaller with thicker photoresist film, when the refractive indexes of photoresist and prism are the same. The larger refractive index of photoresist is beneficial to inscribing the sub-wavelength grating with smaller period when the refractive index of prism and the thickness of photoresist are identical. The prism with higher refractive index can provide wave vector-matching condition with lager propagation constant, and can inscribe sub-wavelength grating with smaller period. Compared with surface plasmons interference lithography which needs the thicker photoresist film due to the finite penetration depth of SPs, TE0 waveguide modes interference can realize adjustableperiod sub-wavelength grating writing for thicker photoresist condition by changing exciting light source, the refractive index of prism, the refractive index of photoresist and especially the thickness of photoresist. The realization of adjustable period sub-wavelength grating inscribed by TE0 waveguide modes interference lithography will provide important theoretical support for reducing the fabrication cost of sub-wavelength gratings and broadening the application scope of sub-wavelength grating.