High Resolution through Graded-Index Microoptics

By solving Helmholtz equations, relationships to describe propagating modes in an arbitrary graded-index planar waveguide are derived. We show that in the quadratic- and secant-index waveguides a minimal mode width is 0.4 , where is the wavelength in free space and is the refractive index on the fiber axis. By modeling in FullWAVE, we show that the high-resolution imaging can be achieved with half-pitch graded-index Mikaelian microlenses (ML) and Maxwell’s “fisheye” lenses. It is shown that using a 2D ML, the point source can be imaged near the lens surface as a light spot with the full width at half maximum (FWHM) of 0.12λ. This value is close to the diffraction limit for silicon ( ) in 2D media λ. We also show that half-pitch ML is able to resolve at half-maximum two close point sources separated by a 0.3λ distance. 1. Introduction Recent advances in microoptics and nanophotonics have made possible the focusing of coherent laser light into a subwavelength spot or the superresolution imaging of a point source of light. The subwavelength focusing beyond the diffraction limit of , where is the wavelength in free space and is the material refractive index at the focus, can be performed using a superlens [1]. In 2D case, instead of conventional diffraction limit one must use . This value can be obtained after replacing the Airy disk by sinc-function sin . The superlens is a 2D planar plate made up of the metamaterial that comprises alternating metallic and dielectric layers. The electric permittivities of the layers are selected so that an effective refractive index of the composite material be equal to . Experiments on the superresolution through superlenses were reported in [2, 3]. In the experiments, a superresolution of was achieved [2]. A similar experiment conducted in [4] with a subwavelength silver layer operating as a superlens has shown that two lines separated by a 145？nm distance can be resolved when illuminated by UV light of wavelength 365？nm, thus producing a superresolution of . A far-field hyperlens reported in [5] was able to resolve two lines of width 35？nm spaced 150？nm apart for a 365？nm wavelength, again achieving a superresolution of . Note, however, that a hyperlens modelled in the form of a grating [6] was shown to achieve a superresolution of at the imaging plane found apart from the surface. Apparently, the absorption and scattering of light by metamaterial that occurs in real experiments was disregarded in modelling. This argument was indirectly verified by results reported in [7], in which the laser light was focused with a