By solving Helmholtz equations, relationships to describe propagating modes in an arbitrary graded-index planar waveguide are\r\nderived. We show that in the quadratic- and secant-index waveguides a minimal mode width is 0.4?/n, where ? is the wavelength\r\nin free space and n is the refractive index on the fiber axis. By modeling in FullWAVE, we show that the high-resolution imaging\r\ncan be achieved with half-pitch graded-index Mikaelian microlenses (ML) and Maxwellââ?¬â?¢s ââ?¬Å?fisheyeââ?¬Â lenses. It is shown that using\r\na 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\r\n0.12?. This value is close to the diffraction limit for silicon (n = 3.47) in 2D media FWHM = 0.44?/n = 0.127?.We also show that\r\nhalf-pitch ML is able to resolve at half-maximum two close point sources separated by a 0.3? distance.
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