Abstract
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 0.4λ/n, where λ is the wavelength in free space and n 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 (n=3.47) in 2D media FWHM=0.44λ/n=0.127λ. We also show that half-pitch ML is able to resolve at half-maximum two close point sources separated by a 0.3λ distance.
Highlights
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
We show that in the quadratic- and secant-index waveguides a minimal mode width is 0.4λ/n, where λ is the wavelength in free space and n is the refractive index on the fiber axis
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
Summary
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. Modelling conducted in [11] has shown that a 2D photonic-crystal slab with permittivity ε = 12 composed of a triangular array of circular holes of radius r = 0.4a (a is the hole array period) can be used as an imaging lens for wavelength λ = a/0.3 In this case, a point source is imaged as a focal spot of size 0.3λ, whereas two point sources placed 0.5λ apart are resolved by the 20% criterion. For a 2D Mikaelian lens, we show that a point source is imaged near the lens surface as a focal spot of size FWHM = 0.12λ (full width at half maximum) This value is close to the diffraction limit for silicon (n = 3.47) in 2D media FWHM = 0.44λ/n = 0.127λ. Solutions in the graded-index planar waveguide that have no constraints on the number of turning points of the refractive index function
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