Full text of article: Russian language.

Abstract:
We obtained modal solutions of the Helmholtz equation for arbitrary gradient-index planar waveguide. Amplitude of the mode is represented as exponent of Tailor series, whose coefficients are determined using recurrent relations. It is shown that minimal mode width in parabolic and secant gradient-index planar waveguides is equal to 0.4 free space wavelengths, divided by refraction index on waveguide axis. Numerical simulation by FullWAVE program it is shown that gradient-index Mikaelian lens and Maxwell’s «fish eye» can create super-resolution images. For 2D Mikaelian microlens we show that point source is imaged near lens surface as light spot with size 0.12 of free space wavelength (spot size measured as FWHM – full with of half-maximum). It is less than diffraction limit for silicon with index 3.47, which equals to 0.144 of free space wavelength. We also show that Mikaelian microlens resolves two close point sources with distance 0.3 of free space wavelength between each others.

Key words: super-resolution, diffraction limit, gradient-index waveguide, planar waveguide, modal solution, mode width, Mikaelian microlens, Maxwell’s «fish eye».

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