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Nanophotonics of gradient metamaterials: Physical fundamentals and mathematical basis

Fundamental physical and mathematical issues of the nanophotonics of gradient metamaterial structures are considered. A main principle of the developed approach is the use of materials having continuous spatial distributions of refractive index. The following basic methods, structures, and features are considered: new closed-form solutions to Maxwell equations, non-Fresnel reflectance and transmittance spectra of gradient structures, reflectionless tunneling of light, periodical arrays of nanogradient dielectric structures, nanofilms of subwavelength thickness.