Gradient-Index Single-Layer Dielectric Films

2 Gradient-Index Single-Layer Dielectric Films 

Different functional dependences may be used for gradient-index AR layers. The simplest one is linear, but various polynomial dependences are met, for instance cubic or quintic. Sinusoidal dependence is also used. Of these, quintic dependence has been reported as the closest to optimum [164]. 

One of the presented structures is a monodispersion of subwavelength inclusions i (spheres) in dielectric host h. Fig. 2.22a. The other is polydispersion. Fig. 2.22b. The first situation can be described by the well-known MaxweU-Gamett model [171], the oldest effective medium model, obtained by the use of Clausius-Mossotti/ Lorenz-Lorentz equation. The other case is polydispersion, described by the implicit Bruggeman expression [172, 173]. 

Diffractive ARS are usually calculated either using the effective medium approximation, or the rigorous coupled-wave analysis [169]. Direct numerical solution of Maxwell equations and the approach using the plane wave theory were also used [174]. 

The effective medium theory (EMT) or the homogenization method regards a structured diffractive medium as a homogeneous material with an effective refractive index equal to a weighted and spatially averaged value of the refractive index of both structural materials. This is a very old theory and it was considered even in the works of Lord Rayleigh near the end of the nineteenth century. 

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