By Alexei A. Maradudin, Eugenio R. Méndez, Tamara A. Leskova

*Designer Surfaces* offers an method of the layout and fabrication of optical components which are in keeping with using one- or two-dimensional randomly tough surfaces to mirror or transmit mild in precise methods. The reader is supplied with an advent to analytical equipment for the answer of direct difficulties in tough floor scattering, and fabrication innovations. those may be invaluable in contexts outdoors the scope of this publication. the benefits and drawbacks of this stochastic technique in comparison to the diffractive optics procedure are mentioned. ultimately, experimental effects that confirm the predictions of the theories constructed during this booklet are presented.

- Authority of authors
- The merely booklet at the topic
- Derivations are given intimately, with many figures illustrating results

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**Extra info for Designer Surfaces**

**Example text**

The results obtained for Np = 30 000 realizations of the surface profile function were used in calculating the average in Eq. 1 From a comparison of the results presented in Figs. 4 we see that not only do the random surfaces generated by our approach act as bandlimited uniform diffusers for |θs | < θm for each angle of incidence, but, also that the results obtained by the rigorous computer simulation approach, for the values of the experimental and roughness parameters assumed, are in complete agreement with those obtained in the Kirchhoff approximation.

A Nonstationary Surface We now relax the assumption of the stationarity of the surface. In this case because ζ (x1 ) has been assumed to be a nonstationary random process, we cannot assume that ζ (x1 ) is a stationary random process. The average exp[i(ω/c)(cos θs + cos θ0 )uζ (x1 )] in Eq. 60) therefore has to be assumed to be a function of x1 , and we cannot carry out the integral over x1 to yield L1 , as we did when ζ (x1 ) was assumed to be a stationary random process. To evaluate the double integral in Eq.

131) If we define L1 as 2Ns b, the expression for the mean differential reflection coefficient given by Eq. 37) becomes [1 + cos(θs + θ0 )]2 b ω ∂R r(θs |θ0 ) = ∂θs 2Ns 2πc cos θ0 (cos θs + cos θ0 )2 2 . , of sets of the slopes {an } and the corresponding {bn }, and for each realization to calculate the corresponding value of |r(θs |θ0 )|2 by the use of Eq. 131). An arithmetic average of the Np results for |r(θs |θ0 )|2 obtained in this way yields the average indicated in Eq. 132). It should be noted that |r(θs |θ0 )|2 must grow linearly with Ns if this result for ∂R/∂θs is to be independent of Ns .