Iterative Fourier synthesis techniques for reflection gratings and corrugated waveguide filters
Abstract
In the first section, the accuracy of coupled mode theory as applied to volume, dielectric reflection gratings which have unslanted fringes and either periodic or aperiodic refractive index profiles is investigated. The accuracy is evaluated by comparing coupled mode theory results with those obtained by Abeles' exact multilayer theory. For the examples considered, coupled mode theory gave accurate results only for gratings having periodic refractive index profiles. In Section 2, a method for designing volume, dielectric, reflection gratings having unslanted fringes is developed. The technique is applicable to two types of problems. The first type is one in which the reflectance, R, vs. angle of incidence and wavelength is specified, and the second type is one in which the amplitude reflection and transmission coefficients, r and t, respectively, vs. angle of incidence and wavelength are specified. In both cases, the technique determines (approximately) the corresponding one dimensional refractive index profile, n(z). The synthesis method is illustrated by two examples, and for these examples, the method is seen to be reasonably accurate. In Section 3, a formal mathematical analogy between reflection gratings and corrugated waveguide filters (CWF) is demonstrated. The possibility of designing CWF, using the iterative Fourier transform technique developed in Section 2, is explored. It is emphasized that the mathematics developed for CWF is not rigorous. Consequently, predicted results should be experimentally verified and attempts should be made to develop a rigorous mathematical approach.
 Publication:

Final Scientific Report
 Pub Date:
 October 1981
 Bibcode:
 1981eri..reptS....W
 Keywords:

 Asymptotic Methods;
 Fourier Analysis;
 Gratings (Spectra);
 Iteration;
 Waveguide Filters;
 Analysis (Mathematics);
 Electromagnetic Wave Filters;
 Numerical Analysis;
 Reflection;
 Waveguides;
 Communications and Radar