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The general problems of TE- and TM-excited slots in screens and conducting strips whose widths are narrow relative to the wavelength are investigated. The narrow width approximation is imposed upon the slotted-screen and strip equations from which result approximate equations that are solved exactly. For general excitation, solutions are presented for both polarizations as products of series of Chebyshev polynomials and appropriate singular functions exhibiting the known edge condition. Special attention is afforded the problem of the slot/strip excited by illumination which can be represented by two terms of a Taylor series due to the practical importance of this situation.
Butler et al. (1980) studied this question.