Radiation from periodic structures excited by an aperiodic source

In the past, periodic structures have been extensively studied for guided waves along the surface, or for plane wave excitation. However, very little has been reported concerning the problem of exciting periodic structures by a localized source. The essential difficulty of this problem is due to the aperiodic nature of the source. This paper presents a study of a two-dimensional periodic structure excited by a magnetic line source. The structure consists of a grounded dielectric slab covered by a periodically slotted conducting plane. From the continuity of the fields in the slots, an infinite system of integral equations for the aperture fields is derived. Under the assumption of narrow slots, these equations are converted into a single integral equation by the use of the sampling technique, and the solution is expressed in an inverse Fourier transform. The integrand is then converted into a form of space harmonics which contains an infinite number of poles and branch points. The relationship between these singularities and the
k-\beta
diagram is clearly demonstrated. The radiation pattern is calculated and compared with experimental data. The Wood anomalies associated with leaky waves and the Rayleigh wavelength, and in particular, the relationship between the behavior of the field near the Rayleigh wavelength and the lateral waves are discusssed.