Experimental results at millimeter wavelengths on dielectric-coated gratings are reported that show sharp anomalous dips in the transmission intensity for both P and S polarizations (i.e., incident electric field parallel and perpendicular to the slits, respectively). These dips almost disappear when either the dielectric is removed or the slits are randomly spaced. Next, a theory is developed for the gratings of finite extent and nonuniform spacings. Theoretical results, although approximate, agree remarkably well with the experiment.
Vishwani D. Agrawal and Yuen T. Lo, "Anomalies of Dielectric-Coated Gratings," Appl. Opt. 11, 1946-1951 (1972)