Analytical theory of resonance diffraction and transformation of light polarization A. V. Kats* Institute of Radiophysics and Electronics Ukrainian National Academy of Sciences, 12 Acad. Proskury Street, 61085 Kharkiv, Ukraine I. S. Spevak Kharkiv Military University, P.O. Box 8847, Kharkiv 61002, Ukraine ~Received 18 April 2001; published 22 April 2002! This paper presents an analytical theory of resonance diffraction in the conical mount. The resonance is caused by plasmon polariton excitation via diffraction from a high reflecting shallow grating. The dependence of polarization, intensity, and phase of specular and resonance waves on the parameters of the problem is presented in explicit form and examined for arbitrary polarization of the incident wave as a function of the angle of incidence and the grating period, orientation and depth. The results obtained enable us to indicate gratings with specific properties, for instance, gratings, ensuring transformation of arbitrarily polarized incident wave into the linearly polarized specular wave. The properties of two-dimensional transformation matrix relating polarization amplitudes of the incident and the specular reflected waves are analyzed. It is shown that the transformation matrix is antisymmetric ~in accordance with the reciprocity theorem! for an arbitrary grating profile in the main approximation. The comparison of the results obtained shows remarkable agreement ~with- out any parameters fitting!! with data of the polarization conversion experiments. Both concrete results and the approach presented may be of use in constructing gratings with the predetermined parameters and, therefore, in solving problems of designing optical devices selective with respect to the polarization, wavelength, and orientation. DOI: 10.1103/PhysRevB.65.195406 PACS number~s!: 42.25.2p I. INTRODUCTION This work presents results of the simple analytical theory of Wood-type anomalies for diffraction in the general geom- etry ~see Refs. 1,2 and works cited therein! in connection with the experimental work. 3 In the work 3 there was demon- strated that diffraction of p-polarized laser radiation at a shal- low harmonic grating for some angles of incidence u and orientations of the grating leads to strong changes in polar- ization of the specular reflected wave in comparison with the case of a flat surface. This effect is caused by the resonance excitation of the surface electromagnetic wave ~SEW!, cf. Refs. 4,5. In Ref. 3, the polarization conversion efficiency ~PCE! was under investigation and in the next works 6 both the conversion efficiency and reflection coefficient were in- vestigated both numerically and experimentally. Here we show that computations for the problems dis- cussed in these works can be fulfilled analytically and radi- cally simplified in comparison with Ref. 6 without the loss of accuracy. The analytical approach presented allows to us deepen our understanding of the problem as a whole, and especially to investigate carefully the dependence on param- eters. In addition to this we present results for more general problem, assuming that polarization of the incident wave is arbitrary. For this case we obtain the explicit form of the corresponding transformation matrix and discuss its proper- ties. As a result we present general symmetry properties and formulate corresponding reciprocity theorem for the s →p and p →s conversion. We also demonstrate some additional unique properties of the resonance diffraction for special val- ues of parameters that may be used in optical devices design. The fact that light diffraction on the reflecting grating formed at high conducting ~metal! surfaces may lead to great changes in the properties of diffracted waves for some values of parameters is well known from the famous Wood’s work. 7 These effects are known in optics as Wood anomalies and were investigated theoretically in a number of works starting from Rayleigh’s one, 8 see reviews in Refs. 4,5. To the re- views we may add the recent book 9 where the reader will find the necessary literature information. We emphasize here two older works 10,11 that made essential contribution to up- to-date understanding of the problem in whole. Note that in the framework of explanation of the stimu- lated scattering at the surface waves and the surface struc- tures generation, there was developed rather simple analyti- cal method for solving resonance diffraction problems for shallow grating, see, for instance Refs. 1,12. The following consideration is based on the results presented in Ref. 1. The crucial point for us is the fact that due to the reso- nance with SEW the amplitude of the corresponding dif- fracted order becomes great for rather shallow grating ~height h to period d ratio smaller than 1/10!. But for a shal- low grating the analytical investigation gives accurate results that may be presented in the explicit form. This allows to consider the problem in details in the cases of specific inter- est. The structure of the paper is as follows. In Sec. II, we formulate the problem and present a brief summary of the necessary results, cf. Ref. 1. The main results are presented in Secs. III and IV. In Sec. III A, we present transformation coefficients ~TC! in the main approximation and discuss their fast ~resonance! dependence on parameters of the problem. Next Sec. III B deals with TC symmetry properties. Section III C is devoted to investigation of the slow dependence of TC on the parameters and presents resonance TC values. Here we present also some interesting special cases of the PHYSICAL REVIEW B, VOLUME 65, 195406 0163-1829/2002/65~19!/195406~9!/$20.00 ©2002 The American Physical Society 65 195406-1