Diffraction from corrugated gratings made with biaxial crystals: Rayleigh methods

Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials

“…T he electromagnetic boundary conditions require that the x and z components of the k vector be conserved across interfaces between di erent spatial regions. Substituting equation (12) into equation (13), we obtain a polynomial equation…”

“…T he coe cients of the polynomial depend on a , kz andẽ , and they can be found in [28], [12] and [17]. Equation (14) can be solved by using one of the standard analytical methods that are available in many mathematical handbooks, or by using a general polynomial root ® nder.…”

“…T he gratings consist of a sinusoidal interface between air and a biaxial crystal whose principal axesê1 andê2 are oriented along directions (1,1,1) and (-1,2,-1) respectively. For the smallest groove depth, the results of Depine and Gigli [12] (here rounded o to four signi® cant digits) are included. T he agreement is good.…”

“…Minor di erences might have resulted from the use of the multilayer approximation. In addition, di raction e ciencies at two greater groove depths, not available in [12], are also provided.…”

“…T he integers enclosed in parentheses are base-ten exponents. T he numbers in square brackets are obtained from table 2 of [12]. T he column headings with subscripts and superscripts are also from [12].…”