1.1 A Calculation model

We have performed rigorous coupled wave analysis (RCWA) calculation [8,9] to simulate the optical properties of the periodically microstructured surfaces. RCWA is a method to analyse the general 3D grating diffraction problem by solving the following Maxwell’s equations rigorously,

‘ V-(*e) = 0 V — H’ = 0 Vx E — — ikoH Vx H’- iko£E

here, E;electric field, H; magnetic field, h = ^eJm0h’ , k =x/2n, s; dielectric constant and X; wavelength. Assuming the Incident electromagnetic wave with wavelength of X, Incident angle 9, azimuthal angle ф and polarization angle ф, the electric and magnetic fields at the grating region is expressed by,

і E2 = ^SP, q (Z)ExP[-i(kx, pX + ку,,У)]

IH 2 = X £ UM (z )Exp[-i(kx, px + kMy)] ^

Here Sp, q^ Up, q is the electric and magnetic amplitude created by the diffracted wave with order of (p, q). The wave vectors and dielectric constant are expressed with the periodicity Лх and Лу,

kx p — k0 {nc sin в cos ф — p(Х/Лх)} I ky q — k0 {nc sin (9 sin ф — q(l/Ay)}

Here, nc is the refractive index of each region, and e’m. n is the (m, n)-th order of Fourier series.

As shown in the above formulation of RCWA, diffraction efficiency for each diffraction order is calculated with inputting the state of incident beam, structural profiles, and optical

constants (n, k) of materials. Any fitting parameters are not used and the accuracy of the solution computed depends solely on the number of terms retained in space harmonic expansion of electromagnetic fields, which corresponds to diffraction order N=(p, q). We have conducted calculations varying N up to 10 and confirmed that spectral feature mostly converge at N > 7. So we consider the diffraction orders up to +7th for x — and y — directions, respectively, and therefore diffraction efficiencies for 225 diffraction orders are calculated for each wavelength in this study. The literature data of optical constants for metals are used in the calculation.

Figure 2 shows schematic diagram of the calculation model in this study. For the ease of calculation, we restrict the grating shape to a simple 2D binary grating with rectangular cavities. Here we define some parameters to describe surface microstructures and the state of incident wave as periodicity Л, aperture size a and depth d. In this study, we set Ax = Лу = Aand ax = ay = a. Incident angle 9 and azimuthal angle ф are also defined as shown in the figure, and polarization angle is defined as у = tan^As/Ap), where As and Ap denote the amplitudes of the s — and p — polarization components of the incident wave, respectively.