Diffraction Gratings in the Quasi-static Limit

Abstract

For gratings having an arbitrary symmetric profile, we prove that when the period becomes much finer than the wavelength the grating becomes equivalent to a graded uniaxial layer . We show for one polarization that this quasi-static equivalence holds when the ratio of wavelength to grating period exceeds 40 . We also present a simple physical model which explains the anisotropic nature of the equivalent layer . We take the case of a finely-textured copper surface, and show that it can be a good selective absorber for polarized light, but that its performance in unpolarized' light is much less satisfactory .

On the effective medium theory of subwavelength periodic structures

“…In the literature, the zeroth-order EMT is also referred to as the quasi-static limit or the long wavelength limit. Note that the above methodology is strictly the same as in [16]. I t is used for the I-D TE and T M problems, and for the 2-D problems.…”

“…We use the Fourier expansion method proposed by Bell et a f . [16]. In particular for T E polarization and I-D structures, we provide simulation results showing that their approach is not restricted to symmetric structures.…”

“…By using a Fourier expansion wave basis of the field inside the periodic structure, Bell et al [16] generalized these previous works to an arbitrary I-D symmetric profile. They showed that symmetric gratings are equivalent to an uniaxial film in the long wavelength limit, and derived a closed-form for the second-order effective index of symmetric I -D gratings and for T E polarization.…”

“…T h e methodology is basically the same as those provided in [16], except that the E M T solution is derived without expanding the field in a power series of the period-to-wavelength ratio. As was pointed out in [17], the existence of such power series would require more study.…”

Rear Side Diffractive Gratings for Silicon Wafer Solar Cells

“…Since the structure is not invariant in the z-direction, these effective optical parameters will depend on z as well. Depending on the dimensionality of the grating and the polarization of the incident light, different rules exist [21,22] for assigning these effective parameters. Details can be found in the indicated literature.…”