Anti-Reflecting Nanostructures - Biomimetic Architectures by Plasma Processing - page 48

of a homogeneous medium possessing a single effective optical
constant (Fig. 2.6). For the specific case of a multilevel (stepped or
discontinuous) surface-relief profile, the EMT assumes a film stack
with each layer corresponding to a distinct level of the surface-relief
profile, where the RI increases layer-by-layer from the value at the
ambient-layer interface to that of the substrate (

n < n < n < n

0 1 2 3

< ) (Fig. 2.6a). For a continuous profile (Fig. 2.6b), the equivalent

effective medium is a gradient film, where RI of the effective medium
increases along the depth

n

s

z ( n < n (z) < n ) [33].

0 s

Figure 2.6 (a, b) Effective mediums for different surface-relief grating

surface profiles. Reprinted from Ref. [33], with permission
from The Optical Society. (c) The calculated spectral reflectivity
of 2D Si pyramid gratings with a periodicity

L

of 100 nm,
approximating the SWG layer by a stack of eight layers (inset).
Reprinted with permission from Ref. [34]. Copyright 2006, AIP
Publishing LLC (http://dx.doi.org/10.1063/1.2205173). (d)
Calculated transmittance of the pyramidal SWGs (inset) with

L

of 200 nm for different grating depths ( ) Reprinted from Ref.

[35], copyright 2005, with permission from Elsevier.

D

In order to optimise the ARG design, Moharam and Gaylord in
1981 [36] proposed the rigorous coupled-wave analysis (RCWA)
model, assuming the cross-section of the grating structure or the
groove as a set of large number of thin layers parallel to the surface.
Besides, the whole structure can be divided into three regions:
incident, grating and exit region. Sai et al. [34] approximated a
pyramidal SWS on silicon surface (Fig. 2.6c) by a stack of eight