For approximately a decade, imaging ellipsometers have been available commercially. These allow one to measure the properties of graphene flakes, organic layers on amorphous substrates, plasmonic structures, among many other examples. These imaging ellipsometers opened a path to recognize and interpret pattern formations on surfaces or mapping field enhancement. However, for a full understanding of the optical response of patterned substrates, one should be aware that the well-known Fresnel reflection and transmission equations are, strictly speaking, not correct anymore. In this contribution, the ellipsometric response is explained in detail using heuristic physical arguments, hopefully without getting lost in the complexities of numerical computations.

1.
R. F.
Cohn
,
J. W.
Wagner
, and
J.
Kruger
,
Appl. Opt.
27
,
4664
(
1988
).
2.
See https://www.accurion.com/thin-film-characterization-applications-nanofilm for graphene and other 2D materials, organic electronics and nanoparticles.
3.
M.
Born
and
E.
Wolf
, “
Chapter 2.4
, Propagation of electromagnetic waves treated by integral equations” in
Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light
, 7th ed. (
Cambridge University Press
,
2005
).
4.
J. P.
Perin
and
K.
Hingerl
,
Appl. Surf. Sci.
421
,
738
(
2017
).
5.
B.
Lehner
and
K.
Hingerl
,
Thin Solid Films
455–456
,
462
(
2004
).
6.
Y.
Foo
and
J. A.
Zapien
,
Appl. Surf. Sci.
421
,
878
(
2017
).
7.
D.
Werdehausen
,
I.
Staude
,
S.
Burger
,
J.
Petschulat
,
T.
Scharf
,
T.
Pertsch
, and
M.
Decker
,
Opt. Mater. Express
8
,
3456
(
2018
).
8.
D. A.
Travo
,
R. A.
Muniz
,
M.
Liscidini
, and
J. E.
Sipe
,
Phys. Rev. B
96
,
205140
(
2017
).
9.
M.
Neviere
and
E.
Popov
,
Light Propagation in Periodic Media: Differential Theory and Design
(
Marcel Dekker
,
New York
,
2003
).
10.
S.
O’Mullane
,
N.
Keller
, and
A. C.
Diebold
,
J. Micro/Nanolithogr. MEMS MOEMS
15
,
044003
(
2016
).
11.
A.
Taflove
,
S. G.
Johnson
, and
A.
Oskooi
,
Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology
(
Artech House
,
Boston
,
2013
).
12.
R.
Ossikovski
and
K.
Hingerl
,
Opt. Lett.
41
,
4044
(
2016
).
13.
H.
Raether
,
Surface Plasmons on Smooth and Rough Surfaces and on Gratings
(
Springer
,
Berlin
,
1988
).
14.
M.
Bergmair
,
Spectroscopic Ellipsometry on Metallic Gratings and the Energy Density in Absorbing Media
(
Trauner Verlag
,
Linz
,
2012
).
15.
T. W. H.
Oates
,
B.
Dastmalchi
,
G.
Isic
,
S.
Tollabimazraehno
,
C.
Helgert
,
T.
Pertsch
,
E.-B.
Kley
,
M. A.
Verschuuren
,
I.
Bergmair
,
K.
Hingerl
, and
K.
Hinrichs
,
Opt. Express
20
,
11166
(
2012
).
16.
A.
Hessel
and
A. A.
Oliner
,
Appl. Opt.
4
,
1275
(
1965
).
17.
E.
Popov
and
E. G.
Loewen
,
Diffraction Gratings and Applications
(
Taylor and Francis
,
Boca Raton
, FL,
1997
).
18.
J. L.
Opsal
,
H.
Chu
,
Y.
Wen
,
Y.
-Chung Chang
, and
G.
Li
,
Proc. SPIE
4689
,
163
(
2002
).
19.
K.
Huang
,
J.
Lee
,
Y.
Wen
, and
J.
Opsal
,
Proc. SPIE
5752
,
536
(
2005
).
20.
J.-P.
Hugonin
and
P.
Lalanne
, “Reticolo software for grating analysis,” Trademark of the Institut d’Optique CNRS, Paris, see https://www.lp2n.institutoptique.fr/equipes-de-recherche-du-lp2n/light-complex-nanostructures (2005).
21.
V.
Rinnerbauer
,
K.
Hingerl
,
M.
Kovalenko
, and
W.
Heiss
,
Appl. Phys. Lett.
89
,
193114
(
2006
).
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