Gerald E. Jellison, Nikolas J. Podraza, and Ambalanath Shan, "Ellipsometry: dielectric functions of anisotropic crystals and symmetry," J. Opt. Soc. Am. A 39, 2225-2237 (2022)
The optical functions of anisotropic materials can be determined using
generalized ellipsometry, which can measure the cross-polarization
coefficients (CPs) of the sample surface reflections. These CPs have
several symmetry relations with respect to the symmetry of the
crystal. This paper explores the symmetry relations of these CPs for
uniaxial, orthorhombic, and monoclinic crystals and the requirements
for generalized ellipsometry. Several ellipsometry measurement
configurations are examined, including the requirements for the
accurate measurements of the dielectric functions of anisotropic
crystals.
Data underlying the results presented in this paper are not publicly
available at this time but may be obtained from the authors upon
reasonable request.
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Specific Mueller Matrix Elements Measured in Various Ellipsometry
Configurations, Showing the Basis Function Whose Coefficient
Measures the Specific Element
RAE
PME
c1: ; c2:
RCE1
; ;
RCE2
; ;
2-MGE1
;
2-MGE2
;
RC RP
2RC
;
Table 2.
Optical Functions of Rutile , Stibnite , and at Specific Wavelengths
The calculation used two angles of incidence (60° and 70°) and
three different crystallographic orientations shown in
Table 4. The # Paras
column shows the number of measured parameters
from each ellipsometer.
DNC = did not converge.
Table 6.
Errors of the Dielectric Functions of Monoclinic Determined at Two Different Sets
of Angles of Incidence, Using Three Different Sets of
Crystallographic Orientation, Shown in Table 4
1 AOI (65°)
3 AOI (55°, 65°, 75°)
Ellipsometer
Orient. 3
Orient. 4
Orient. 5
Orient. 3
Orient. 4
Orient. 5
2-MGE 1Z
0.4286
0.0284
0.0073
0.0141
0.0107
0.0044
RC RP
0.3380
0.0265
0.0068
0.0133
0.0098
0.0041
2-MGE 2Z
0.2432
0.0246
0.0059
0.0114
0.0085
0.0035
MME
0.2058
0.0202
0.0053
0.0101
0.0076
0.0028
Tables (6)
Table 1.
Specific Mueller Matrix Elements Measured in Various Ellipsometry
Configurations, Showing the Basis Function Whose Coefficient
Measures the Specific Element
RAE
PME
c1: ; c2:
RCE1
; ;
RCE2
; ;
2-MGE1
;
2-MGE2
;
RC RP
2RC
;
Table 2.
Optical Functions of Rutile , Stibnite , and at Specific Wavelengths
The calculation used two angles of incidence (60° and 70°) and
three different crystallographic orientations shown in
Table 4. The # Paras
column shows the number of measured parameters
from each ellipsometer.
DNC = did not converge.
Table 6.
Errors of the Dielectric Functions of Monoclinic Determined at Two Different Sets
of Angles of Incidence, Using Three Different Sets of
Crystallographic Orientation, Shown in Table 4