A general theory of multilayers with enhanced reflectance has been developed based on the superposition of sub-quarterwave layers of various highly radiation-absorbing materials. The theory has been developed by second-order expansion of the multilayer reflectance with respect to the optical-constant differences between the materials in the multilayer. The current paper completes and improves the theory that was developed in a previous paper [J. Opt. Soc. Am. A 18, 1406 (2001)] by including the case of nonnormal incidence and general radiation polarization and by providing more-accurate film thickness values of the optimized multilayer than with the previous theory. The theory provides an accurate approach to the design of a new concept of multilayer coatings with more than two materials. The new multilayers are adequate to enhance the reflectance of the materials particularly in the far and the extreme ultraviolet.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
The methods are the one from Ref. 1, the current approach to first order in
the current approach to second order in
and by exact calculation. The exact reflectance for the four designs is also shown. The optimization was performed for the highest possible reflectance at 83.4 nm at normal incidence. The reflectance of single layers of the materials is also shown (first five entries in rightmost column).
Table 2
Reflectance at 83.4 nm at Normal Incidence of Different Sub-Quarterwave Multilayers Calculated by Three Different Methodsa
Multilayer
Reflectance Approximations with Different Theories
1st Order
2nd Order
Exact
SiC/C
0.3903
0.3904
0.3916
0.3825
0.3826
0.3832
0.3971
0.3991
0.4004
0.4046
0.4075
0.4088
0.4054
0.4099
0.4104
The methods are the current theory to first order in
(Eq. 22), the current theory to second order in
(Eq. 37), and the exact calculation. The film thicknesses were obtained by optimization with the corresponding theory and are given in Table 1.
Table 3
Reflectance of Sub-Quarterwave Multilayers Optimized at 53.6 nm, 45° Incidence Angle, and
-polarized
and Nonpolarized
Radiation
The methods are the one from Ref. 1, the current approach to first order in
the current approach to second order in
and by exact calculation. The exact reflectance for the four designs is also shown. The optimization was performed for the highest possible reflectance at 83.4 nm at normal incidence. The reflectance of single layers of the materials is also shown (first five entries in rightmost column).
Table 2
Reflectance at 83.4 nm at Normal Incidence of Different Sub-Quarterwave Multilayers Calculated by Three Different Methodsa
Multilayer
Reflectance Approximations with Different Theories
1st Order
2nd Order
Exact
SiC/C
0.3903
0.3904
0.3916
0.3825
0.3826
0.3832
0.3971
0.3991
0.4004
0.4046
0.4075
0.4088
0.4054
0.4099
0.4104
The methods are the current theory to first order in
(Eq. 22), the current theory to second order in
(Eq. 37), and the exact calculation. The film thicknesses were obtained by optimization with the corresponding theory and are given in Table 1.
Table 3
Reflectance of Sub-Quarterwave Multilayers Optimized at 53.6 nm, 45° Incidence Angle, and
-polarized
and Nonpolarized
Radiation