Abstract

An all-transparent symmetric trilayer structure, which consists of a high-index center layer coated on both sides by a low-index film and embedded in a high-index prism, can function as an efficient polarizer or polarizing beam splitter under conditions of frustrated total internal reflection over a wide range of incidence angles. For a given set of refractive indices, all possible solutions for the thicknesses of the layers that suppress the reflection of either the p or s polarization at a specified angle, as well as the reflectance of the system for the orthogonal polarization, are determined. A 633  nm design that uses a MgF2ZnSMgF2 trilayer embedded in a ZnS prism achieves an extinction ratio (ER)>40  dB from 50° to 80° in reflection and an ER>20  dB from 58° to 80° in transmission. IR polarizers that use CaF2GeCaF2 trilayers embedded in a ZnS prism are also considered.

© 2006 Optical Society of America

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Corrections

Rasheed M. A. Azzam and Siva R. Perla, "Polarizing properties of embedded symmetric trilayer stacks under conditions of frustrated total internal reflection: erratum," Appl. Opt. 46, 431-433 (2007)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-46-3-431

References

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  1. H. A. Macleod, Thin Film Optical Filters, 2nd ed. (McGraw-Hill, 1986).
    [Crossref]
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  4. J. M. Bennett, 'Polarizers,' in Handbook of Optics, Vol. II, M. Bass, E. W. van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995).
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    [Crossref]
  6. S. M. MacNeille, 'Beam splitter,' U.S. patent 2,403,731 (6 July 1946).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  10. CVD, Inc., 35 Industrial Parkway, Woburn, Mass. 01801.
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    [Crossref]

2004 (1)

2000 (1)

1978 (1)

1952 (1)

1947 (1)

Azzam, R. M. A.

Banning, M.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Bennett, J. M.

J. M. Bennett, 'Polarizers,' in Handbook of Optics, Vol. II, M. Bass, E. W. van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995).

Dobrowolski, J. A.

L. Li and J. A. Dobrowolski, 'High-performance thin-film polarizing beam splitter operating at angles greater than the critical angle,' Appl. Opt. 39, 2754-2771 (2000).
[Crossref]

J. A. Dobrowolski, 'Optical properties of films and coatings,' in Handbook of Optics, Vol. I, M. Bass, E. W. van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995).

Epstein, L. I.

Li, L.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (McGraw-Hill, 1986).
[Crossref]

MacNeille, S. M.

S. M. MacNeille, 'Beam splitter,' U.S. patent 2,403,731 (6 July 1946).

Ohmer, M. C.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Other (7)

S. M. MacNeille, 'Beam splitter,' U.S. patent 2,403,731 (6 July 1946).

CVD, Inc., 35 Industrial Parkway, Woburn, Mass. 01801.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (McGraw-Hill, 1986).
[Crossref]

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

J. A. Dobrowolski, 'Optical properties of films and coatings,' in Handbook of Optics, Vol. I, M. Bass, E. W. van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995).

J. M. Bennett, 'Polarizers,' in Handbook of Optics, Vol. II, M. Bass, E. W. van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995).

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Figures (16)

Fig. 1
Fig. 1

Embedded trilayer structure as a polarizing beam splitter (PBS). A PBS in which the p polarization is transmitted and the s polarization is reflected is also considered. See text for discussion.

Fig. 2
Fig. 2

Plot of Z 2 as a function of Z 1 such that rp = 0 at angles of incidence ϕ0 from 45° to 85° in steps of 5°. We assume MgF2–ZnS–MgF2 trilayers embedded in a ZnS substrate with refractive indices n 0 = 2.35 (ZnS), n 1 = 1.38 (MgF2), and n 2 = 2.35 (ZnS) in the visible spectrum. Notice that all curves appear to have a common point of intersection at A.

Fig. 3
Fig. 3

Reflectance Rs = |rs |2 for the s polarization is plotted versus Z 1 at the same angles of incidence as in Fig. 2 and under the rp = 0 condition.

Fig. 4
Fig. 4

Magnified view of the region of high reflectance in Fig. 3.

Fig. 5
Fig. 5

High-resolution view of the family of curves of Fig. 2 near point A shows that there is not strictly one common point of intersection for all the curves.

Fig. 6
Fig. 6

Plot of Z 2 as a function of Z 1 such that rs = 0 at angles of incidence ϕ0 from 45° to 85° in steps of 5°. All the curves appear to pass through a common point B.

Fig. 7
Fig. 7

Reflectance Rp = |rp |2 for the p polarization is plotted versus Z 1 at the same angles of incidence as in Fig. 6 and under the rs = 0 condition.

Fig. 8
Fig. 8

Expanded view of Fig. 7 in the region of high reflectance.

Fig. 9
Fig. 9

Magnified view of the family of curves of Fig. 6 in the neighborhood of point B shows that there is not strictly one common point of intersection for all the curves.

Fig. 10
Fig. 10

Reflectances Rp and Rs as functions of the angle of incidence ϕ0 from 40° to 85° for a polarizer using a MgF2–ZnS–MgF2 trilayer embedded in a ZnS substrate with refractive indices n 0 = 2.35 (ZnS), n 1 = 1.38 (MgF2), and n 2 = 2.35 (ZnS). The metric film thicknesses (d 1 = 78.31 nm, d 2 = 117.62 nm) and wavelength (633 nm) are kept constant.

Fig. 11
Fig. 11

Extinction ratios in reflection and transmission (ER r and ER t ) in decibels are plotted versus the angle of incidence ϕ0 from 50° to 80° for the wide-angle polarizer of Fig. 10.

Fig. 12
Fig. 12

Extinction ratios ER r and ER t in decibels as functions of wavelength λ for the wide-angle polarizer of Fig. 10. The metric film thicknesses (d 1 = 78.31 nm, d 2 = 117.62 nm) and angle of incidence ϕ0 (65°) are kept constant.

Fig. 13
Fig. 13

Constraint between Z 2 and Z 1 such that rp = 0 at angles of incidence ϕ0 from 45° to 85° in 5° steps for CaF2–Ge–CaF2 trilayers embedded in a ZnS substrate with refractive indices n 0 = 2.2 (ZnS), n 1 = 1.4 (CaF2), and n 2 = 4 (Ge) in the infrared.

Fig. 14
Fig. 14

Reflectance Rs = |rs |2 for the s polarization plotted versus Z 1 under the rp = 0 condition and at the same angles of incidence as in Fig. 13.

Fig. 15
Fig. 15

Plot of Z 2 versus Z 1such that rs = 0 at angles of incidence ϕ0 from 45° to 85° in 5° steps for CaF2–Ge–CaF2 trilayers embedded in ZnS substrate in the infrared. All the curves appear to share a common point of intersection at C.

Fig. 16
Fig. 16

Reflectance Rp = |rp |2 for the p polarization plotted versus Z 1 under the rs = 0 condition and at the same angles of incidence as in Fig. 15.

Equations (20)

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r ν = l + m X 1 + n X 2 m X 1 X 2 n X 1     2 l X 2 X 1     2 1 + b X 1 + c X 2 + d X 1     2 b X 1 X 2 + e X 2 X 1     2 ,
l = r 01 ν ,
m = r 12 ν ( 1 + r 01 ν 2 ) ,
n = r 01 ν r 12 ν 2 ,
b = 2 r 01 ν r 12 ν ,
c = r 12 ν 2 ,
d = r 01 ν 2 r 12 ν 2 ,
e = r 01 ν 2 .
X i = exp ( j π Z i cos ϕ i ) ,
Z i = 4 d i n i λ .
r i j p = n j   cos   ϕ i n i   cos   ϕ j n j   cos   ϕ i + n i   cos   ϕ j , r i j s = n i   cos   ϕ i n j   cos   ϕ j n i   cos   ϕ i + n j   cos   ϕ j .
r ν = 0
X 2 = l + m X 1 n X 1     2 n + m X 1 + l X 1     2 .
R ν = | r ν | 2
X 2 = ( r 12 2 ) r 12 - 2 + r 12 - 1 ( r 01 - 1 + r 01 ) X 1 + X 1     2 r 12 2 + r 12 ( r 01 - 1 + r 01 ) X 1 + X 1     2 .
r i j = exp ( j δ i j ) ,
r i j - 1 = r i j * = exp ( j δ i j ) ,
r i j - 1 + r i j = 2   cos ( δ i j ) ,
X 2 = ( r 12 2 ) ( W / W * ) .
| X 2 | = 1.

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