Abstract

An analytically tractable design procedure is presented for a polarizing beam splitter (PBS) that uses frustrated total internal reflection and optical tunneling by a symmetric LHL trilayer thin-film stack embedded in a high-index prism. Considerable simplification arises when the refractive index of the high-index center layer H matches the refractive index of the prism and its thickness is quarter-wave. This leads to a cube design in which zero reflection for the p polarization is achieved at a 45° angle of incidence independent of the thicknesses of the identical symmetric low-index tunnel layers L and L. Arbitrarily high reflectance for the s polarization is obtained at subwavelength thicknesses of the tunnel layers. This is illustrated by an IR Si-cube PBS that uses an embedded ZnS–Si–ZnS trilayer stack.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. M. MacNeille, “Beam splitter,” U. S. patent 2,403,731 (9 July 1946).
  2. M. Banning, “Practical methods of making and using multilayer filters,” J. Opt. Soc. Am. 37, 792–795 (1947).
    [CrossRef] [PubMed]
  3. R. P. Netterfield, “Practical thin-film polarizing beam splitters,” J. Mod. Opt. 24, 69–79 (1977).
    [CrossRef]
  4. D. Lees and P. Baumeister, “Versatile frustrated-total-reflection polarizer for the infrared,” Opt. Lett. 4, 66–67(1979).
    [CrossRef] [PubMed]
  5. R. M. A. Azzam, “Polarizing beam splitters for infrared and millimeter waves using single-layer-coated dielectric slab or unbacked films,” Appl. Opt. 25, 4225–4227 (1986).
    [CrossRef] [PubMed]
  6. M. Gilo and K. Rabinovitch, “Design parameters of thin-film cubic-type polarizers for high power lasers,” Appl. Opt. 26, 2518–2521 (1987).
    [CrossRef] [PubMed]
  7. J. Mouchart, J. Begel, and E. Duda, “Modified MacNeille cube polarizer for a wide angular field,” Appl. Opt. 28, 2847–2853(1989).
    [CrossRef] [PubMed]
  8. L. Li and J. A. Dobrowolski, “Visible broadband, wide-angle, thin-film multilayer polarizing beam splitter,” Appl. Opt. 35, 2221–2225 (1996).
    [CrossRef] [PubMed]
  9. 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]
  10. B. V. Blanckenhagen, “Practical layer design for polarizing beam-splitter cubes,” Appl. Opt. 45, 1539–1543 (2006).
    [CrossRef]
  11. R. M. A. Azzam and S. R. Perla, “Polarizing properties of embedded symmetric trilayer stacks under conditions of frustrated total internal reflection,” Appl. Opt. 45, 1650–1656(2006).
    [CrossRef] [PubMed]
  12. R. M. A. Azzam and S. R. Perla, “Errata,” Appl. Opt. 46, 431–433 (2007).
    [CrossRef]
  13. R. M. A. Azzam, “Phase shifts that accompany total internal reflection at a dielectric-dielectric interface,” J. Opt. Soc. Am. A 21, 1559–1563 (2004).
    [CrossRef]
  14. F. Abelès, “Un théoreme relatif à la réflexion métallique,” C. R. Hebd. Seances Acad. Sci. 230, 1942–1943 (1950).
  15. S. R. Perla and R. M. A. Azzam, “Wide-angle, high-extinction-ratio, infrared polarizing beam splitters using frustrated total internal reflection by an embedded centro-symmetric multilayer,” Appl. Opt. 46, 4604–4612(2007).
    [CrossRef] [PubMed]

2007 (2)

2006 (2)

2004 (1)

2000 (1)

1996 (1)

1989 (1)

1987 (1)

1986 (1)

1979 (1)

1977 (1)

R. P. Netterfield, “Practical thin-film polarizing beam splitters,” J. Mod. Opt. 24, 69–79 (1977).
[CrossRef]

1950 (1)

F. Abelès, “Un théoreme relatif à la réflexion métallique,” C. R. Hebd. Seances Acad. Sci. 230, 1942–1943 (1950).

1947 (1)

Abelès, F.

F. Abelès, “Un théoreme relatif à la réflexion métallique,” C. R. Hebd. Seances Acad. Sci. 230, 1942–1943 (1950).

Azzam, R. M. A.

Banning, M.

Baumeister, P.

Begel, J.

Blanckenhagen, B. V.

Dobrowolski, J. A.

Duda, E.

Gilo, M.

Lees, D.

Li, L.

MacNeille, S. M.

S. M. MacNeille, “Beam splitter,” U. S. patent 2,403,731 (9 July 1946).

Mouchart, J.

Netterfield, R. P.

R. P. Netterfield, “Practical thin-film polarizing beam splitters,” J. Mod. Opt. 24, 69–79 (1977).
[CrossRef]

Perla, S. R.

Rabinovitch, K.

Appl. Opt. (9)

M. Gilo and K. Rabinovitch, “Design parameters of thin-film cubic-type polarizers for high power lasers,” Appl. Opt. 26, 2518–2521 (1987).
[CrossRef] [PubMed]

L. Li and J. A. Dobrowolski, “Visible broadband, wide-angle, thin-film multilayer polarizing beam splitter,” Appl. Opt. 35, 2221–2225 (1996).
[CrossRef] [PubMed]

J. Mouchart, J. Begel, and E. Duda, “Modified MacNeille cube polarizer for a wide angular field,” Appl. Opt. 28, 2847–2853(1989).
[CrossRef] [PubMed]

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]

B. V. Blanckenhagen, “Practical layer design for polarizing beam-splitter cubes,” Appl. Opt. 45, 1539–1543 (2006).
[CrossRef]

R. M. A. Azzam and S. R. Perla, “Polarizing properties of embedded symmetric trilayer stacks under conditions of frustrated total internal reflection,” Appl. Opt. 45, 1650–1656(2006).
[CrossRef] [PubMed]

R. M. A. Azzam and S. R. Perla, “Errata,” Appl. Opt. 46, 431–433 (2007).
[CrossRef]

S. R. Perla and R. M. A. Azzam, “Wide-angle, high-extinction-ratio, infrared polarizing beam splitters using frustrated total internal reflection by an embedded centro-symmetric multilayer,” Appl. Opt. 46, 4604–4612(2007).
[CrossRef] [PubMed]

R. M. A. Azzam, “Polarizing beam splitters for infrared and millimeter waves using single-layer-coated dielectric slab or unbacked films,” Appl. Opt. 25, 4225–4227 (1986).
[CrossRef] [PubMed]

C. R. Hebd. Seances Acad. Sci. (1)

F. Abelès, “Un théoreme relatif à la réflexion métallique,” C. R. Hebd. Seances Acad. Sci. 230, 1942–1943 (1950).

J. Mod. Opt. (1)

R. P. Netterfield, “Practical thin-film polarizing beam splitters,” J. Mod. Opt. 24, 69–79 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Lett. (1)

Other (1)

S. M. MacNeille, “Beam splitter,” U. S. patent 2,403,731 (9 July 1946).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Embedded symmetric trilayer stack as a PBS operating under conditions of FTIR. p and s are the linear polarizations parallel and perpendicular to the plane of incidence, respectively, and ϕ 0 is the angle of incidence.

Fig. 2
Fig. 2

Normalized center-layer phase thickness θ 2 / π is plotted as a function of the tunnel-layer thickness parameter X 1 using Eq. (6) at discrete values of the 01-interface reflection phase shift δ = q π / 8 , q = 0 , 1 , 2 , , 8 such that zero reflection is achieved for the p or s polarization.

Fig. 3
Fig. 3

Intensity reflectance for the orthogonal polarization | R o | 2 is plotted as a function of X 1 using Eq. (10) at selected values of δ o = q π / 8 , q = 0 , 1 , 2 , 3 , 5 , 6 , 7 , 8 .

Tables (1)

Tables Icon

Table 1 Selected Prism and Film Refractive Indices That Satisfy Eq. (12) a

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

X 2 = + m X 1 n X 1 2 n + m X 1 + X 1 2 .
= r 01 ν , m = r 01 ν ( 1 + r 01 ν 2 ) , n = r 01 ν 3 .
X 2 = 1 r 01 ν 2 X 1 r 01 ν 2 X 1 .
X i = exp [ j 4 π ( n i d i / λ ) cos ϕ i ] , i = 1 , 2.
r 01 ν = exp ( j δ ) , X 2 = exp ( j θ 2 ) ,
θ 2 = 2 δ + 2 arg [ 1 X 1 exp ( j 2 δ ) ] .
d 2 / λ = [ ( 4 π n 0 ) 1 sec ϕ 0 ] θ 2 .
d 1 / λ = ln X 1 ( 4 π n 1 ) ( N 2 sin 2 ϕ 0 ) 1 / 2 .
R o = ( 1 X 1 ) 2 exp ( j δ o ) 1 2 X 1 sec δ o exp ( j δ o ) + X 1 2 exp ( j 2 δ o ) .
| R o | 2 = ( 1 X 1 ) 4 ( 1 X 1 ) 4 + 4 ( sec δ o cos δ o ) 2 X 1 2 .
sin 2 ϕ 0 = 1 / 2 = ( N 2 + 1 ) / ( N 4 + 1 ) .
N = n 0 / n 1 = ( 2 + 1 ) 1 / 2 = 1.55377 .
d 2 = 0.10399 λ .
δ o = δ s = δ p / 2 = π / 4.
| R s | 2 = ( 1 X 1 ) 4 ( 1 X 1 ) 4 + 2 X 1 2 .
d 1 = 0.18159 λ .
d tot = d 2 + 2 d 1 = 0.46717 λ .

Metrics