Abstract

A centrosymmetric multilayer stack of two transparent materials, which is embedded in a high-index prism, can function as a complete-transmission quarter-wave or half-wave retarder (QWR or HWR) under conditions of frustrated total internal reflection. The multilayer consists of a high-index center layer sandwiched between two identical low-index films with high-index–low-index bilayers repeated on both sides of the central trilayer, maintaining the symmetry of the entire stack and constituting a QWR (Δt=90° or 270°) or HWR (Δt=180°) in transmission. A QWR design at wavelength λ=1.55μm is presented that employs an 11-layer stack of Si and SiO2 thin films, which is embedded in a GaP cube prism. The intensity transmittances for the p and s polarizations remain >99% and Δt deviates from 90° by <±3° over a 100nm spectral bandwidth (1.5λ1.6μm), and by ±7° over an internal field view of ±1° (incidence angle 44°ϕ046° inside the prism). An HWR design at λ=1.55μm employs seven layers of Si and SiO2 thin films embedded in a Si cube, has an average transmittance >93%, and Δt that differs from 180° by <±0.3° over a 100nm bandwidth (1.5λ1.6μm) and by <±17° over an internal field view of ±1°. The sensitivity of these devices to film-thickness errors is also considered.

© 2007 Optical Society of America

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References

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  1. R. M. A. Azzam and N. M. Bashara, Elliposmetry and Polarized Light (North-Holland, 1987).
  2. D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).
  3. J. M. Bennett, "A critical evaluation of rhomb-type quarterwave retarders," Appl. Opt. 9, 2123-2129 (1970).
    [CrossRef]
  4. R. M. A. Azzam and C. L. Spinu, "Achromatic angle-insensitive infrared quarter-wave retarder based on total internal reflection at the Si-SiO2 interface," J. Opt. Soc. Am. A 21, 2019-2022 (2004).
    [CrossRef]
  5. E. Spiller, "Totally reflecting thin-film phase retarders," Appl. Opt. 23, 3544-3549 (1984).
    [CrossRef]
  6. E. Cojocaru, R. Dabu, V. Draganescu, T. Julea, and F. Nichitiu, "Achromatic thin-film totally reflecting quarterwave retarders," Appl. Opt. 28, 211-212 (1989).
    [CrossRef]
  7. E. Cojocaru, T. Julea, and F. Nichitiu, "Infrared thin-film totally reflecting quarter-wave retarders," Appl. Opt. 30, 4124-4125 (1991).
    [CrossRef]
  8. A.-R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, "An angle-of-incidence-tunable SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å," Opt. Commun. 14, 260-262 (1975).
    [CrossRef]
  9. S. Kawabata and M. Suzuki, "MgF2-Ag tunable reflection retrader," Appl. Opt. 19, 484-486 (1980).
    [CrossRef] [PubMed]
  10. R. M. A. Azzam and B. E. Perilloux, "Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence," Appl. Opt. 24, 1171-1179 (1985).
    [CrossRef] [PubMed]
  11. W. H. Southwell, "Multilayer coating design achieving a broadband 90° phase shift," Appl. Opt. 19, 2688-2692 (1980).
    [CrossRef] [PubMed]
  12. J. H. Apfel, "Graphical method to design multilayer phase retarders," Appl. Opt. 20, 1024-1029 (1981).
    [CrossRef] [PubMed]
  13. M. M. K. Howlader and R. M. A. Azzam, "Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence," Opt. Eng. 34, 869-875 (1995).
    [CrossRef]
  14. W. H. Southwell, "Thin film transmissive phase retarders," in Proceedings of International Conference on Lasers, C.B.Collins, ed. (STS, 1981), pp. 578-585.
  15. R. M. A. Azzam and F. A. Mahmoud, "Tilted bilayer membranes as simple transmission quarter-wave retardation plates," J. Opt. Soc. Am. A 18, 421-425 (2001).
    [CrossRef]
  16. J. B. Kortright, M. Rice, and K. D. Franck, "Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
    [CrossRef]
  17. D.-E. Kim, S.-M. Lee, and I. Jeon, "Transmission characteristics of multilayer structure in the soft x-ray region and its application to the design of quarter-wave plates at 13 and 4.4 nm," J. Vac. Sci. Technol. A 17, 398-402 (1999).
    [CrossRef]
  18. R. M. A. Azzam and A. De, "Circular polarization beam splitter that uses frustrated total internal reflection by an embedded symmetric achiral multilayer coating," Opt. Lett. 28, 355-357 (2003).
    [CrossRef] [PubMed]
  19. R. M. A. Azzam and C. L. Spinu, "Linear-to-circular polarization transformation upon optical tunneling through an embedded low-index film," Opt. Lett. 30, 3183-3185 (2005).
    [CrossRef] [PubMed]
  20. Ref. , Chap. 4.
  21. R. H. Muller, "Definitions and conventions in ellipsometry," Surf. Sci. 16, 14-33 (1996).
    [CrossRef]
  22. E. Spiller, "Phase conventions in thin film optics and ellipsometry," Appl. Opt. 23, 3036-3037 (1984).
    [CrossRef] [PubMed]
  23. A. M. Kan'an and R. M. A. Azzam, "In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism," Opt. Eng. 33, 2029-2033 (1994).
    [CrossRef]
  24. W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw Hill, 1995), Vol. II, Chap. 33.
  25. M. Herzberger and C. D. Salzberg, "Refractive indices of infrared optical materials and color correction of infrared lenses," J. Opt. Soc. Am. 52, 420-425 (1962).
    [CrossRef]
  26. 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]
  27. 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 centrosymmetric multilayer," Appl. Opt. 46, 4604-4612 (2007).
    [CrossRef] [PubMed]

2007

2005

2004

2003

2001

2000

1999

D.-E. Kim, S.-M. Lee, and I. Jeon, "Transmission characteristics of multilayer structure in the soft x-ray region and its application to the design of quarter-wave plates at 13 and 4.4 nm," J. Vac. Sci. Technol. A 17, 398-402 (1999).
[CrossRef]

1996

R. H. Muller, "Definitions and conventions in ellipsometry," Surf. Sci. 16, 14-33 (1996).
[CrossRef]

1995

M. M. K. Howlader and R. M. A. Azzam, "Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence," Opt. Eng. 34, 869-875 (1995).
[CrossRef]

J. B. Kortright, M. Rice, and K. D. Franck, "Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
[CrossRef]

1994

A. M. Kan'an and R. M. A. Azzam, "In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism," Opt. Eng. 33, 2029-2033 (1994).
[CrossRef]

1991

1989

1985

1984

1981

1980

1975

A.-R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, "An angle-of-incidence-tunable SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å," Opt. Commun. 14, 260-262 (1975).
[CrossRef]

1970

1962

Apfel, J. H.

Azzam, R. M. A.

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 centrosymmetric multilayer," Appl. Opt. 46, 4604-4612 (2007).
[CrossRef] [PubMed]

R. M. A. Azzam and C. L. Spinu, "Linear-to-circular polarization transformation upon optical tunneling through an embedded low-index film," Opt. Lett. 30, 3183-3185 (2005).
[CrossRef] [PubMed]

R. M. A. Azzam and C. L. Spinu, "Achromatic angle-insensitive infrared quarter-wave retarder based on total internal reflection at the Si-SiO2 interface," J. Opt. Soc. Am. A 21, 2019-2022 (2004).
[CrossRef]

R. M. A. Azzam and A. De, "Circular polarization beam splitter that uses frustrated total internal reflection by an embedded symmetric achiral multilayer coating," Opt. Lett. 28, 355-357 (2003).
[CrossRef] [PubMed]

R. M. A. Azzam and F. A. Mahmoud, "Tilted bilayer membranes as simple transmission quarter-wave retardation plates," J. Opt. Soc. Am. A 18, 421-425 (2001).
[CrossRef]

M. M. K. Howlader and R. M. A. Azzam, "Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence," Opt. Eng. 34, 869-875 (1995).
[CrossRef]

A. M. Kan'an and R. M. A. Azzam, "In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism," Opt. Eng. 33, 2029-2033 (1994).
[CrossRef]

R. M. A. Azzam and B. E. Perilloux, "Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence," Appl. Opt. 24, 1171-1179 (1985).
[CrossRef] [PubMed]

A.-R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, "An angle-of-incidence-tunable SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å," Opt. Commun. 14, 260-262 (1975).
[CrossRef]

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

Bashara, N. M.

A.-R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, "An angle-of-incidence-tunable SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å," Opt. Commun. 14, 260-262 (1975).
[CrossRef]

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

Bennett, J. M.

Clarke, D.

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

Cojocaru, E.

Dabu, R.

De, A.

Dobrowolski, J. A.

Draganescu, V.

Franck, K. D.

J. B. Kortright, M. Rice, and K. D. Franck, "Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
[CrossRef]

Grainger, J. F.

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

Harris, T. J.

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw Hill, 1995), Vol. II, Chap. 33.

Herzberger, M.

Howlader, M. M. K.

M. M. K. Howlader and R. M. A. Azzam, "Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence," Opt. Eng. 34, 869-875 (1995).
[CrossRef]

Jeon, I.

D.-E. Kim, S.-M. Lee, and I. Jeon, "Transmission characteristics of multilayer structure in the soft x-ray region and its application to the design of quarter-wave plates at 13 and 4.4 nm," J. Vac. Sci. Technol. A 17, 398-402 (1999).
[CrossRef]

Julea, T.

Kan'an, A. M.

A. M. Kan'an and R. M. A. Azzam, "In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism," Opt. Eng. 33, 2029-2033 (1994).
[CrossRef]

Kawabata, S.

Kim, D.-E.

D.-E. Kim, S.-M. Lee, and I. Jeon, "Transmission characteristics of multilayer structure in the soft x-ray region and its application to the design of quarter-wave plates at 13 and 4.4 nm," J. Vac. Sci. Technol. A 17, 398-402 (1999).
[CrossRef]

Kortright, J. B.

J. B. Kortright, M. Rice, and K. D. Franck, "Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
[CrossRef]

Lee, S.-M.

D.-E. Kim, S.-M. Lee, and I. Jeon, "Transmission characteristics of multilayer structure in the soft x-ray region and its application to the design of quarter-wave plates at 13 and 4.4 nm," J. Vac. Sci. Technol. A 17, 398-402 (1999).
[CrossRef]

Li, L.

Mahmoud, F. A.

Muller, R. H.

R. H. Muller, "Definitions and conventions in ellipsometry," Surf. Sci. 16, 14-33 (1996).
[CrossRef]

Nichitiu, F.

Perilloux, B. E.

Perla, S. R.

Rice, M.

J. B. Kortright, M. Rice, and K. D. Franck, "Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
[CrossRef]

Salzberg, C. D.

Southwell, W. H.

W. H. Southwell, "Multilayer coating design achieving a broadband 90° phase shift," Appl. Opt. 19, 2688-2692 (1980).
[CrossRef] [PubMed]

W. H. Southwell, "Thin film transmissive phase retarders," in Proceedings of International Conference on Lasers, C.B.Collins, ed. (STS, 1981), pp. 578-585.

Spiller, E.

Spinu, C. L.

Suzuki, M.

Thomas, M. E.

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw Hill, 1995), Vol. II, Chap. 33.

Tropf, W. J.

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw Hill, 1995), Vol. II, Chap. 33.

Zaghloul, A.-R. M.

A.-R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, "An angle-of-incidence-tunable SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å," Opt. Commun. 14, 260-262 (1975).
[CrossRef]

Appl. Opt.

J. H. Apfel, "Graphical method to design multilayer phase retarders," Appl. Opt. 20, 1024-1029 (1981).
[CrossRef] [PubMed]

E. Spiller, "Phase conventions in thin film optics and ellipsometry," Appl. Opt. 23, 3036-3037 (1984).
[CrossRef] [PubMed]

E. Spiller, "Totally reflecting thin-film phase retarders," Appl. Opt. 23, 3544-3549 (1984).
[CrossRef]

R. M. A. Azzam and B. E. Perilloux, "Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence," Appl. Opt. 24, 1171-1179 (1985).
[CrossRef] [PubMed]

E. Cojocaru, T. Julea, and F. Nichitiu, "Infrared thin-film totally reflecting quarter-wave retarders," Appl. Opt. 30, 4124-4125 (1991).
[CrossRef]

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]

W. H. Southwell, "Multilayer coating design achieving a broadband 90° phase shift," Appl. Opt. 19, 2688-2692 (1980).
[CrossRef] [PubMed]

J. M. Bennett, "A critical evaluation of rhomb-type quarterwave retarders," Appl. Opt. 9, 2123-2129 (1970).
[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 centrosymmetric multilayer," Appl. Opt. 46, 4604-4612 (2007).
[CrossRef] [PubMed]

S. Kawabata and M. Suzuki, "MgF2-Ag tunable reflection retrader," Appl. Opt. 19, 484-486 (1980).
[CrossRef] [PubMed]

E. Cojocaru, R. Dabu, V. Draganescu, T. Julea, and F. Nichitiu, "Achromatic thin-film totally reflecting quarterwave retarders," Appl. Opt. 28, 211-212 (1989).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. A

D.-E. Kim, S.-M. Lee, and I. Jeon, "Transmission characteristics of multilayer structure in the soft x-ray region and its application to the design of quarter-wave plates at 13 and 4.4 nm," J. Vac. Sci. Technol. A 17, 398-402 (1999).
[CrossRef]

Opt. Commun.

A.-R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, "An angle-of-incidence-tunable SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å," Opt. Commun. 14, 260-262 (1975).
[CrossRef]

Opt. Eng.

M. M. K. Howlader and R. M. A. Azzam, "Periodic and quasiperiodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence," Opt. Eng. 34, 869-875 (1995).
[CrossRef]

A. M. Kan'an and R. M. A. Azzam, "In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism," Opt. Eng. 33, 2029-2033 (1994).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

J. B. Kortright, M. Rice, and K. D. Franck, "Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
[CrossRef]

Surf. Sci.

R. H. Muller, "Definitions and conventions in ellipsometry," Surf. Sci. 16, 14-33 (1996).
[CrossRef]

Other

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw Hill, 1995), Vol. II, Chap. 33.

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

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

W. H. Southwell, "Thin film transmissive phase retarders," in Proceedings of International Conference on Lasers, C.B.Collins, ed. (STS, 1981), pp. 578-585.

Ref. , Chap. 4.

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Figures (5)

Fig. 1
Fig. 1

Embedded multilayer thin-film transmission device that operates 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. This near-complete-transmission QWR or HWR transforms incident linearly polarized light (LPL) at 45° azimuth into circularly polarized light (CPL) or linearly polarized light at 45 ° azimuth, respectively, depending on the parameters of the multilayer stack and angle of incidence.

Fig. 2
Fig. 2

Panels A1, A2 and B1, B2 show the spectral and angular sensitivities, respectively, of a QWR cube design that operates at λ = 1.55 μ m and ϕ 0 = 45 ° . The design uses an 11-layer stack of Si ( n 0 = 3.4777 ) and Si O 2 ( n 1 = 1.4444 ) thin films embedded in a high-index GaP ( n 2 = 3.0535 ) prism. The thicknesses of the Si O 2 and Si thin films are 17.5 and 67.1 nm , respectively. Both the p and s transmittances T p 2 and T s 2 and the differential transmission phase shift Δ t are represented.

Fig. 3
Fig. 3

Panels A1, A2, A3 and B1, B2, B3 show the sensitivities of the QWR cube design that operates at λ = 1.55 μ m and ϕ 0 = 45 ° to errors of thickness of the odd- and even-numbered films, respectively. Both the p and s transmittances T p 2 and T s 2 and the differential transmission phase shift Δ t are represented in this figure. The design uses an 11-layer stack of Si ( n 2 = 3.4777 ) and Si O 2 ( n 1 = 1.4444 ) thin films embedded in a high-index GaP ( n 0 = 3.0535 ) prism. The thicknesses of the Si O 2 and Si thin films are changed by ± 5 % around the design values of 17.5 and 67.1 nm , respectively.

Fig. 4
Fig. 4

Panels A1, A2 and B1, B2 show the spectral and angular sensitivities, respectively, of an HWR cube design that operates at λ = 1.55 μ m and ϕ 0 = 45 ° and that uses a centrosymmetric seven-layer stack of Si ( n 2 = 3.4777 ) and Si O 2 ( n 1 = 1.4444 ) thin films embedded in a Si prism ( n 0 = 3.4777 ) . The design thicknesses of the Si O 2 and Si thin films are 44.0 nm and d 2 = 223.0 nm , respectively. Both the p and s transmittances T p 2 and T s 2 and the differential transmission phase shift Δ t are represented.

Fig. 5
Fig. 5

Transmittances T p 2 and T s 2 for p- and s-polarized light and differential transmission phase shift Δ t of an HWR cube design, which operates at λ = 1.55 μ m and ϕ 0 = 45 ° , are plotted versus the error of thickness of each film. The design uses a seven-layer stack of Si ( n 2 = 3.4777 ) and Si O 2 ( n 1 = 1.4444 ) thin films embedded in a high-index Si ( n 0 = 3.4777 ) prism. The thicknesses of the Si O 2 and Si thin films are changed by ± 5 % around the design values of 44.0 and 223.0 nm , respectively.

Equations (10)

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z i = d i D i ,
D i = λ 4 n i , i = 1 , 2 , 3 , , m ,
R ν 2 + T ν 2 = 1 , ν = p , s ,
T p ± j T s = 0 ( QWR ) ,
T p + T s = 0 ( HWR )
R p 2 = R s 2 0 .
( z 1 , z 2 ) = ( 0.0651 , 0.6019 ) ,
( d 1 , d 2 ) = ( 17.5 , 67.1 ) nm .
( z 1 , z 2 ) = ( 0.1641 , 2.0013 ) ,
( d 1 , d 2 ) = ( 44.0 , 223.0 ) nm .

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