Abstract

The net differential phase shift Δt introduced between the orthogonal p and s linear polarizations after four successive total internal reflections inside an in-line chevron dual-Fresnel-rhomb retarder is a function of the first internal angle of incidence φ and prism refractive index n. Retardance of 3λ/4 (i.e., Δt=270°) is achieved with minimum angular sensitivity when φ=45° and n=1.900822. Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of Δt from 270° is 4° over a wave length range of 0.55λ1.1μm in the visible and near-IR spectrum. For a SiC prism, whose totally reflecting surfaces are coated with an optically thick MgF2 film, Δt=270° at two wavelengths: λ1=0.707μm and λ2=4.129μm. This coated prism has a maximum retardance error of 5° over>three octaves (0.5 to 4.5μm) in the visible, near-, and mid-IR spectral range. Another mid-IR 3λ/4 retarder uses a Si prism, which is coated by an optically thick silicon oxynitride film of the proper composition, to achieve retardance that differs from 270° by <0.5° over the 35μm spectral range.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).
  2. R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617-622 (1966).
    [CrossRef]
  3. J. M. Bennett, “Critical evaluation of rhomb-type quarter-wave retarders,” Appl. Opt. 9, 2123-2129 (1970).
    [CrossRef] [PubMed]
  4. I. Filinski and T. Skettrup, “Achromatic phase retarders constructed from right-angle prisms: design,” Appl. Opt. 23, 2747-2751 (1984).
    [CrossRef] [PubMed]
  5. E. Spiller, “Totally reflecting thin-film phase retarders,” Appl. Opt. 23, 3544-3549 (1984).
    [CrossRef] [PubMed]
  6. A. M. Kan'an and R. M. A. Azzam, “In-line quarter-wave retarders for the IR using total refraction and total internal reflection in a prism,” Opt. Eng. 33, 2029-2033 (1994).
    [CrossRef]
  7. E. Cojocaru, “Simple relations for thin-film-coated phase-retarding totally reflecting prisms,” Appl. Opt. 33, 2678-2682 (1994).
    [CrossRef] [PubMed]
  8. R. M. A. Azzam and M. M. K. Howlader, “Silicon-based polarization optics for the 1.30 and 1.55 μm communication wavelengths,” J. Lightwave Technol. 14, 873-878 (1996).
    [CrossRef]
  9. 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]
  10. R. M. A. Azzam and H. K. Khanfar, “Polarization properties of retroreflecting right-angle prisms,” Appl. Opt. 47, 359-364(2008).
    [CrossRef] [PubMed]
  11. http://www.us.schott.com/optics_devices/english/products/flash/abbediagramm_flash.html.
  12. http://www.ohara-inc.co.jp/en/product/optical/opticalglass/data.html.
  13. W. J. Tropf and M. E. Thomas, “Infrared refractive index and thermo-optic coefficient measurement at APL,” Johns Hopkins APL Tech. Dig. 19, 293-298 (1998).
  14. W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Chap. 33, Vol. 2.
  15. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
  16. T. Bååk, “Silicon oxynitride: a material for GRIN optics,” Appl. Opt. 21, 1069-1072 (1982).
    [CrossRef] [PubMed]
  17. W. L. Wolfe and G. J. Zissis, eds., The Infrared Handbook (Office of Naval Research, 1978).

2008 (1)

2004 (1)

1998 (1)

W. J. Tropf and M. E. Thomas, “Infrared refractive index and thermo-optic coefficient measurement at APL,” Johns Hopkins APL Tech. Dig. 19, 293-298 (1998).

1996 (1)

R. M. A. Azzam and M. M. K. Howlader, “Silicon-based polarization optics for the 1.30 and 1.55 μm communication wavelengths,” J. Lightwave Technol. 14, 873-878 (1996).
[CrossRef]

1994 (2)

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

E. Cojocaru, “Simple relations for thin-film-coated phase-retarding totally reflecting prisms,” Appl. Opt. 33, 2678-2682 (1994).
[CrossRef] [PubMed]

1984 (2)

1982 (1)

1970 (1)

1966 (1)

R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617-622 (1966).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and H. K. Khanfar, “Polarization properties of retroreflecting right-angle prisms,” Appl. Opt. 47, 359-364(2008).
[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 M. M. K. Howlader, “Silicon-based polarization optics for the 1.30 and 1.55 μm communication wavelengths,” J. Lightwave Technol. 14, 873-878 (1996).
[CrossRef]

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

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

Bååk, T.

Bashara, N. M.

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

Bennett, J. M.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).

Cojocaru, E.

Filinski, I.

Harris, T. J.

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Chap. 33, Vol. 2.

Howlader, M. M. K.

R. M. A. Azzam and M. M. K. Howlader, “Silicon-based polarization optics for the 1.30 and 1.55 μm communication wavelengths,” J. Lightwave Technol. 14, 873-878 (1996).
[CrossRef]

Kan'an, A. M.

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

Khanfar, H. K.

King, R. J.

R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617-622 (1966).
[CrossRef]

Skettrup, T.

Spiller, E.

Spinu, C. L.

Thomas, M. E.

W. J. Tropf and M. E. Thomas, “Infrared refractive index and thermo-optic coefficient measurement at APL,” Johns Hopkins APL Tech. Dig. 19, 293-298 (1998).

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Chap. 33, Vol. 2.

Tropf, W. J.

W. J. Tropf and M. E. Thomas, “Infrared refractive index and thermo-optic coefficient measurement at APL,” Johns Hopkins APL Tech. Dig. 19, 293-298 (1998).

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Chap. 33, Vol. 2.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).

Appl. Opt. (6)

J. Lightwave Technol. (1)

R. M. A. Azzam and M. M. K. Howlader, “Silicon-based polarization optics for the 1.30 and 1.55 μm communication wavelengths,” J. Lightwave Technol. 14, 873-878 (1996).
[CrossRef]

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

J. Sci. Instrum. (1)

R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617-622 (1966).
[CrossRef]

Johns Hopkins APL Tech. Dig. (1)

W. J. Tropf and M. E. Thomas, “Infrared refractive index and thermo-optic coefficient measurement at APL,” Johns Hopkins APL Tech. Dig. 19, 293-298 (1998).

Opt. Eng. (1)

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

Other (6)

http://www.us.schott.com/optics_devices/english/products/flash/abbediagramm_flash.html.

http://www.ohara-inc.co.jp/en/product/optical/opticalglass/data.html.

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Chap. 33, Vol. 2.

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

W. L. Wolfe and G. J. Zissis, eds., The Infrared Handbook (Office of Naval Research, 1978).

M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).

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 (9)

Fig. 1
Fig. 1

In-line symmetric chevron dual-Fresnel-rhomb prism retarder that uses four TIRs at the same angle of incidence φ = 45 ° . Light enters and leaves the prism normal to its entrance and exit faces, which are ARC. p and s are the linear polarizations parallel and perpendicular to the common plane of incidence, respectively. The length/aperture aspect ratio of this compact prism is L / a = 2 .

Fig. 2
Fig. 2

Cumulative retardance Δ t ( φ ) [Eq. (1)] plotted versus angle of incidence φ in the range of 43 ° φ 47 ° for a prism with refractive index n = 1.900822 . Notice that Δ t = 270 ° and Δ t / φ = 0 are satisfied at φ = 45 ° .

Fig. 3
Fig. 3

Refractive index n ( λ ) of Schott glasses SF66 and P-SF67 and Ohara glasses S-NPH 2 and L-NBH54 plotted versus wavelength λ. The coefficients of the dispersion formulas of theses glasses [Eq. (8)] are listed in Table 1. All curves intersect the line n = 1.900822 at wavelengths λ that are also listed in Table 1.

Fig. 4
Fig. 4

Cumulative retardance Δ t ( λ ) plotted versus wavelength λ over the spectral range of 0.55 λ 1.1 μm for uncoated in-line chevron four-reflection retarders that are made of optical glasses whose properties are summarized in Table 1.

Fig. 5
Fig. 5

Relative refractive index n ( λ ) = n ( Si C ) / n ( Mg F 2 ) of Mg F 2 -coated SiC plotted as a function of wavelength λ over the spectral range of 0.5 λ 4.5 μm . Index ratio n ( λ ) = 1.900822 at wavelengths λ 1 = 0.707 μm and λ 2 = 4.129 μm .

Fig. 6
Fig. 6

Cumulative retardance Δ t ( λ ) of chevron four-reflection Mg F 2 -coated SiC retarder plotted versus wavelength λ in the spectral range of 0.5 λ 4.5 μm . Exact retardance, Δ t = 270 ° , is achieved at wavelengths λ 1 = 0.707 μm and λ 2 = 4.129 μm .

Fig. 7
Fig. 7

Index ratio, n = n ( Si ) / n ( Si O N ) , calculated as function of wavelength λ ( μm ) for discrete values of x = 0.1 to 0.5 in equal steps of 0.1, where x is the mole fraction of Si O 2 in the SiON film.

Fig. 8
Fig. 8

Mole fraction x of Si O 2 in SiON film calculated using Eq. (15), at which n = 1.900822 is plotted versus wave length λ in the spectral range of 1.2 λ 5.0 μm .

Fig. 9
Fig. 9

Relative refractive index, n = n ( Si ) / n ( Si O N ) , and cumulative retardance Δ t ( λ ) plotted versus wavelength λ, in the spectral range of 3.0 λ 5.0 μm , for a chevron four-reflection SiON-coated Si retarder. Δ t = 270 ° is achieved at center wavelength λ = 4.0 μm with retardance error of < 0.5 ° over the 3 5 μm mid-IR spectral range.

Tables (2)

Tables Icon

Table 1 Constants of Dispersion Relations [Eq. (8)] of Four Optical Glasses [11, 12] a

Tables Icon

Table 2 Constants of Dispersion Relations [Eq. (8)] of SiC and Mg F 2 a

Equations (18)

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

Δ t ( φ ) = 2 [ Δ ( φ ) + Δ ( 90 ° φ ) ] ,
Δ ( φ ) = 2 tan 1 [ ( n 2 sin 2 φ 1 ) 1 / 2 / ( n sin φ tan φ ) ] .
Δ t ( 45 ° ) = 8 tan 1 [ ( n 2 2 ) 1 / 2 / n ] .
Δ t ( 45 ° ) = 3 π / 2 ,
[ ( n 2 2 ) 1 / 2 / n ] = tan ( 3 π / 16 ) .
n = ( 2 + 1 ) [ ( 4 + 2 2 ) 1 / 2 1 ] 1 / 2 = 1.900822.
Δ t = 270 ° , Δ t / φ = 0 ,
n 2 1 = B 1 λ 2 λ 2 C 1 + B 2 λ 2 λ 2 C 2 + B 3 λ 2 λ 2 C 3 .
n / λ = ( λ / n ) i = 1 3 B i C i ( λ 2 C i ) 2 ,
n = n ( Si C ) / n ( Mg F 2 ) .
η = cos 2 [ ( Δ t 270 ° ) / 2 ] .
n = n ( Si ) / n ( Si O N ) ,
n ( Si O N ) = x n ( Si O 2 ) + ( 1 x ) n ( Si 3 N 4 ) .
Si O 2 : B 1 = 1.09877 , C 1 = ( 0.0924317 ) 2 , Si 3 N 4 : B 1 = 2.8939 , C 1 = ( 0.13967 ) 2 , B 2 = B 3 = 0.
x = n ( Si 3 N 4 ) 0.526088 n ( Si ) n ( Si 3 N 4 ) n ( Si O 2 ) .
γ = ( n / n ) 2 , x = λ 2 .
( γ 1 ) Q 0 Q 0 + γ Q 0 i = 1 3 Q i Q 0 i = 1 3 Q i = 0.
Q 0 = ( x C 1 ) ( x C 2 ) ( x C 3 ) , Q 1 = B 1 x ( x C 2 ) ( x C 3 ) , Q 2 = B 2 x ( x C 1 ) ( x C 3 ) , Q 3 = B 3 x ( x C 1 ) ( x C 2 ) .

Metrics