Abstract

We adopted an existing formalism and modified it to simulate, with high precision, the transmission, reflection, and absorption of multiple-plate birefringent devices as a function of frequency. To validate the model, we use it to compare the measured properties of an achromatic five-plate device with a broadband antireflection coating to expectations derived from the material optical constants and its geometric configuration. The half-wave plate presented here is observed to perform well with a phase shift variation of <2° from the ideal 180° over a bandwidth of Δν/ν1 at millimeter wavelengths. This formalism represents a powerful design tool for birefringent polarization modulators and enables its optical properties to be specified with high accuracy.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Pisano, G. Savini, P. A. R. Ade, W. K. Gear, and V. Haynes, "Achromatic half-wave plate for submillimeter instruments in cosmic microwave background astronomy: experimental characterization," Appl. Opt. 45, 6982-6989 (2006).
    [CrossRef] [PubMed]
  2. E. Hecht and A. Zajac, Optics (Addison-Wesley, 2003).
  3. S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
    [CrossRef]
  4. J. Tinbergen, "Precision spectropolarimetry of starlight: development of a wide-band version of the Dollfus polarization modulator," Astron. Astrophys. 23, 25-48 (1973).
  5. S. Pancharatnam, "Achromatic combinations of birefringent plates--Part II. An achromatic quarter wave plate," Proc. Indian Acad. Sci., Sect. A 42, 24-31 (1955).
  6. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2001).
  7. S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).
  8. A. M. Title and W. J. Rosenberg, "Achromatic retardation plates," in Proc. SPIE 307,120-131 (1981).
  9. C. W. Oseen, "The theory of liquid crystals," Trans. Faraday Soc. 29, 883-899 (1933).
    [CrossRef]
  10. F. Abelés, "Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieus stratifies," Ann. Phys. (Paris) 5, 598-604 (1950).
  11. S. Adachi and E. M. Kennaugh, "The analysis of a broad-band circular polarizer including interface reactions," IRE Trans. Microwave Theory Tech. 8, 520-524 (1960).
  12. D. W. Berreman, "Optics in stratified and anisotropic media: 4 × 4-matrix formulation," J. Opt. Soc. Am. A 62, 502-510 (1972).
    [CrossRef]
  13. S. Teitler and B. W. Henvis, "Refraction in stratified, anisotropic media," J. Opt. Soc. Am. 60, 830-834 (1970).
    [CrossRef]
  14. D. W. Berreman and T. J. Scheffer, "Bragg reflection of light from single-domain cholesteric liquid-crystal films," Phys. Rev. Lett. 25, 577-581 (1970).
    [CrossRef]
  15. R. Dreher and G. Meier, "Optical properties of cholesteric liquid crystals," Phys. Rev. A 8, 1616-1623 (1973).
    [CrossRef]

2006

2003

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

1991

S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
[CrossRef]

1973

J. Tinbergen, "Precision spectropolarimetry of starlight: development of a wide-band version of the Dollfus polarization modulator," Astron. Astrophys. 23, 25-48 (1973).

R. Dreher and G. Meier, "Optical properties of cholesteric liquid crystals," Phys. Rev. A 8, 1616-1623 (1973).
[CrossRef]

1972

D. W. Berreman, "Optics in stratified and anisotropic media: 4 × 4-matrix formulation," J. Opt. Soc. Am. A 62, 502-510 (1972).
[CrossRef]

1970

S. Teitler and B. W. Henvis, "Refraction in stratified, anisotropic media," J. Opt. Soc. Am. 60, 830-834 (1970).
[CrossRef]

D. W. Berreman and T. J. Scheffer, "Bragg reflection of light from single-domain cholesteric liquid-crystal films," Phys. Rev. Lett. 25, 577-581 (1970).
[CrossRef]

1955

S. Pancharatnam, "Achromatic combinations of birefringent plates--Part II. An achromatic quarter wave plate," Proc. Indian Acad. Sci., Sect. A 42, 24-31 (1955).

1950

F. Abelés, "Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieus stratifies," Ann. Phys. (Paris) 5, 598-604 (1950).

1933

C. W. Oseen, "The theory of liquid crystals," Trans. Faraday Soc. 29, 883-899 (1933).
[CrossRef]

Abelés, F.

F. Abelés, "Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieus stratifies," Ann. Phys. (Paris) 5, 598-604 (1950).

Adachi, S.

S. Adachi and E. M. Kennaugh, "The analysis of a broad-band circular polarizer including interface reactions," IRE Trans. Microwave Theory Tech. 8, 520-524 (1960).

Ade, P.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Ade, P. A. R.

Berreman, D. W.

D. W. Berreman, "Optics in stratified and anisotropic media: 4 × 4-matrix formulation," J. Opt. Soc. Am. A 62, 502-510 (1972).
[CrossRef]

D. W. Berreman and T. J. Scheffer, "Bragg reflection of light from single-domain cholesteric liquid-crystal films," Phys. Rev. Lett. 25, 577-581 (1970).
[CrossRef]

Bock, J.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2001).

Bowden, M.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Carlstrom, J.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Church, S.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Davidson, J. A.

S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
[CrossRef]

Dreher, R.

R. Dreher and G. Meier, "Optical properties of cholesteric liquid crystals," Phys. Rev. A 8, 1616-1623 (1973).
[CrossRef]

Ganga, K.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Gear, W.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Gear, W. K.

Haynes, V.

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 2003).

Henvis, B. W.

Hildebrand, R. H.

S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
[CrossRef]

Hinderks, J.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Hu, W.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Keating, B.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Kennaugh, E. M.

S. Adachi and E. M. Kennaugh, "The analysis of a broad-band circular polarizer including interface reactions," IRE Trans. Microwave Theory Tech. 8, 520-524 (1960).

Kovac, J.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Lange, A.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Leitch, E.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Mallie, O.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Meier, G.

R. Dreher and G. Meier, "Optical properties of cholesteric liquid crystals," Phys. Rev. A 8, 1616-1623 (1973).
[CrossRef]

Melhuish, S.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Murphy, A.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Novak, G.

S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
[CrossRef]

Oseen, C. W.

C. W. Oseen, "The theory of liquid crystals," Trans. Faraday Soc. 29, 883-899 (1933).
[CrossRef]

O'Sullivan, C.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Pancharatnam, S.

S. Pancharatnam, "Achromatic combinations of birefringent plates--Part II. An achromatic quarter wave plate," Proc. Indian Acad. Sci., Sect. A 42, 24-31 (1955).

Pernic, R. J.

S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
[CrossRef]

Piccirillo, L.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Pisano, G.

Platt, S. R.

S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
[CrossRef]

Pryke, C.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Rosenberg, W. J.

A. M. Title and W. J. Rosenberg, "Achromatic retardation plates," in Proc. SPIE 307,120-131 (1981).

Rusholme, B.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Savini, G.

Scheffer, T. J.

D. W. Berreman and T. J. Scheffer, "Bragg reflection of light from single-domain cholesteric liquid-crystal films," Phys. Rev. Lett. 25, 577-581 (1970).
[CrossRef]

Taylor, A.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Teitler, S.

Thompson, K.

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

Tinbergen, J.

J. Tinbergen, "Precision spectropolarimetry of starlight: development of a wide-band version of the Dollfus polarization modulator," Astron. Astrophys. 23, 25-48 (1973).

Title, A. M.

A. M. Title and W. J. Rosenberg, "Achromatic retardation plates," in Proc. SPIE 307,120-131 (1981).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2001).

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 2003).

Ann. Phys.

F. Abelés, "Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieus stratifies," Ann. Phys. (Paris) 5, 598-604 (1950).

Appl. Opt.

Astron. Astrophys.

J. Tinbergen, "Precision spectropolarimetry of starlight: development of a wide-band version of the Dollfus polarization modulator," Astron. Astrophys. 23, 25-48 (1973).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

D. W. Berreman, "Optics in stratified and anisotropic media: 4 × 4-matrix formulation," J. Opt. Soc. Am. A 62, 502-510 (1972).
[CrossRef]

Phys. Rev. A

R. Dreher and G. Meier, "Optical properties of cholesteric liquid crystals," Phys. Rev. A 8, 1616-1623 (1973).
[CrossRef]

Phys. Rev. Lett.

D. W. Berreman and T. J. Scheffer, "Bragg reflection of light from single-domain cholesteric liquid-crystal films," Phys. Rev. Lett. 25, 577-581 (1970).
[CrossRef]

Proc. Indian Acad. Sci., Sect.

S. Pancharatnam, "Achromatic combinations of birefringent plates--Part II. An achromatic quarter wave plate," Proc. Indian Acad. Sci., Sect. A 42, 24-31 (1955).

Publ. Astron. Soc. Pac.

S. R. Platt, R. H. Hildebrand, R. J. Pernic, J. A. Davidson, and G. Novak, "100 μm array polarimetry from the Kuiper Airborne Observatory: instrumentation, techniques, and first results," Publ. Astron. Soc. Pac. 103, 1193-1210 (1991).
[CrossRef]

Trans. Faraday Soc.

C. W. Oseen, "The theory of liquid crystals," Trans. Faraday Soc. 29, 883-899 (1933).
[CrossRef]

Other

E. Hecht and A. Zajac, Optics (Addison-Wesley, 2003).

S. Adachi and E. M. Kennaugh, "The analysis of a broad-band circular polarizer including interface reactions," IRE Trans. Microwave Theory Tech. 8, 520-524 (1960).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2001).

S. Church, P. Ade, J. Bock, M. Bowden, J. Carlstrom, K. Ganga, W. Gear, J. Hinderks, W. Hu, B. Keating, J. Kovac, A. Lange, E. Leitch, O. Mallie, S. Melhuish, A. Murphy, B. Rusholme, C. O'Sullivan, L. Piccirillo, C. Pryke, A. Taylor, and K. Thompson, "QUEST on DASI: a south pole cosmic microwave background polarization experiment," New Astron. Rev 47, 1083-1089 (2003).

A. M. Title and W. J. Rosenberg, "Achromatic retardation plates," in Proc. SPIE 307,120-131 (1981).

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 (7)

Fig. 1
Fig. 1

Polarization states on the Poincaré sphere.

Fig. 2
Fig. 2

Rotations on the Poincaré sphere for a five-plate HWP. The rotations by different amounts proportional to the frequencies are performed by the initial polarized state (1) in the order (2, 3, 4, 5, 6). After the five rotations, all the frequencies (here selected to be in a 30% variation of the central frequency ν 0 ) will regroup in a small area denoting the achromatic nature of the device. This result is independent of the initial position on the sphere equator.

Fig. 3
Fig. 3

Concept figure with exploded view of the QUaD HWP build.

Fig. 4
Fig. 4

Sapphire ordinary and extraordinary real part of the refraction indices as a function of frequency.

Fig. 5
Fig. 5

Ordinary and extraordinary sapphire absorption coefficient as a function of frequency.

Fig. 6
Fig. 6

Graphical representation of the Mueller matrix of the HWP at a given angle ( θ = 0 ° ) as a function of frequency. The Mueller matrix of the HWP as a part of a specific instrument can be obtained by integrating each matrix element over the spectral band of the instrument.

Fig. 7
Fig. 7

Simulation of the normalized Q, U, and V Stokes parameters for the reflected component as a function of frequency for the QUaD HWP 100   GHz band.

Equations (105)

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

< 2 °
Δ ν / ν 1
λ / 2
n e , n o , α e , α o
Δ φ = ( k e k o ) d = 2 π ν d c ( n e n o ) ,
150   GHz
( n e , n o )
Ψ ( z ) = ( E x ( z ) H y ( z ) E y ( z ) H x ( z ) ) .
Ψ ( 0 ) = Q ^ i Ψ ( d ) ,
Q ^ i
Q ^ i = [ cos k e d j η e sin k e d 0 0 j sin k e d / η e cos k e d 0 0 0 0 cos k o d j η o sin k o d 0 0 j sin k o d / η o cos k o d ] ,
k e , o
η = μ / ε = μ / n ( ν )
z i
z f
Ψ ( z i ) = P ^ Ψ ( z f ) ,
P ^
P ^ = i P ^ i = i ( Φ i Q ^ i Φ i 1 ) ,
Φ i
Φ ^ i ( φ ) = [ cos φ i I ^ sin φ i I ^ sin φ i I ^ cos φ i I ^ ] ,
I ^
φ i
E x ( z i ) = E x i + E x r , E y ( z i ) = E y i + E y r ,
H x ( z i ) = H x i H x r , H y ( z i ) = H y i H y r .
z f
( E x i + E x r E x i E x r E y i + E y r E y i E y r ) = P ^ ( E x t E x t E y t E y t ) .
P ^
P ^
[ E x t ( ν ) E y t ( ν ) ] = T ^ ( ν ) ( E x i E y i ) ,
[ E x r ( ν ) E y r ( ν ) ] = R ^ ( ν ) ( E x i E y i ) .
E i
E t ( ν ) = [ E x t ( ν ) , E y t ( ν ) ]
E r ( ν ) = [ E x r ( ν ) , E y r ( ν ) ]
E i = ( E x i , E y i )
( i , j )
P ^
p i j , ( i , j = 0, , 3 )
E x i + E x r = ( p 00 + p 01 ) E x t + ( p 02 + p 03 ) E y t ,
E x i E x r = ( p 10 + p 11 ) E x t + ( p 12 + p 13 ) E y t ,
E y i + E y r = ( p 20 + p 21 ) E x t + ( p 22 + p 23 ) E y t ,
E y i E y r = ( p 30 + p 31 ) E x t + ( p 32 + p 33 ) E y t .
2 E i = A ^ E t
A ^ = [ a b c d ] ,
a = p 00 + p 01 + p 10 + p 11 = i = 0 , 1 ; j = 0 , 1 p i j ,
b = p 02 + p 03 + p 12 + p 13 = i = 0 , 1 ; j = 2 , 3 p i j ,
c = p 20 + p 21 + p 30 + p 31 = i = 2 , 3 ; j = 0 , 1 p i j ,
d = p 22 + p 23 + p 30 + p 31 = i = 2 , 3 ; j = 2 , 3 p i j ;
E t = 2 A ^ 1 E i
T ^ = 2 det ( A ^ ) [ d b c a ] .
E r
E t
( n e , n o , α e , α o )
2 × 2
Q ^ i ( e ) = [ cos k e d j η e sin k e d j sin k e d η e cos k e d ] 1 2 [ e j k e d + e + j k e d η e ( e j k e d e + j k e d ) e j k e d e + j k e d η e e j k e d + e + j k e d ] .
2 × 2
Q ^ i = [ e α e d Q ^ i ( e ) 0 0 e α o d Q ^ i ( o ) ] .
Q ^ i
Q ^ i
Q ^ i
A ( ν ) = 1 | E t ( ν ) | 2 | E r ( ν ) | 2 .
E x ( ν , θ )
E y ( ν , θ )
δ ( ν , θ )
QUaD 7
n 1 = 1.2
n 2 = 1.74
n 3 = 2.66
d 1 = 533   μm
d 2 = 283   μm
d 3 = 166   μm
120   GHz
1   THz
n o ( ν ) = 3.053 + 4.7 × 10 4 ν + 2.2 × 10 10 ν 2 + 1.1 × 10 12 ν 3 ,
n e ( ν ) = 3.387 + 1.3 × 10 5 ν ,
α o ( ν ) = 8.7 × 10 5 ν + 3.1 × 10 7 ν 2 + 3.0 × 10 10 ν 3 ,
α e ( ν ) = 1.47 × 10 7 ν 2.2 .
E out ( ν ; θ , ξ ) = T ^ ( ν ) E in ( θ , ξ ) ,
E in ( θ , ξ ) = ( E x in E y in ) = ( cos ( θ ) sin ( θ ) e i ξ ) ,
tan   θ = E y in / E x in
I out ( ε ) ( θ , ξ ) = ε ( ν ) | T ^ ( ν ) E in ( θ , ξ ) | 2 d ν .
( x O y ¯ )
Q = ± 1
U = ± 1
V = ± 1
( θ , ξ )
Q = ± 1 θ = 0 ° / 90 ° ,     ξ = 0 ° ,
U = ± 1 θ = ± 45 ° ,     ξ = 0 ° ,
V = ± 1 θ = 45 ° ,     ξ = ± 90 ° .
Q = 1
Q = 1
[ a 00 a 01 a 02 a 03 a 10 a 11 a 12 a 13 a 20 a 21 a 22 a 23 a 30 a 31 a 32 a 33 ] ( 1 ± 1 0 0 ) = ( a 00 ± a 01 a 10 ± a 11 a 20 ± a 21 a 30 ± a 31 ) .
U = ± 1
V = ± 1
( a 00 ± a 0 K a 10 ± a 1 K a 20 ± a 2 K a 30 ± a 3 K ) ,
K = 1 , 2 , 3
{ a i j }
a 00 = I o u t ( ε ) ( 0 ° , 0 ° ) + I out ( ε ) ( 90 ° , 0 ° ) 2 ;
a 00 = I Q = 1 + I Q = 1 2 , a 01 = I Q = 1 I Q = 1 2 ,
a 10 = Q Q = 1 + Q Q = 1 2 , a 11 = Q Q = 1 Q Q = 1 2 ,
a 20 = U Q = 1 + U Q = 1 2 , a 21 = U Q = 1 U Q = 1 2 ,
a 30 = V Q = 1 + V Q = 1 2 , a 31 = V Q = 1 V Q = 1 2 ,
( > 90   GHz )
ν 0
( θ = 0 ° )
100   GHz

Metrics