Abstract

Driving on an analogy with the technique of composite pulses in quantum physics, we propose highly efficient broadband polarization converters composed of sequences of ordinary retarders rotated at specific angles with respect to their fast-polarization axes.

© 2012 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).
  2. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1977).
  3. D. Goldstein and E. Collett, Polarized Light (CRC, 2003).
  4. C. D. West and A. S. Makas, “The spectral dispersion of birefringence, especially of birefringent plastic sheets,” J. Opt. Soc. Am. 39, 791–794 (1949).
    [CrossRef]
  5. M. G. Destriau and J. Prouteau, “Réalisation d’un quart d’onde quasi achromatique par juxtaposition de deux lames cristallines de méme nature,” J. Phys. Radium 10, 53–55 (1949).
    [CrossRef]
  6. S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I: An achromatic circular polarizer,” Proc. Indian Acad. Sci. A41, 130–136 (1955).
  7. S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II: An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. A41, 137–144 (1955).
  8. S. E. Harris, E. O. Ammann, and A. C. Chang, “Optical network synthesis using birefringent crystals. I. Synthesis of lossless networks of equal-length crystals,” J. Opt. Soc. Am. 54, 1267–1279 (1964).
    [CrossRef]
  9. C. M. McIntyre and S. E. Harris, “Achromatic wave plates for the visible spectrum,” J. Opt. Soc. Am. 58, 1575–1580 (1968).
    [CrossRef]
  10. H. Kubo and R. Nagata, “Equations of light propagation in an inhomogeneous crystal,” Opt. Commun. 27, 201–206 (1978).
    [CrossRef]
  11. H. Kubo and R. Nagata, “Stokes parameters representation of the light propagation equations in inhomogeneous anisotropic, optically active media,” Opt. Commun. 34, 306–308 (1980).
    [CrossRef]
  12. H. Kuratsuji and S. Kakigi, “Maxwell-Schrodinger equation for polarized light and evolution of the Stokes parameters,” Phys. Rev. Lett. 80, 1888–1891 (1998).
    [CrossRef]
  13. H. Kuratsuji, R. Botet, and R. Seto, “Electromagnetic gyration,” Prog. Theor. Phys. 117, 195–217 (2007).
    [CrossRef]
  14. A. A. Rangelov, U. Gaubatz, and N. V. Vitanov, “Broadband adiabatic conversion of light polarization,” Opt. Commun. 283, 3891–3894 (2010).
    [CrossRef]
  15. R. Botet and H. Kuratsuji, “Light-polarization tunneling in optically active media,” J. Phys. A 41, 035301 (2008).
    [CrossRef]
  16. R. Botet, and H. Kuratsuji, “Stochastic theory of the Stokes parameters in randomly twisted fiber,” Phys. Rev. E 81, 036602 (2010).
    [CrossRef]
  17. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
    [CrossRef]
  18. M. H. Levitt, “Composite pulses,” Prog. Nucl. Magn. Reson. Spectrosc. 18, 61–122 (1986).
    [CrossRef]
  19. R. Freeman, Spin Choreography (Spektrum, 1997).
  20. S. Wimperis, “Broadband, narrowband and passband composite pulses for use in advanced NMR experiments,” J. Magn. Reson. Ser. A 109, 221–231 (1994).
    [CrossRef]
  21. S. S. Ivanov and N. V. Vitanov, “High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses,” Opt. Lett. 36, 1275–1277 (2011).
    [CrossRef]
  22. B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-fidelity quantum information processing,” Phys. Rev. A 83, 053420 (2011).
    [CrossRef]
  23. B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106, 233001 (2011).
    [CrossRef]
  24. H. Häffner, C. F. Roos, and R. Blatt, “Quantum computing with trapped ions,” Phys. Rep. 469, 155–203 (2008).
    [CrossRef]
  25. S. S. Ivanov and N. V. Vitanov, “Scalable uniform construction of highly conditional quantum gates,” Phys. Rev. A 84, 022319 (2011).
    [CrossRef]
  26. A. Ardavan, “Exploiting the Poincare–Bloch symmetry to design high-fidelity broadband composite linear retarders,” New J. Phys. 9, 24 (2007).
    [CrossRef]
  27. K. R. Brown, A. W. Harrow, and I. L. Chuang, “Arbitrarily accurate composite pulse sequences,” Phys. Rev. A 70, 052318 (2004).
    [CrossRef]
  28. W. G. Alway and J. A. Jones, “Arbitrary precision composite pulses for NMR quantum computing,” J. Magn. Reson. 189, 114–120 (2007).
    [CrossRef]
  29. D. Mc Hugh and J. Twamley, “Sixth-order robust gates for quantum control,” Phys. Rev. A 71, 012327 (2005).
    [CrossRef]
  30. H. Hurvitz and R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 493–495 (1941).
    [CrossRef]

2011 (4)

B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-fidelity quantum information processing,” Phys. Rev. A 83, 053420 (2011).
[CrossRef]

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106, 233001 (2011).
[CrossRef]

S. S. Ivanov and N. V. Vitanov, “Scalable uniform construction of highly conditional quantum gates,” Phys. Rev. A 84, 022319 (2011).
[CrossRef]

S. S. Ivanov and N. V. Vitanov, “High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses,” Opt. Lett. 36, 1275–1277 (2011).
[CrossRef]

2010 (2)

A. A. Rangelov, U. Gaubatz, and N. V. Vitanov, “Broadband adiabatic conversion of light polarization,” Opt. Commun. 283, 3891–3894 (2010).
[CrossRef]

R. Botet, and H. Kuratsuji, “Stochastic theory of the Stokes parameters in randomly twisted fiber,” Phys. Rev. E 81, 036602 (2010).
[CrossRef]

2008 (2)

R. Botet and H. Kuratsuji, “Light-polarization tunneling in optically active media,” J. Phys. A 41, 035301 (2008).
[CrossRef]

H. Häffner, C. F. Roos, and R. Blatt, “Quantum computing with trapped ions,” Phys. Rep. 469, 155–203 (2008).
[CrossRef]

2007 (3)

A. Ardavan, “Exploiting the Poincare–Bloch symmetry to design high-fidelity broadband composite linear retarders,” New J. Phys. 9, 24 (2007).
[CrossRef]

W. G. Alway and J. A. Jones, “Arbitrary precision composite pulses for NMR quantum computing,” J. Magn. Reson. 189, 114–120 (2007).
[CrossRef]

H. Kuratsuji, R. Botet, and R. Seto, “Electromagnetic gyration,” Prog. Theor. Phys. 117, 195–217 (2007).
[CrossRef]

2005 (1)

D. Mc Hugh and J. Twamley, “Sixth-order robust gates for quantum control,” Phys. Rev. A 71, 012327 (2005).
[CrossRef]

2004 (1)

K. R. Brown, A. W. Harrow, and I. L. Chuang, “Arbitrarily accurate composite pulse sequences,” Phys. Rev. A 70, 052318 (2004).
[CrossRef]

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

1998 (1)

H. Kuratsuji and S. Kakigi, “Maxwell-Schrodinger equation for polarized light and evolution of the Stokes parameters,” Phys. Rev. Lett. 80, 1888–1891 (1998).
[CrossRef]

1994 (1)

S. Wimperis, “Broadband, narrowband and passband composite pulses for use in advanced NMR experiments,” J. Magn. Reson. Ser. A 109, 221–231 (1994).
[CrossRef]

1986 (1)

M. H. Levitt, “Composite pulses,” Prog. Nucl. Magn. Reson. Spectrosc. 18, 61–122 (1986).
[CrossRef]

1980 (1)

H. Kubo and R. Nagata, “Stokes parameters representation of the light propagation equations in inhomogeneous anisotropic, optically active media,” Opt. Commun. 34, 306–308 (1980).
[CrossRef]

1978 (1)

H. Kubo and R. Nagata, “Equations of light propagation in an inhomogeneous crystal,” Opt. Commun. 27, 201–206 (1978).
[CrossRef]

1968 (1)

1964 (1)

1955 (2)

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I: An achromatic circular polarizer,” Proc. Indian Acad. Sci. A41, 130–136 (1955).

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II: An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. A41, 137–144 (1955).

1949 (2)

M. G. Destriau and J. Prouteau, “Réalisation d’un quart d’onde quasi achromatique par juxtaposition de deux lames cristallines de méme nature,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

C. D. West and A. S. Makas, “The spectral dispersion of birefringence, especially of birefringent plastic sheets,” J. Opt. Soc. Am. 39, 791–794 (1949).
[CrossRef]

1941 (1)

Alway, W. G.

W. G. Alway and J. A. Jones, “Arbitrary precision composite pulses for NMR quantum computing,” J. Magn. Reson. 189, 114–120 (2007).
[CrossRef]

Ammann, E. O.

Ardavan, A.

A. Ardavan, “Exploiting the Poincare–Bloch symmetry to design high-fidelity broadband composite linear retarders,” New J. Phys. 9, 24 (2007).
[CrossRef]

Azzam, M. A.

M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1977).

Bashara, N. M.

M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1977).

Blatt, R.

H. Häffner, C. F. Roos, and R. Blatt, “Quantum computing with trapped ions,” Phys. Rep. 469, 155–203 (2008).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

Botet, R.

R. Botet, and H. Kuratsuji, “Stochastic theory of the Stokes parameters in randomly twisted fiber,” Phys. Rev. E 81, 036602 (2010).
[CrossRef]

R. Botet and H. Kuratsuji, “Light-polarization tunneling in optically active media,” J. Phys. A 41, 035301 (2008).
[CrossRef]

H. Kuratsuji, R. Botet, and R. Seto, “Electromagnetic gyration,” Prog. Theor. Phys. 117, 195–217 (2007).
[CrossRef]

Brown, K. R.

K. R. Brown, A. W. Harrow, and I. L. Chuang, “Arbitrarily accurate composite pulse sequences,” Phys. Rev. A 70, 052318 (2004).
[CrossRef]

Chang, A. C.

Chuang, I. L.

K. R. Brown, A. W. Harrow, and I. L. Chuang, “Arbitrarily accurate composite pulse sequences,” Phys. Rev. A 70, 052318 (2004).
[CrossRef]

Collett, E.

D. Goldstein and E. Collett, Polarized Light (CRC, 2003).

Destriau, M. G.

M. G. Destriau and J. Prouteau, “Réalisation d’un quart d’onde quasi achromatique par juxtaposition de deux lames cristallines de méme nature,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

Freeman, R.

R. Freeman, Spin Choreography (Spektrum, 1997).

Gaubatz, U.

A. A. Rangelov, U. Gaubatz, and N. V. Vitanov, “Broadband adiabatic conversion of light polarization,” Opt. Commun. 283, 3891–3894 (2010).
[CrossRef]

Goldstein, D.

D. Goldstein and E. Collett, Polarized Light (CRC, 2003).

Guérin, S.

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106, 233001 (2011).
[CrossRef]

Häffner, H.

H. Häffner, C. F. Roos, and R. Blatt, “Quantum computing with trapped ions,” Phys. Rep. 469, 155–203 (2008).
[CrossRef]

Harris, S. E.

Harrow, A. W.

K. R. Brown, A. W. Harrow, and I. L. Chuang, “Arbitrarily accurate composite pulse sequences,” Phys. Rev. A 70, 052318 (2004).
[CrossRef]

Hurvitz, H.

Ivanov, S. S.

S. S. Ivanov and N. V. Vitanov, “Scalable uniform construction of highly conditional quantum gates,” Phys. Rev. A 84, 022319 (2011).
[CrossRef]

S. S. Ivanov and N. V. Vitanov, “High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses,” Opt. Lett. 36, 1275–1277 (2011).
[CrossRef]

Jones, J. A.

W. G. Alway and J. A. Jones, “Arbitrary precision composite pulses for NMR quantum computing,” J. Magn. Reson. 189, 114–120 (2007).
[CrossRef]

Jones, R. C.

Kakigi, S.

H. Kuratsuji and S. Kakigi, “Maxwell-Schrodinger equation for polarized light and evolution of the Stokes parameters,” Phys. Rev. Lett. 80, 1888–1891 (1998).
[CrossRef]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Kubo, H.

H. Kubo and R. Nagata, “Stokes parameters representation of the light propagation equations in inhomogeneous anisotropic, optically active media,” Opt. Commun. 34, 306–308 (1980).
[CrossRef]

H. Kubo and R. Nagata, “Equations of light propagation in an inhomogeneous crystal,” Opt. Commun. 27, 201–206 (1978).
[CrossRef]

Kuratsuji, H.

R. Botet, and H. Kuratsuji, “Stochastic theory of the Stokes parameters in randomly twisted fiber,” Phys. Rev. E 81, 036602 (2010).
[CrossRef]

R. Botet and H. Kuratsuji, “Light-polarization tunneling in optically active media,” J. Phys. A 41, 035301 (2008).
[CrossRef]

H. Kuratsuji, R. Botet, and R. Seto, “Electromagnetic gyration,” Prog. Theor. Phys. 117, 195–217 (2007).
[CrossRef]

H. Kuratsuji and S. Kakigi, “Maxwell-Schrodinger equation for polarized light and evolution of the Stokes parameters,” Phys. Rev. Lett. 80, 1888–1891 (1998).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Levitt, M. H.

M. H. Levitt, “Composite pulses,” Prog. Nucl. Magn. Reson. Spectrosc. 18, 61–122 (1986).
[CrossRef]

Makas, A. S.

Mc Hugh, D.

D. Mc Hugh and J. Twamley, “Sixth-order robust gates for quantum control,” Phys. Rev. A 71, 012327 (2005).
[CrossRef]

McIntyre, C. M.

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

Nagata, R.

H. Kubo and R. Nagata, “Stokes parameters representation of the light propagation equations in inhomogeneous anisotropic, optically active media,” Opt. Commun. 34, 306–308 (1980).
[CrossRef]

H. Kubo and R. Nagata, “Equations of light propagation in an inhomogeneous crystal,” Opt. Commun. 27, 201–206 (1978).
[CrossRef]

Pancharatnam, S.

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I: An achromatic circular polarizer,” Proc. Indian Acad. Sci. A41, 130–136 (1955).

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II: An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. A41, 137–144 (1955).

Prouteau, J.

M. G. Destriau and J. Prouteau, “Réalisation d’un quart d’onde quasi achromatique par juxtaposition de deux lames cristallines de méme nature,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

Rangelov, A. A.

A. A. Rangelov, U. Gaubatz, and N. V. Vitanov, “Broadband adiabatic conversion of light polarization,” Opt. Commun. 283, 3891–3894 (2010).
[CrossRef]

Roos, C. F.

H. Häffner, C. F. Roos, and R. Blatt, “Quantum computing with trapped ions,” Phys. Rep. 469, 155–203 (2008).
[CrossRef]

Seto, R.

H. Kuratsuji, R. Botet, and R. Seto, “Electromagnetic gyration,” Prog. Theor. Phys. 117, 195–217 (2007).
[CrossRef]

Torosov, B. T.

B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-fidelity quantum information processing,” Phys. Rev. A 83, 053420 (2011).
[CrossRef]

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106, 233001 (2011).
[CrossRef]

Twamley, J.

D. Mc Hugh and J. Twamley, “Sixth-order robust gates for quantum control,” Phys. Rev. A 71, 012327 (2005).
[CrossRef]

Vitanov, N. V.

S. S. Ivanov and N. V. Vitanov, “Scalable uniform construction of highly conditional quantum gates,” Phys. Rev. A 84, 022319 (2011).
[CrossRef]

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106, 233001 (2011).
[CrossRef]

S. S. Ivanov and N. V. Vitanov, “High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses,” Opt. Lett. 36, 1275–1277 (2011).
[CrossRef]

B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-fidelity quantum information processing,” Phys. Rev. A 83, 053420 (2011).
[CrossRef]

A. A. Rangelov, U. Gaubatz, and N. V. Vitanov, “Broadband adiabatic conversion of light polarization,” Opt. Commun. 283, 3891–3894 (2010).
[CrossRef]

West, C. D.

Wimperis, S.

S. Wimperis, “Broadband, narrowband and passband composite pulses for use in advanced NMR experiments,” J. Magn. Reson. Ser. A 109, 221–231 (1994).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

J. Magn. Reson. (1)

W. G. Alway and J. A. Jones, “Arbitrary precision composite pulses for NMR quantum computing,” J. Magn. Reson. 189, 114–120 (2007).
[CrossRef]

J. Magn. Reson. Ser. A (1)

S. Wimperis, “Broadband, narrowband and passband composite pulses for use in advanced NMR experiments,” J. Magn. Reson. Ser. A 109, 221–231 (1994).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Phys. A (1)

R. Botet and H. Kuratsuji, “Light-polarization tunneling in optically active media,” J. Phys. A 41, 035301 (2008).
[CrossRef]

J. Phys. Radium (1)

M. G. Destriau and J. Prouteau, “Réalisation d’un quart d’onde quasi achromatique par juxtaposition de deux lames cristallines de méme nature,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

Nature (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef]

New J. Phys. (1)

A. Ardavan, “Exploiting the Poincare–Bloch symmetry to design high-fidelity broadband composite linear retarders,” New J. Phys. 9, 24 (2007).
[CrossRef]

Opt. Commun. (3)

A. A. Rangelov, U. Gaubatz, and N. V. Vitanov, “Broadband adiabatic conversion of light polarization,” Opt. Commun. 283, 3891–3894 (2010).
[CrossRef]

H. Kubo and R. Nagata, “Equations of light propagation in an inhomogeneous crystal,” Opt. Commun. 27, 201–206 (1978).
[CrossRef]

H. Kubo and R. Nagata, “Stokes parameters representation of the light propagation equations in inhomogeneous anisotropic, optically active media,” Opt. Commun. 34, 306–308 (1980).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

H. Häffner, C. F. Roos, and R. Blatt, “Quantum computing with trapped ions,” Phys. Rep. 469, 155–203 (2008).
[CrossRef]

Phys. Rev. A (4)

S. S. Ivanov and N. V. Vitanov, “Scalable uniform construction of highly conditional quantum gates,” Phys. Rev. A 84, 022319 (2011).
[CrossRef]

B. T. Torosov and N. V. Vitanov, “Smooth composite pulses for high-fidelity quantum information processing,” Phys. Rev. A 83, 053420 (2011).
[CrossRef]

K. R. Brown, A. W. Harrow, and I. L. Chuang, “Arbitrarily accurate composite pulse sequences,” Phys. Rev. A 70, 052318 (2004).
[CrossRef]

D. Mc Hugh and J. Twamley, “Sixth-order robust gates for quantum control,” Phys. Rev. A 71, 012327 (2005).
[CrossRef]

Phys. Rev. E (1)

R. Botet, and H. Kuratsuji, “Stochastic theory of the Stokes parameters in randomly twisted fiber,” Phys. Rev. E 81, 036602 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequences of chirped pulses,” Phys. Rev. Lett. 106, 233001 (2011).
[CrossRef]

H. Kuratsuji and S. Kakigi, “Maxwell-Schrodinger equation for polarized light and evolution of the Stokes parameters,” Phys. Rev. Lett. 80, 1888–1891 (1998).
[CrossRef]

Proc. Indian Acad. Sci. (2)

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I: An achromatic circular polarizer,” Proc. Indian Acad. Sci. A41, 130–136 (1955).

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II: An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. A41, 137–144 (1955).

Prog. Nucl. Magn. Reson. Spectrosc. (1)

M. H. Levitt, “Composite pulses,” Prog. Nucl. Magn. Reson. Spectrosc. 18, 61–122 (1986).
[CrossRef]

Prog. Theor. Phys. (1)

H. Kuratsuji, R. Botet, and R. Seto, “Electromagnetic gyration,” Prog. Theor. Phys. 117, 195–217 (2007).
[CrossRef]

Other (4)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1977).

D. Goldstein and E. Collett, Polarized Light (CRC, 2003).

R. Freeman, Spin Choreography (Spektrum, 1997).

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Figures (5)

Fig. 1.
Fig. 1.

Implementations of different BB composite retarders composed of N half- and quarter-wave plates, each rotated by angle θk (k=1,2,,N) with respect to the fast axis. (a) BB half-wave retarder composed of N half-wave plates; (b) BB quarter-wave retarder composed of N1 half-wave plates and a quarter-wave plate; (c) BB half-wave retarder composed of N1 half-wave plates, a quarter-wave plate, and a mirror; (d) BB quarter-wave retarder composed of N2 half-wave plates, two quarter-wave plates, and a mirror.

Fig. 2.
Fig. 2.

Fidelity F versus phase shift φ for BB half-wave retarders [frame (a) with φ0=π; see Fig. 1(a)] and BB quarter-wave retarders [frame (b) with φ0=π/2; see Fig. 1(b)], for different number of constituent plates N. The rotation angles are given in Table 1. The fidelities of the single-plate retarder and the BB1 retarder [26] are shown with labels “1” and “A,” while the fidelities of the six- and 10-plate retarders of Harris and co-workers [8,9] are shown by dashed lines with labels “H6” and “H10.” As one can clearly see, our retarders outperform the others for N>5.

Fig. 3.
Fig. 3.

Retardance error versus phase shift φ for BB half-wave retarders without a mirror [frame (a) with φ0=π; see Fig. 1(a)] and BB quarter-wave retarders without a mirror [frame (b) with φ0=π/2; see Fig. 1(b)], for different number of constituent plates N. The rotation angles are given in Table 1.

Fig. 4.
Fig. 4.

Fidelity F versus phase shift φ for BB half-wave retarders with a mirror [frame (a) with φ0=π; see Fig. 1(c)] and BB quarter-wave retarders with a mirror [frame (b) with φ0=π/2; see Fig. 1(d)], for different number of constituent plates N. The rotation angles are given in Table 1.

Fig. 5.
Fig. 5.

Retardance error versus phase shift φ for BB half-wave retarders with a mirror [frame (a) with φ0=π; see Fig. 1(c)] and BB quarter-wave retarders with a mirror [frame (b) with φ0=π/2; see Fig. 1(d)], for different number of constituent plates N. The rotation angles are given in Table 1.

Tables (1)

Tables Icon

Table 1. Rotation Angles θk (in Degrees) for BB Retarders with Different Number N of Constituent Half-Wave Platesa

Equations (19)

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

R(θ)=[cosθsinθsinθcosθ].
J(φ)=[eiφ/200eiφ/2],
Jθ(φ)=R(θ)J(φ)R(θ).
W=12[11ii].
Jθ(φ)=[cos(φ/2)isin(φ/2)e2iθisin(φ/2)e2iθcos(φ/2)].
J(N)=JθN(φN)JθN1(φN1)Jθ1(φ1).
J0(π)=[0ii0].
J(N)=JθN(π)JθN1(π)Jθ1(π),
[φkJ12(N)]φ=π=0(k=1,2,,N2),
Re[φN1J12(N)]φ=π=0orIm[φN1J12(N)]φ=π=0.
J0(±π/2)=12[1±i±i1].
J(N)=JθN(π)JθN1(π)Jθ2(π)J0(π/2).
[φkJ12(N)]φ=π=0(k=1,2,,(N1)/2),
Re[φN/2J12(N)]φ=π=0orIm[φN/2J12(N)]φ=π=0.
J(2N)=Jθ1(π)Jθ2(π)JθN1(π)JθN(π/2)σx×JθN(π/2)JθN1(π)Jθ2(π)Jθ1(π),
[φkJ12(2N)]φ=π=0(k=1,2,,N2),
Re[φN1J12(2N)]φ=π=0orIm[φN1J12(2N)]φ=π=0.
J(2N)=Jθ1(π/2)Jθ2(π)JθN1(π)JθN(π/2)σx×JθN(π/2)JθN1(π)Jθ2(π)Jθ1(π/2).
[φkJ12(2N)]φ=π=0(k=1,2,,N2).

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