Abstract

Designs are given for gallium–arsenide subwavelength grating retarders operating at 10.6 μm. A design procedure is detailed that takes into account the reflections at all surfaces and that uses numerical optimization to improve the transmittance of the retarders to nearly 100%. It is shown that the homogeneous uniaxial layer model for subwavelength gratings can be used to provide starting points for the Nelder–Mead simplex optimization, obviating the need for stochastic optimization techniques such as simulated annealing. An analysis of the designs with respect to wavelength, angle of incidence, and fabrication tolerances indicates that such grating retarders will perform favorably compared with commercial alternatives.

© 1996 Optical Society of America

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References

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  1. R. J. Drake, “Solving problems of polarization in cutting and scribing applications,” Ind. Laser Rev. 2, 16–18 (1988).
  2. W. H. Southwell, “Multilayer coating design achieving a broadband 90° phase shift,” Appl. Opt. 19, 2688–2692 (1980).
    [CrossRef] [PubMed]
  3. S. J. Elston, G. P. Bryan, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
    [CrossRef]
  4. C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Modern Opt. 40, 675–686 (1993).
    [CrossRef]
  5. V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
    [CrossRef]
  6. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [CrossRef]
  7. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
    [CrossRef] [PubMed]
  8. L. Cescato, E. Gluch, N. Streibl, “Holographic quarterwave plates,” Appl. Opt. 29, 3286–3290 (1990).
    [CrossRef] [PubMed]
  9. N. Davidson, A. A. Friesem, E. Hasman, “Computergenerated relief gratings as space-variant polarization elements,” Opt. Lett. 17, 1223–1227 (1991).
  10. R. E. Collin, J. Brown, “The design of quarter-wave matching layers for dielectric surfaces,” Proc. Inst. Electr. Eng. Part C 103, 153–158 (1956).
  11. R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
    [CrossRef]
  12. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  13. R. C. McPhedran, L. C. Botten, M. S. Craig, M. Neviere, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, 289–312 (1982).
    [CrossRef]
  14. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef] [PubMed]
  15. E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
    [CrossRef] [PubMed]
  16. E. Gluch, P. Kipfer, J. T. Sheridan, N. Streibel, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
    [CrossRef]
  17. D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [CrossRef] [PubMed]
  18. C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10, 2217–2225 (1993).
    [CrossRef]
  19. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
    [CrossRef] [PubMed]
  20. H. S. Kirschbaum, S. Chen, “A method of producing broadband circular polarization employing an anisotropic dielectric,” IRE Trans. Microwave Theory and Tech. MTT-5, 199–203 (1957).
    [CrossRef]
  21. R. E. VanDoeren, R. J. Plugge, “Nomogram speeds design of anisotropic dielectric devices,” Microwaves 5, 28–31 (1966).
  22. L. L. Goldstone, “Mm wave transmission polarizer,” in Antennas and Propagation: 1979 International Symposium Digest (IEEE, New York, 1979), Vol. 2, pp. 606–609.
    [CrossRef]
  23. Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
    [CrossRef] [PubMed]
  24. E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
    [CrossRef]
  25. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  26. D. Berreman, “Optics in stratified and anisotropic media: 4 × 4 matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972).
    [CrossRef]
  27. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. A 72, 1385–1392 (1982).
    [CrossRef]
  28. L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Modern Opt. 40, 553–573 (1993).
    [CrossRef]
  29. I. Richter, P. Sun, F. Xu, Y. Fainman, “Design considerations of form birefringent microstructures,” Appl. Opt. 34, 2421–2429 (1995).
    [CrossRef] [PubMed]
  30. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
  31. A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm,” Assoc. Comput. Mach. Trans. Math. Software 13, 262–280 (1987).
    [CrossRef]

1995 (1)

1994 (3)

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef] [PubMed]

V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
[CrossRef]

E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
[CrossRef]

1993 (4)

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10, 2217–2225 (1993).
[CrossRef]

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Modern Opt. 40, 675–686 (1993).
[CrossRef]

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Modern Opt. 40, 553–573 (1993).
[CrossRef]

D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
[CrossRef] [PubMed]

1992 (2)

E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
[CrossRef] [PubMed]

E. Gluch, P. Kipfer, J. T. Sheridan, N. Streibel, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

1991 (2)

S. J. Elston, G. P. Bryan, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Computergenerated relief gratings as space-variant polarization elements,” Opt. Lett. 17, 1223–1227 (1991).

1990 (1)

1988 (1)

R. J. Drake, “Solving problems of polarization in cutting and scribing applications,” Ind. Laser Rev. 2, 16–18 (1988).

1987 (2)

Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
[CrossRef] [PubMed]

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm,” Assoc. Comput. Mach. Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

1986 (1)

1983 (2)

R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
[CrossRef] [PubMed]

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

1982 (2)

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Neviere, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. A 72, 1385–1392 (1982).
[CrossRef]

1980 (1)

1972 (1)

1966 (1)

R. E. VanDoeren, R. J. Plugge, “Nomogram speeds design of anisotropic dielectric devices,” Microwaves 5, 28–31 (1966).

1965 (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

1957 (1)

H. S. Kirschbaum, S. Chen, “A method of producing broadband circular polarization employing an anisotropic dielectric,” IRE Trans. Microwave Theory and Tech. MTT-5, 199–203 (1957).
[CrossRef]

1956 (3)

R. E. Collin, J. Brown, “The design of quarter-wave matching layers for dielectric surfaces,” Proc. Inst. Electr. Eng. Part C 103, 153–158 (1956).

R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Baird, W. E.

Berreman, D.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Botten, L. C.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Neviere, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Brown, J.

R. E. Collin, J. Brown, “The design of quarter-wave matching layers for dielectric surfaces,” Proc. Inst. Electr. Eng. Part C 103, 153–158 (1956).

Brundrett, D. L.

Bryan, G. P.

S. J. Elston, G. P. Bryan, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Case, S. K.

Cescato, L.

Chen, S.

H. S. Kirschbaum, S. Chen, “A method of producing broadband circular polarization employing an anisotropic dielectric,” IRE Trans. Microwave Theory and Tech. MTT-5, 199–203 (1957).
[CrossRef]

Collin, R. E.

R. E. Collin, J. Brown, “The design of quarter-wave matching layers for dielectric surfaces,” Proc. Inst. Electr. Eng. Part C 103, 153–158 (1956).

R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

Corana, A.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm,” Assoc. Comput. Mach. Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Craig, M. S.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Neviere, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Davidson, N.

N. Davidson, A. A. Friesem, E. Hasman, “Computergenerated relief gratings as space-variant polarization elements,” Opt. Lett. 17, 1223–1227 (1991).

Drake, R. J.

R. J. Drake, “Solving problems of polarization in cutting and scribing applications,” Ind. Laser Rev. 2, 16–18 (1988).

Elston, S. J.

S. J. Elston, G. P. Bryan, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Enger, R. C.

Fainman, Y.

Flanders, D. C.

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Friesem, A. A.

N. Davidson, A. A. Friesem, E. Hasman, “Computergenerated relief gratings as space-variant polarization elements,” Opt. Lett. 17, 1223–1227 (1991).

Fujita, T.

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Modern Opt. 40, 675–686 (1993).
[CrossRef]

Gaylord, T. K.

Gluch, E.

E. Gluch, P. Kipfer, J. T. Sheridan, N. Streibel, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

L. Cescato, E. Gluch, N. Streibl, “Holographic quarterwave plates,” Appl. Opt. 29, 3286–3290 (1990).
[CrossRef] [PubMed]

Glytsis, E. N.

Goldstone, L. L.

L. L. Goldstone, “Mm wave transmission polarizer,” in Antennas and Propagation: 1979 International Symposium Digest (IEEE, New York, 1979), Vol. 2, pp. 606–609.
[CrossRef]

Grann, E. B.

E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
[CrossRef]

Haggans, C. W.

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Modern Opt. 40, 675–686 (1993).
[CrossRef]

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10, 2217–2225 (1993).
[CrossRef]

Hasman, E.

N. Davidson, A. A. Friesem, E. Hasman, “Computergenerated relief gratings as space-variant polarization elements,” Opt. Lett. 17, 1223–1227 (1991).

Kimura, Y.

Kipfer, P.

E. Gluch, P. Kipfer, J. T. Sheridan, N. Streibel, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

Kirschbaum, H. S.

H. S. Kirschbaum, S. Chen, “A method of producing broadband circular polarization employing an anisotropic dielectric,” IRE Trans. Microwave Theory and Tech. MTT-5, 199–203 (1957).
[CrossRef]

Kostuk, R. K.

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10, 2217–2225 (1993).
[CrossRef]

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Modern Opt. 40, 675–686 (1993).
[CrossRef]

Li, L.

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Modern Opt. 40, 675–686 (1993).
[CrossRef]

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Modern Opt. 40, 553–573 (1993).
[CrossRef]

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10, 2217–2225 (1993).
[CrossRef]

Marchesi, M.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm,” Assoc. Comput. Mach. Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Martini, C.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm,” Assoc. Comput. Mach. Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Maystre, D.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Neviere, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

McPhedran, R. C.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Neviere, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Moharam, M. G.

E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
[CrossRef]

T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
[CrossRef] [PubMed]

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. A 72, 1385–1392 (1982).
[CrossRef]

Morris, G. M.

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Neviere, M.

R. C. McPhedran, L. C. Botten, M. S. Craig, M. Neviere, D. Maystre, “Lossy lamellar gratings in the quasistatic limit,” Opt. Acta 29, 289–312 (1982).
[CrossRef]

Nishida, N.

Ohta, Y.

Okorkov, V. N.

V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
[CrossRef]

Ono, Y.

Panchenko, A. Y.

V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
[CrossRef]

Plugge, R. J.

R. E. VanDoeren, R. J. Plugge, “Nomogram speeds design of anisotropic dielectric devices,” Microwaves 5, 28–31 (1966).

Pommet, D. A.

E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
[CrossRef]

Raguin, D. H.

Richter, I.

Ridella, S.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm,” Assoc. Comput. Mach. Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Russkikh, B. V.

V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sambles, J. R.

S. J. Elston, G. P. Bryan, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Seminogov, V. N.

V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
[CrossRef]

Sheridan, J. T.

E. Gluch, P. Kipfer, J. T. Sheridan, N. Streibel, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

Sokolov, V. I.

V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
[CrossRef]

Southwell, W. H.

Streibel, N.

E. Gluch, P. Kipfer, J. T. Sheridan, N. Streibel, “Form birefringence of surface relief gratings and its angular dependence,” Opt. Commun. 89, 173–177 (1992).
[CrossRef]

Streibl, N.

Sun, P.

VanDoeren, R. E.

R. E. VanDoeren, R. J. Plugge, “Nomogram speeds design of anisotropic dielectric devices,” Microwaves 5, 28–31 (1966).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Xu, F.

Yakunin, V. P.

V. N. Okorkov, A. Y. Panchenko, B. V. Russkikh, V. N. Seminogov, V. I. Sokolov, V. P. Yakunin, “Phase retarder for transformation of high-power infrared laser beams based on resonant excitation of surface electromagnetic waves on metal diffraction gratings,” Opt. Eng. 33, 3145–3155 (1994).
[CrossRef]

Appl. Opt. (9)

R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
[CrossRef] [PubMed]

T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
[CrossRef] [PubMed]

Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
[CrossRef] [PubMed]

E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
[CrossRef] [PubMed]

D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
[CrossRef] [PubMed]

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef] [PubMed]

I. Richter, P. Sun, F. Xu, Y. Fainman, “Design considerations of form birefringent microstructures,” Appl. Opt. 34, 2421–2429 (1995).
[CrossRef] [PubMed]

L. Cescato, E. Gluch, N. Streibl, “Holographic quarterwave plates,” Appl. Opt. 29, 3286–3290 (1990).
[CrossRef] [PubMed]

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

Appl. Phys. Lett. (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Assoc. Comput. Mach. Trans. Math. Software (1)

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm,” Assoc. Comput. Mach. Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Can. J. Phys. (1)

R. E. Collin, “Reflection and transmission at a slotted dielectric interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

Comput. J. (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Ind. Laser Rev. (1)

R. J. Drake, “Solving problems of polarization in cutting and scribing applications,” Ind. Laser Rev. 2, 16–18 (1988).

IRE Trans. Microwave Theory and Tech. (1)

H. S. Kirschbaum, S. Chen, “A method of producing broadband circular polarization employing an anisotropic dielectric,” IRE Trans. Microwave Theory and Tech. MTT-5, 199–203 (1957).
[CrossRef]

J. Modern Opt. (2)

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Modern Opt. 40, 675–686 (1993).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

(a) Electro-optic amplitude modulator, normally configured, with a quarter-wave transmissive retarder preceding the electro-optic material. (b) The volume, weight, and expense of the retarder can be eliminated by etching an appropriate subwavelength grating into the entrance surface of the electro-optic material.

Fig. 2
Fig. 2

(a) Gratings consist of binary structures of period Λ, groove depth d, and filling factor F, with cover and groove refractive indices nc , and substrate and ridge refractive indices ns . (b) Extension of the structure in (a) to three layers; all layers have the same period, each layer with its own filling factor Fi and groove depth di, i = 1, 2, 3.

Fig. 3
Fig. 3

(a) Response of a Λ = 3.0 μm period single layer GaAs grating to a normally incident plane wave of wavelength λ 0 = 10.6 μm as a function of filling factor F and groove depth d around F = 0.5, d = d π/2, as given by the HULM. (b) Response of a GaAs three-layer grating as a function of filling factor F 3 and total groove depth D = d 1 + d 2 + d 3 for the same conditions. For this plot the design parameters are constrained such that F 2 = 2F 1, F 3 = 3F 1, and d 1 = d 2 = d 3.

Fig. 4
Fig. 4

Same as Fig. 3, but now in the region F = 0.5, d = d π.

Fig. 5
Fig. 5

Comparison of the retardation phase sensitivity to the maximum allowed fabrication errors for both the RCWA and HULM designs as a function of wavelength. The kinks in the RCWA curves are due to the turn on of the i = ±1 diffracted orders in the substrate.

Fig. 6
Fig. 6

Distributions of retardation phases δ at the center wavelength and at the wavelength extremes. The solid line in the δ–λ 0 plane is the curve for the unperturbed design; the ensemble mean lies on the same curve. Dashed lines in the plane are the ensemble mean ±1 STD. Histogram bins are 0.5° wide.

Fig. 7
Fig. 7

Quarter-wave design and ensemble statistical curves for the retardation phase, ellipticity, and transmittance as a function of wavelength.

Fig. 8
Fig. 8

Half-wave design and ensemble statistical curves for the retardation phase, ellipticity, and transmittance as a function of wavelength.

Fig. 9
Fig. 9

(a) Retardation phase at normal incidence as a function of wavelength for the quarter-wave grating retarder and commercial alternatives. (b) The same curves, but now at a 5° angle of incidence in the xz plane. The kink in the GR curve near λ 0 = 10.6 μm is due to the cut on of the i = +1 forward diffracted order in the substrate. GR, grating retarder; ZP and MP, λ 0/4 and 5 λ0/4 ideal CdS wave plates, respectively; RR, reflective retarder design (see text for details); and FR, GaAs Fresnel rhomb.

Tables (1)

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Table 1 Optimized Quarter- and Half-Wave Retarder Designs and Their Performance

Equations (11)

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d = δ / k 0 | Δ n | ,
n o = [ F n r 2 + ( 1 F ) n g 2 ] 1 / 2 ,
n E = [ F / n r 2 + ( 1 F ) / n g 2 ] 1 / 2 ,
E = x ̂ T x exp ( j Φ x ) + y ̂ T y exp ( j Φ y ) ,
δ Φ y Φ x .
α tan 1 ( T x / T y ) ,
ε tan [ sin 1 ( sin 2 α sin δ ) / 2 ] .
( n r 2 n O 2 ) 1 / 2 tan [ π F Λ λ 0 ( n r 2 n O 2 ) 1 / 2 ] = ( n g 2 n O 2 ) 1 / 2 tan [ π ( 1 F ) Λ λ 0 ( n g 2 n O 2 ) 1 / 2 ] ,
( n r 2 n E 2 ) 1 / 2 n r 2 tan [ π F Λ λ 0 ( n r 2 n E 2 ) 1 / 2 ] = ( n g 2 n E 2 ) 1 / 2 n g 2 tan [ π ( 1 F ) Λ λ 0 ( n g 2 n E 2 ) 1 / 2 ] .
f π / 2 = W 1 | 1 ε | + W 2 ( 1 T x T y ) ,
f π = W 1 | ε | + W 2 ( 1 T x T y ) + W 3 | π / 4 α | ,

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