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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 14, Iss. 5 — May. 1, 1997
  • pp: 1124–1136

Design of high-efficiency dielectric reflection gratings

B. W. Shore, M. D. Perry, J. A. Britten, R. D. Boyd, M. D. Feit, H. T. Nguyen, R. Chow, G. E. Loomis, and Lifeng Li  »View Author Affiliations

JOSA A, Vol. 14, Issue 5, pp. 1124-1136 (1997)

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We discuss examples of designs for all-dielectric reflection gratings that tolerate high intensity and are potentially capable of placing up to 99% of the incident light into a single diffraction order, such as are needed for contemporary high-power lasers utilizing chirped-pulse amplification. The designs are based on placing a dielectric transmission grating atop a high-reflectivity (HR) multilayer dielectric stack. We comment on the connection between transmission gratings and reflection gratings and note that the grating and the HR stack can, to a degree, be treated independently. Because many combinations of gratings and multilayer stacks offer high efficiency, it is possible to attain secondary objectives in the design. We describe examples of such designs aimed toward improving fabrication and lowering the susceptibility to laser-induced damage. We present examples of the dependence of grating efficiency on grating characteristics. We describe examples of high-efficiency (95%) gratings that we have fabricated by using hafnia and silica multilayers.

© 1997 Optical Society of America

Original Manuscript: February 29, 1996
Revised Manuscript: August 26, 1996
Manuscript Accepted: November 11, 1996
Published: May 1, 1997

B. W. Shore, M. D. Perry, J. A. Britten, R. D. Boyd, M. D. Feit, H. T. Nguyen, R. Chow, G. E. Loomis, and Lifeng Li, "Design of high-efficiency dielectric reflection gratings," J. Opt. Soc. Am. A 14, 1124-1136 (1997)

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  1. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969). [CrossRef]
  2. O. E. Martinez, J. P. Gordon, R. L. Fork, “Negative group-velocity dispersion using refraction,” J. Opt. Soc. Am. A 1, 1003–1006 (1984). [CrossRef]
  3. D. Strickland, G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985). [CrossRef]
  4. O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in 1.3–1.6 µm region,” IEEE J. Quantum Electron. QE-23, 59–64 (1987). [CrossRef]
  5. P. Maine, D. Strickland, P. Bado, M. Pessot, G. Mourou, “Generation of ultrahigh peak power pulses by chirped pulse amplification,” IEEE J. Quantum Electron. 24, 398–402 (1988). [CrossRef]
  6. M. Pessot, J. Squier, G. Mourou, D. Harter, “Chirped-pulse amplification of 100-fsec pulses,” Opt. Lett. 14, 797–799 (1989). [CrossRef] [PubMed]
  7. W. Rudolph, B. Wilhelmi, Light Pulse Compression (Harwood, London, 1989).
  8. M. Ferray, L. A. Lompré, O. Gobert, A. L’Huilleir, G. Mainfray, C. Manus, A. Sanchéz, “Multiterawatt picosecond Nd–glass laser system at 1053 nm,” Opt. Commun. 75, 278–282 (1990). [CrossRef]
  9. M. D. Perry, F. G. Patterson, J. Weston, “Spectral shaping in chirped-pulse amplification,” Opt. Lett. 15, 381–383 (1990). [CrossRef] [PubMed]
  10. C. N. Danson, L. J. Barzanti, Z. Chang, A. R. Damerell, C. B. Edwards, S. Hancock, M. R. H. Hutchinson, M. H. Key, S. Luan, R. r. Mahadeo, I. P. Mercer, P. Norreys, D. A. Pepler, D. A. Rodkiss, I. N. Ross, M. A. Smith, P. Taday, W. T. Toner, K. W. Wogmore, T. B. Winstone, R. W. W. Wyatt, F. Zhou, “High contrast multi-terawatt pulse generation using chirped pulse amplification on the Vulcan laser facility,” Opt. Commun. 108, 392–397 (1992).
  11. T. Ditmire, M. D. Perry, “Terawatt Cr-LiSrAlF6 laser system,” Opt. Lett. 18, 426–428 (1993). [CrossRef] [PubMed]
  12. J. V. Rudd, G. Korn, S. Kane, J. Squier, G. Mourou, P. Bado, “Chirped-pulse amplification of 55-fs pulses at a 1-kHz repetition rate in a Ti-Al2O3 regenerative amplifier,” Opt. Lett. 18, 2044–2046 (1993). [CrossRef]
  13. M. D. Perry, G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917–924 (1994). [CrossRef] [PubMed]
  14. B. C. Stuart, S. Herman, M. D. Perry, “Chirped-pulse amplification in Ti-sapphire beyond 1 mµ,” IEEE J. Quantum Electron. 31, 528–538 (1995). [CrossRef]
  15. R. Boyd, J. Britten, D. Decker, B. W. Shore, B. Stuart, M. D. Perry, L. Li, “High-efficiency metallic diffraction gratings for laser applications,” Appl. Opt. 34, 1697–1706 (1995). [CrossRef] [PubMed]
  16. B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995). [CrossRef] [PubMed]
  17. M. D. Perry, R. D. Boyd, J. A. Britten, D. Decker, B. W. Shore, C. Shannon, E. Shults, L. Li, “High-efficiency multilayer dielectric diffraction gratings,” Opt. Lett. 20, 940–942 (1995). [CrossRef] [PubMed]
  18. M. C. Hutley, “Interference diffraction gratings,” Sci. Prog. (London) 61, 301–321 (1972).
  19. L. Mashev, S. Tonchev, “Formation of holographic diffraction gratings in photoresist,” Appl. Phys. A 26, 143–149 (1981). [CrossRef]
  20. R. C. Enger, S. K. Case, “High-frequency holographic transmission gratings in photoresist,” J. Opt. Soc. Am. 73, 1113–1118 (1983). [CrossRef]
  21. K. Yokomori, “Dielectric surface relief gratings with high diffraction efficiency,” Appl. Opt. 23, 2303–2310 (1984). [CrossRef]
  22. E. K. Popov, L. V. Tsonev, M. L. Sabeva, “Technological problems in holographic recording of plane gratings,” Opt. Eng. 31, 2168–2173 (1992). [CrossRef]
  23. J. J. Armstrong, “Holographic generation of ultra-high-efficiency large-aperture transmission diffraction gratings,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1993).
  24. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” Appl. Opt. 19, 282–288 (1978).
  25. D. E. Tremain, K. K. Mei, “Application of the unimoment method to scattering from periodic dielectric structures,” J. Opt. Soc. Am. 68, 775–783 (1978). [CrossRef]
  26. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982). [CrossRef]
  27. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983). [CrossRef] [PubMed]
  28. D. M. Pai, K. A. Awada, “Analysis of dielectric gratings of arbitrary profiles and thicknesses,” J. Opt. Soc. Am. A 9, 755–762 (1991). [CrossRef]
  29. A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Diffraction gratings with high optical strength for laser resonators,” Quantum Electron. 24, 233–235 (1994). [CrossRef]
  30. A. S. Svakhin, V. A. Sychugov, A. E. Tikhomirov, “Efficient diffraction elements for TE-polarized waves,” Sov. Phys. Tech. Phys. 36, 1038–1040 (1991).
  31. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).
  32. P. Baumeister, “Interference and optical interference coatings,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, New York, 1965), Vol. 1, pp. 285–323.
  33. Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).
  34. A. Macleod, Thin Film Optical Filters (Hilger, Bristol, UK, 1986).
  35. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  36. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).
  37. J. C. Rife, W. R. Hunter, T. W. Barbee, R. G. Cruddace, “Multilayer-coated blazed grating performance in the soft x-ray region,” Appl. Opt. 28, 2984–2986 (1989). [CrossRef] [PubMed]
  38. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986). [CrossRef]
  39. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983). [CrossRef]
  40. A. I. Erko, B. Vidal, P. Vincent, Y. A. Agafonov, V. V. Martynov, D. V. Roschupkin, M. Brunel, “Multilayer gratings efficiency—numerical and physical experiments,” Nucl. Instrum. Methods A 333, 599–606 (1993). [CrossRef]
  41. V. Martynov, B. Vidal, P. Vincent, M. Brunel, D. V. Roschupkin, Y. Agafonov, A. Erko, A. Yuakshin, “Comparison of modal and differential methods for multilayer gratings,” Nucl. Instrum. Methods A 339, 617–625 (1994). [CrossRef]
  42. A. Erko, V. Martynov, D. Roshchoupkin, A. Yuakshin, B. Vidal, P. Vincent, M. Brunel, “Multilayer diffraction grating properties,” J. Phys. (Paris) III 4, 1649–1658 (1994).
  43. L. Mashev, E. Popov, “Diffraction efficiency anomalies of multicoated dielectric gratings,” Opt. Commun. 51, 131–136 (1984). [CrossRef]
  44. J. M. Elson, L. F. DeSandre, J. L. Stanford, “Analysis of anomalous resonance effects in multilayer-overcoated, low-efficiency gratings,” J. Opt. Soc. Am. A 5, 74–88 (1988). [CrossRef]
  45. L. F. DeSandre, J. M. Elson, “Extinction-theorem analysis of diffraction anomalies in overcoated gratings,” J. Opt. Soc. Am. A 8, 763–777 (1991). [CrossRef]
  46. L. Li, J. Hirsch, “All-dielectric high-efficiency reflection gratings made with multilayer thin-film coatings,” Opt. Lett. 20, 1349–1351 (1995). [CrossRef] [PubMed]
  47. J. A. Britten, R. D. Boyd, B. W. Shore, “In situ end-point detection during development of submicrometer grating structures in photoresist,” Opt. Eng. 34, 474–479 (1995). [CrossRef]
  48. S. Lindau, “The groove profile formation of holographic gratings,” Opt. Acta 29, 1371–1381 (1982). [CrossRef]
  49. A. R. Neureuther, W. G. Oldham, “Resist modeling and profile simulation,” Solid State Technol. 28, 139–144 (1985).
  50. M. G. Moharam, T. K. Gaylord, G. T. Sincerbox, H. Werlich, B. Yung, “Diffraction characteristics of photoresist surface-relief gratings,” Appl. Opt. 23, 3214–3220 (1984). [CrossRef] [PubMed]
  51. H. L. Garvin, A. Au, M. L. Minden, “Ion-etched gratings for laser applications,” in Periodic Structures, Gratings, Moire Patterns, and Diffraction Phenomena I, C. H. Chi, ed., Proc. SPIE240, 63–68 (1981). [CrossRef]
  52. R. A. Powell, Dry Etching for Microelectronics (Elsevier, New York, 1984).
  53. L. Li, M. Xu, G. I. Stegeman, C. T. Seaton, “Fabrication of photoresist masks for submicrometer surface relief gratings,” in Integrated Optical Circuit Engineering V, M. A. Mentzer, ed., Proc. SPIE835, 72–82 (1988). [CrossRef]
  54. D. M. Manos, D. L. Flamm, eds., Plasma Etching, An Introduction (Academic, San Diego, Calif., 1989).
  55. H. Berrouane, J. M. Andre, R. Barchewitz, T. Moreno, A. Sammar, C. K. Malek, B. Pardo, R. Rivoira, “Experimental and theoretical performances of an etched lamellar multilayer grating in the 1 keV region,” Nucl. Instrum. Methods A 312, 521–530 (1992). [CrossRef]
  56. I. Brodie, J. J. Muray, The Physics of Micro/Nanofabrication (Plenum, New York, 1992).
  57. R. Magnusson, T. K. Gaylord, “Analysis of multiwave diffraction of thick gratings,” J. Opt. Soc. Am. 67, 1165–1170 (1977). [CrossRef]
  58. D. Maystre, “A new general integral theory for dielectric coated gratings,” J. Opt. Soc. Am. 68, 490–495 (1978). [CrossRef]
  59. K. Yasuura, M. Tomita, “Numerical analysis of plane wave scattering from dielectric gratings,” Trans. Inst. Electr. Commun. Eng. Jpn. J61-B, 662–669 (1978).
  60. J. M. Elson, “Diffraction and diffuse scattering from dielectric multilayers,” J. Opt. Soc. Am. 69, 48–54 (1979). [CrossRef]
  61. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981). [CrossRef]
  62. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
  63. S. L. Chuang, J. A. Kong, “Wave scattering from a periodic dielectric surface for a general angle of incidence,” Radio Sci. 17, 545–557 (1982). [CrossRef]
  64. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983). [CrossRef]
  65. R. A. Depine, C. I. Valencia, “Diffraction from corrugated dielectric gratings: general case of oblique incidence,” J. Mod. Opt. 39, 2089–2112 (1992). [CrossRef]
  66. M. Nevière, E. Popov, “Analysis of dielectric gratings of arbitrary profiles and thicknesses: comment,” J. Opt. Soc. Am. A 9, 2095–2096 (1992). [CrossRef]
  67. M. Nevière, F. Montiel, “Deep gratings: a combination of the differential theory and the multiple reflection series,” Opt. Commun. 108, 1–7 (1994). [CrossRef]
  68. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, M. D. Perry, “Nanosecond to femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1995). [CrossRef]
  69. E. Popov, “Light diffraction by relief gratings: a macroscopic and microscopic view,” Prog. Opt. 31, 141–190 (1993).
  70. M. Nevière, P. Vincent, R. Petit, “Theory of conducting gratings and their applications to optics,” Nouv. Rev. Opt. 2, 65–77 (1974). [CrossRef]
  71. R. Petit, “Electromagnetic grating theories: limitations and successes,” Nouv. Rev. Opt. 3, 129–135 (1975). [CrossRef]
  72. J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979). [CrossRef]
  73. G. M. Whitman, D. M. Leskiw, F. Schwering, “Rigorous theory of scattering by perfectly conducting periodic surfaces with trapezoidal height profile. TE and TM polarization,” J. Opt. Soc. Am. 70, 1495–1503 (1980). [CrossRef]
  74. D. Maystre, M. Nevière, R. Petit, “Experimental verifications and applications of the theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer, New York, 1980), pp. 159–225.
  75. M. Cadilhac, “Some mathematical aspects of the grating theory,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 101–156.
  76. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981). [CrossRef]
  77. L. C. Botten, M. S. Craig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981). [CrossRef]
  78. R. A. Depine, J. M. Simon, “Diffraction grating efficiencies: an exact differential algorithm valid for high conductivities,” Opt. Acta 30, 1273–1286 (1983). [CrossRef]
  79. A. Wirgin, A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B 31, 5573–5576 (1985). [CrossRef]
  80. R. A. Depine, “Perfectly conducting diffraction grating formalisms extended to good conductors via the surface impedance boundary condition,” Appl. Opt. 26, 2348–2354 (1987). [CrossRef] [PubMed]
  81. L. Mashev, E. Popov, “Anomalies of metallic diffraction gratings,” J. Opt. Soc. Am. A 6, 1561–1567 (1989). [CrossRef]
  82. D. Maystre, M. Nevière, M. Renisch, J. L. Coutaz, “Integral theory for metallic gratings in nonlinear optics and comparison with experimental results on second-harmonic generation,” J. Opt. Soc. Am. B 5, 338–351 (1988). [CrossRef]
  83. E. Popov, L. Tsonev, D. Maystre, “Gratings—general properties of the Littrow mounting and energy flow distribution,” J. Mod. Opt. 37, 367–377 (1990). [CrossRef]
  84. R. Petit, ed., Electromagnetic Theory of Gratings (Springer, Berlin, 1980).
  85. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993). [CrossRef]
  86. L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993). [CrossRef]
  87. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994). [CrossRef]
  88. L. Li, “Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings,” J. Opt. Soc. Am. A 11, 2829–2836 (1994). [CrossRef]
  89. L. C. Botten, M. S. Craig, R. C. McPhedran, “Complex zeros of analytic functions,” Comput. Phys. Commun. 29, 245–259 (1983). [CrossRef]
  90. M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).
  91. J. A. Britten, M. D. Perry, B. W. Shore, R. D. Boyd, “Universal grating design for pulse stretching and compression in the 800–1100-nm range,” Opt. Lett. 21, 540–542 (1996). [CrossRef] [PubMed]
  92. M. R. Kozlowski, R. Chow, I. M. Thomas, “Optical coatings for high power lasers,” in CRC Handbook of Laser Science and Technology Supplement 2, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1995), pp. 767–812.
  93. K. C. Chang, V. Shah, T. Tamir, “Scattering and guiding of waves by dielectric gratings with arbitrary profiles,” J. Opt. Soc. Am. 70, 804–813 (1980). [CrossRef]
  94. R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975). [CrossRef]
  95. S. F. Su, T. K. Gaylord, “Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape,” J. Opt. Soc. Am. 65, 59–64 (1975). [CrossRef]
  96. M. Nieto Vesperinas, J. M. Soto Crespo, “Light diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250–7259 (1988). [CrossRef]
  97. M. Breidne, D. Maystre, “Equivalence of ruled, holographic, and lamellar gratings in constant deviation mountings,” Appl. Opt. 19, 1812–1821 (1980). [CrossRef] [PubMed]
  98. H. G. Booker, “The elements of wave propagation using the impedance concept,” J. Inst. Electr. Eng. Part 3 94, 171–184 (1947).
  99. A. K. Cousins, S. C. Gottschalk, “Application of the impedance formalism to diffraction gratings with multiple coating layers,” Appl. Opt. 29, 4268–4271 (1990). [CrossRef] [PubMed]
  100. R. Hermann, “Quarterwave layers: simulation by three thin layers of two materials,” Appl. Opt. 24, 1183–1188 (1985). [CrossRef]
  101. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13, 459–468 (1995). [CrossRef]

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