Abstract

A fast, efficient thin-film synthesis technique is described. Dielectric films are subdivided into thin layers whose refractive indices and thicknesses are varied simultaneously. Because of the large number of optimized parameters, speed and accuracy are given special attention. The efficiency of the method is demonstrated by the successful reproduction of several complex nonpolarizing filters synthesized in the past with the needle method, one of the best approaches currently available.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Baumeister, “Design of multilayer filters by successive approximations,” J. Opt. Soc. Am. 48, 955–958 (1958).
    [CrossRef]
  2. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [CrossRef] [PubMed]
  3. A. Premoli, M. L. Rastello, “Minimax refining of wideband antireflection coatings for wide angular incidence,” Appl. Opt. 33, 2018–2024 (1994).
    [CrossRef] [PubMed]
  4. J. A. Dobrowolski, “Completely automatic synthesis of optical thin film systems,” Appl. Opt. 4, 937–946 (1965).
    [CrossRef]
  5. C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732A (1982).
  6. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef] [PubMed]
  7. A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
    [CrossRef] [PubMed]
  8. P. G. Verly, “Fourier transform technique with refinement in the frequency domain for the synthesis of optical thin films,” Appl. Opt. 35, 5148–5154 (1996).
    [CrossRef] [PubMed]
  9. T. Boudet, P. Chaton, “Thin film design using simulated annealing and study of the filter robustness,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 27–38 (1996).
    [CrossRef]
  10. S. Martin, J. Rivory, M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt. 34, 2247–2254 (1995).
    [CrossRef] [PubMed]
  11. D. G. Li, A. C. Watson, “Global optimization for optical thin film design using Latin Squares,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 8–15 (1997).
    [CrossRef]
  12. P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
    [CrossRef] [PubMed]
  13. W. H. Press, S. A. Teukolski, W. T. Vetterlin, B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992), 418–423.
  14. J. A. Dobrowolski, S. Piotrowski, “Refractive index as a variable in the numerical design of optical thin film systems,” Appl. Opt. 21, 1502–1510 (1982).
    [CrossRef] [PubMed]
  15. H. A. Macleod, “Half wave holes, leaks and other problems,” in Proceedings of the 39th Annual Technical Conference of the Society of Vacuum Coaters, J. N. Lingscheit, A. A. Bromfield, eds. (Society of Vacuum Coaters, Washington, D.C., 1996), pp. 193–198.
  16. B. G. Bovard, “Graded index rugate filters: power sine rugate structures,” in Inhomogeneous and Quasi-inhomogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 109–125 (1993).
    [CrossRef]
  17. P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 46–52 (1997).
    [CrossRef]

1997

1996

1995

1994

1990

1985

1982

1965

1958

Baumeister, P.

Boudet, T.

T. Boudet, P. Chaton, “Thin film design using simulated annealing and study of the filter robustness,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 27–38 (1996).
[CrossRef]

Bovard, B. G.

B. G. Bovard, “Graded index rugate filters: power sine rugate structures,” in Inhomogeneous and Quasi-inhomogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 109–125 (1993).
[CrossRef]

Chaton, P.

T. Boudet, P. Chaton, “Thin film design using simulated annealing and study of the filter robustness,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 27–38 (1996).
[CrossRef]

DeBell, G. W.

Dobrowolski, J. A.

Flannery, B. P.

W. H. Press, S. A. Teukolski, W. T. Vetterlin, B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992), 418–423.

Kemp, R. A.

Li, D. G.

D. G. Li, A. C. Watson, “Global optimization for optical thin film design using Latin Squares,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 8–15 (1997).
[CrossRef]

Macleod, H. A.

H. A. Macleod, “Half wave holes, leaks and other problems,” in Proceedings of the 39th Annual Technical Conference of the Society of Vacuum Coaters, J. N. Lingscheit, A. A. Bromfield, eds. (Society of Vacuum Coaters, Washington, D.C., 1996), pp. 193–198.

Martin, S.

Piotrowski, S.

Premoli, A.

Press, W. H.

W. H. Press, S. A. Teukolski, W. T. Vetterlin, B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992), 418–423.

Rastello, M. L.

Rivory, J.

Schoenauer, M.

Snedaker, C. G.

C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732A (1982).

Southwell, W. H.

Teukolski, S. A.

W. H. Press, S. A. Teukolski, W. T. Vetterlin, B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992), 418–423.

Tikhonravov, A. V.

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 46–52 (1997).
[CrossRef]

Trubetskov, M. K.

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 46–52 (1997).
[CrossRef]

Verly, P. G.

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
[CrossRef] [PubMed]

P. G. Verly, “Fourier transform technique with refinement in the frequency domain for the synthesis of optical thin films,” Appl. Opt. 35, 5148–5154 (1996).
[CrossRef] [PubMed]

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 46–52 (1997).
[CrossRef]

Vetterlin, W. T.

W. H. Press, S. A. Teukolski, W. T. Vetterlin, B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992), 418–423.

Watson, A. C.

D. G. Li, A. C. Watson, “Global optimization for optical thin film design using Latin Squares,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 8–15 (1997).
[CrossRef]

Appl. Opt.

J. A. Dobrowolski, “Completely automatic synthesis of optical thin film systems,” Appl. Opt. 4, 937–946 (1965).
[CrossRef]

J. A. Dobrowolski, S. Piotrowski, “Refractive index as a variable in the numerical design of optical thin film systems,” Appl. Opt. 21, 1502–1510 (1982).
[CrossRef] [PubMed]

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[CrossRef] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[CrossRef] [PubMed]

A. Premoli, M. L. Rastello, “Minimax refining of wideband antireflection coatings for wide angular incidence,” Appl. Opt. 33, 2018–2024 (1994).
[CrossRef] [PubMed]

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement algorithm for the synthesis of inhomogeneous optical coatings,” Appl. Opt. 36, 1487–1495 (1997).
[CrossRef] [PubMed]

S. Martin, J. Rivory, M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt. 34, 2247–2254 (1995).
[CrossRef] [PubMed]

P. G. Verly, “Fourier transform technique with refinement in the frequency domain for the synthesis of optical thin films,” Appl. Opt. 35, 5148–5154 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

P. Baumeister, “Design of multilayer filters by successive approximations,” J. Opt. Soc. Am. 48, 955–958 (1958).
[CrossRef]

C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732A (1982).

Other

T. Boudet, P. Chaton, “Thin film design using simulated annealing and study of the filter robustness,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 27–38 (1996).
[CrossRef]

D. G. Li, A. C. Watson, “Global optimization for optical thin film design using Latin Squares,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 8–15 (1997).
[CrossRef]

W. H. Press, S. A. Teukolski, W. T. Vetterlin, B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1992), 418–423.

H. A. Macleod, “Half wave holes, leaks and other problems,” in Proceedings of the 39th Annual Technical Conference of the Society of Vacuum Coaters, J. N. Lingscheit, A. A. Bromfield, eds. (Society of Vacuum Coaters, Washington, D.C., 1996), pp. 193–198.

B. G. Bovard, “Graded index rugate filters: power sine rugate structures,” in Inhomogeneous and Quasi-inhomogeneous Optical Coatings, J. A. Dobrowolski, P. G. Verly, eds., Proc. SPIE2046, 109–125 (1993).
[CrossRef]

P. G. Verly, A. V. Tikhonravov, M. K. Trubetskov, “Efficient refinement of inhomogeneous optical coatings: synthesis by simultaneous thickness and refractive index optimization,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 46–52 (1997).
[CrossRef]

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 (5)

Fig. 1
Fig. 1

Synthesis of a nonpolarizing low-pass filter for 45° incidence: (a) solution obtained by refractive-index refinement only, (b) intermediate solution obtained by simultaneous refractive-index and thickness refinement, (c) final solution, (d) solution obtained by the needle method in Ref. 7. See text for details.

Fig. 2
Fig. 2

Convergence of the merit function value in Fig. 1. Solid curve, refractive-index refinement; dashed curve, simultaneous refractive-index and thickness refinement. The markers correspond to the solutions shown in Figs. 1(a)1(c).

Fig. 3
Fig. 3

Nonpolarizing antireflection coating for 0°, 30°, 45°, 60°, and 70° incidence: (a) inhomogeneous and five-material multilayer designs obtained by the present method and (b) comparison with a solution obtained by the needle method.7

Fig. 4
Fig. 4

Nonpolarizing high-pass filter for 45° incidence: (a), (b) solution obtained by the present method; (c) solution obtained by the needle method.7 See text for details.

Fig. 5
Fig. 5

Reflector with nonpolarized reflectance and phase shift in reflection at 45° incidence.16 The layers are QW’s at λ = 1 μm.

Equations (4)

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

r n j = Tr Pre j M j n j Post j ψ r     j = 1 ,   2 ,     ,   J ,
Pre j = m = 1 j - 1   M j , Post j = m = j + 1 J   M j ,
ψ r = t 2 n a n a 1 - r - 1 + r n a n s 1 - r - n s 1 + r .
η S = n   cos θ   s   pol . ,   η P = n cos θ   p   pol . ,

Metrics