Abstract

The design of optical filters relies on powerful computer-assisted methods. Many of these methods are provided by commercial programs, but, in order to adapt and improve them, or to develop new methods, one needs to create his own software. To help people interested in such a process, we decided to release our in-house software, called OpenFilters, under the GNU General Public License, an open-source license. It is programmed in Python and C++, and the graphical user interface is implemented with wxPython. It allows creation of multilayer and graded-index filters and calculation of reflection, transmission, absorption, phase, group delay, group delay dispersion, color, ellipsometric variables, admittance diagram, circle diagram, electric field distribution, and generation of reflection, transmission, and ellipsometric monitoring curves. It also provides the refinement, needle, step, and Fourier transform methods.

© 2008 Optical Society of America

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    [CrossRef]
  2. J. A. Dobrowolski, "The impact of computers on the design and manufacture of optical multilayer coatings during the past 50 years," in 50th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2008), pp. 289-301.
  3. J. Kruschwitz, "Software tools speed optical thin-film design," Laser Focus World 39, 153-157 (2003).
  4. Free Software Foundation, "GNU general public license," http://fsf.org/.
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  6. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publishing, 2001).
    [CrossRef]
  7. Sh. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Éditions Frontières, 1992).
  8. R. H. Muller, "Definitions and conventions in ellipsometry," Surf. Sci. 16, 14-33 (1969).
    [CrossRef]
  9. CIE, Colorimetry, 3rd ed. CIE 15:2004 (Commission Internationale de l'Éclairage, 2004).
  10. P. J. Leurgans, "The impedance concept in thin film optics," J. Opt. Soc. Am. 41, 714-717 (1951).
    [CrossRef]
  11. J. H. Apfel, "Graphics in optical coating design," Appl. Opt. 11, 1303-1312 (1972).
    [CrossRef] [PubMed]
  12. V. V. Veremei and I. M. Minkov, "Distribution of light intensity within a dielectric mirror," Opt. Spectrosc. (USSR) 33, 1175-1178 (1972); translation, Opt. Spectrosc. 33, 640-641 (1972).
  13. Y. H. Yang and J. R. Abelson, "Spectroscopic ellipsometry of thin films on transparent substrates: a formalism for data interpretation," J. Vac. Sci. Technol. A 13, 1145-1149 (1995).
    [CrossRef]
  14. P. Baumeister, "Simulation of a rugate filter via a stepped-index dielectric multilayer," Appl. Opt. 25, 2644-2645 (1986).
    [CrossRef] [PubMed]
  15. J. J. Moré, "The Levenberg-Marquardt algorithm: implementation and theory," Lect. Notes Math. 630, 105-116 (1978).
    [CrossRef]
  16. C. J. van der Laan and H. J. Frankena, "Fast computation method for derivatives of multilayer stack reflectance," Appl. Opt. 17, 538-541 (1978).
    [CrossRef]
  17. P. G. Verly, "Modified needle method with simultaneous thickness and refractive-index refinement for the synthesis of inhomogeneous and multilayer optical thin films," Appl. Opt. 40, 5718-5725 (2001).
    [CrossRef]
  18. S. Larouche and L. Martinu, "Optical filters with constant optical thickness and refined refractive indices," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. TuD8.
  19. A. V. Tikhonravov, "A method of synthesis of optical coverings which uses the necessary optimality conditions," Vestn. Mosk. Univ. Fiz. Astronomiya 37, 91-93 (1982); translation, Mosc. Univ. Phys. Bull. 37, 108-110 (1982).
  20. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Application of the needle optimization technique to the design of optical coatings," Appl. Opt. 35, 5493-5508 (1996).
    [CrossRef] [PubMed]
  21. B. T. Sullivan and J. A. Dobrowolski, "Implementation of a numerical needle method for thin-film design," Appl. Opt. 35, 5484-5492 (1996).
    [CrossRef] [PubMed]
  22. S. Larouche and L. Martinu, "A new step method for the synthesis of optical filters with arbitrary indices," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 305-308.
  23. E. Delano, "Fourier synthesis of multilayer filters," J. Opt. Soc. Am. 57, 1529-1533 (1967).
    [CrossRef]
  24. L. Sossi, "A method for the synthesis of multilayer dielectric interference coatings," Eesti NSV Teaduste Akadeemia Toimetised Füüsika, Matemaatika 23, 229-237 (1974). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI).
  25. J. A. Dobrowolski and D. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
    [CrossRef] [PubMed]
  26. B. G. Bovard, "Rugate filter theory: an overview," Appl. Opt. 32, 5427-5442 (1993).
    [CrossRef] [PubMed]
  27. L. Sossi, "On the theory of the synthesis of multilayer dielectric light filters," Eesti NSV Teaduste Akadeemia Toimetised Füüsika, Matemaatika 25, 171-176 (1976). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI).
  28. P. G. Verly, J. A. Dobrowolski, W. J. Wild, and R. L. Burton, "Synthesis of high rejection filters with the Fourier transform method," Appl. Opt. 28, 2864-2875 (1989).
    [CrossRef] [PubMed]
  29. B. G. Bovard, "Derivation of a matrix describing a rugate dielectric thin film," Appl. Opt. 27, 1998-2005 (1988).
    [CrossRef] [PubMed]
  30. B. G. Bovard, "Fourier transform technique applied to quarterwave optical coatings," Appl. Opt. 27, 3062-3063 (1988).
    [CrossRef] [PubMed]
  31. R. Szipöcs and A. Köházi-Kis, "Theory and design of chirped dielectric laser mirrors," Appl. Phys. B 65, 115-135 (1997).
    [CrossRef]
  32. H. Chang, S.-S. Lee, M. R. Chol, and S. Lim, "Inhomogeneous optical filter design with the use of a Riccati equation," Microwave Opt. Technol. Lett. 22, 140-144 (1999).
    [CrossRef]
  33. P. G. Verly and J. A. Dobrowolski, "Iterative correction process for optical thin film synthesis with the Fourier transform method," Appl. Opt. 29, 3672-3684 (1990).
    [CrossRef] [PubMed]
  34. S. Larouche and L. Martinu, "Dispersion implementation in optical filter design by the Fourier transform method using correction factors," Appl. Opt. 46, 7436-7441 (2007).
    [CrossRef] [PubMed]
  35. D. Poitras, S. Larouche, and L. Martinu, "Design and plasma deposition of dispersion-corrected multiband rugate filters," Appl. Opt. 41, 5249-5255 (2002).
    [CrossRef] [PubMed]
  36. W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
    [CrossRef] [PubMed]
  37. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
  38. E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic, 1991).
  39. "Python," http://www.python.org/.
  40. "wxpython," http://wxpython.org/.
  41. J. Moré, B. Garbow, and K. Hillstrom, "MINPACK," http://www.netlib.org/minpack.
  42. M. Tilsch and K. Hendrix, "Optical Interference Coatings design contest 2007: triple bandpass and nonpolarizing beam splitter," Appl. Opt. 47, C55-C69 (2008).
    [CrossRef] [PubMed]
  43. J. A. Dobrowolski, "Completely automatic synthesis of optical thin film systems," Appl. Opt. 4, 937-946 (1965).
    [CrossRef]
  44. J. A. Dobrowolski, "Versatile computer program for absorbing optical thin film systems," Appl. Opt. 20, 74-81 (1981).
    [CrossRef] [PubMed]
  45. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Optical coating design approaches based on the needle optimization technique," Appl. Opt. 46, 704-710 (2007).
    [CrossRef] [PubMed]
  46. P. W. Baumeister, "Methods of altering the characteristics of a multilayer stack," J. Opt. Soc. Am. 52, 1149-1152 (1962).
    [CrossRef]
  47. W. P. Thoeni, "Deposition of optical coatings: process control and automation," Thin Solid Films 88, 385-397 (1982).
    [CrossRef]
  48. H. Zorc, "Optimum multilayer design selection in relation to production errors," Vacuum 37, 101-102 (1987).
    [CrossRef]
  49. A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
    [CrossRef] [PubMed]
  50. S. Larouche and L. Martinu, "OpenFilters: an open source software for the design and optimization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. WB6.

2008 (2)

J. A. Dobrowolski, "The impact of computers on the design and manufacture of optical multilayer coatings during the past 50 years," in 50th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2008), pp. 289-301.

M. Tilsch and K. Hendrix, "Optical Interference Coatings design contest 2007: triple bandpass and nonpolarizing beam splitter," Appl. Opt. 47, C55-C69 (2008).
[CrossRef] [PubMed]

2007 (4)

S. Larouche and L. Martinu, "Dispersion implementation in optical filter design by the Fourier transform method using correction factors," Appl. Opt. 46, 7436-7441 (2007).
[CrossRef] [PubMed]

S. Larouche and L. Martinu, "Optical filters with constant optical thickness and refined refractive indices," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. TuD8.

S. Larouche and L. Martinu, "OpenFilters: an open source software for the design and optimization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. WB6.

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Optical coating design approaches based on the needle optimization technique," Appl. Opt. 46, 704-710 (2007).
[CrossRef] [PubMed]

2006 (1)

S. Larouche and L. Martinu, "A new step method for the synthesis of optical filters with arbitrary indices," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 305-308.

2005 (1)

A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
[CrossRef] [PubMed]

2004 (1)

CIE, Colorimetry, 3rd ed. CIE 15:2004 (Commission Internationale de l'Éclairage, 2004).

2003 (1)

J. Kruschwitz, "Software tools speed optical thin-film design," Laser Focus World 39, 153-157 (2003).

2002 (1)

2001 (2)

1999 (1)

H. Chang, S.-S. Lee, M. R. Chol, and S. Lim, "Inhomogeneous optical filter design with the use of a Riccati equation," Microwave Opt. Technol. Lett. 22, 140-144 (1999).
[CrossRef]

1997 (1)

R. Szipöcs and A. Köházi-Kis, "Theory and design of chirped dielectric laser mirrors," Appl. Phys. B 65, 115-135 (1997).
[CrossRef]

1996 (2)

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

B. T. Sullivan and J. A. Dobrowolski, "Implementation of a numerical needle method for thin-film design," Appl. Opt. 35, 5484-5492 (1996).
[CrossRef] [PubMed]

1995 (1)

Y. H. Yang and J. R. Abelson, "Spectroscopic ellipsometry of thin films on transparent substrates: a formalism for data interpretation," J. Vac. Sci. Technol. A 13, 1145-1149 (1995).
[CrossRef]

1993 (1)

B. G. Bovard, "Rugate filter theory: an overview," Appl. Opt. 32, 5427-5442 (1993).
[CrossRef] [PubMed]

1992 (1)

Sh. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Éditions Frontières, 1992).

1991 (1)

E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic, 1991).

1990 (1)

1989 (1)

1988 (2)

B. G. Bovard, "Derivation of a matrix describing a rugate dielectric thin film," Appl. Opt. 27, 1998-2005 (1988).
[CrossRef] [PubMed]

B. G. Bovard, "Fourier transform technique applied to quarterwave optical coatings," Appl. Opt. 27, 3062-3063 (1988).
[CrossRef] [PubMed]

1987 (1)

H. Zorc, "Optimum multilayer design selection in relation to production errors," Vacuum 37, 101-102 (1987).
[CrossRef]

1986 (1)

1985 (1)

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

1983 (1)

W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
[CrossRef] [PubMed]

1982 (2)

A. V. Tikhonravov, "A method of synthesis of optical coverings which uses the necessary optimality conditions," Vestn. Mosk. Univ. Fiz. Astronomiya 37, 91-93 (1982); translation, Mosc. Univ. Phys. Bull. 37, 108-110 (1982).

W. P. Thoeni, "Deposition of optical coatings: process control and automation," Thin Solid Films 88, 385-397 (1982).
[CrossRef]

1981 (1)

J. A. Dobrowolski, "Versatile computer program for absorbing optical thin film systems," Appl. Opt. 20, 74-81 (1981).
[CrossRef] [PubMed]

1978 (3)

J. J. Moré, "The Levenberg-Marquardt algorithm: implementation and theory," Lect. Notes Math. 630, 105-116 (1978).
[CrossRef]

J. A. Dobrowolski and D. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
[CrossRef] [PubMed]

C. J. van der Laan and H. J. Frankena, "Fast computation method for derivatives of multilayer stack reflectance," Appl. Opt. 17, 538-541 (1978).
[CrossRef]

1976 (1)

L. Sossi, "On the theory of the synthesis of multilayer dielectric light filters," Eesti NSV Teaduste Akadeemia Toimetised Füüsika, Matemaatika 25, 171-176 (1976). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI).

1974 (1)

L. Sossi, "A method for the synthesis of multilayer dielectric interference coatings," Eesti NSV Teaduste Akadeemia Toimetised Füüsika, Matemaatika 23, 229-237 (1974). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI).

1972 (2)

J. H. Apfel, "Graphics in optical coating design," Appl. Opt. 11, 1303-1312 (1972).
[CrossRef] [PubMed]

V. V. Veremei and I. M. Minkov, "Distribution of light intensity within a dielectric mirror," Opt. Spectrosc. (USSR) 33, 1175-1178 (1972); translation, Opt. Spectrosc. 33, 640-641 (1972).

1969 (1)

R. H. Muller, "Definitions and conventions in ellipsometry," Surf. Sci. 16, 14-33 (1969).
[CrossRef]

1967 (1)

E. Delano, "Fourier synthesis of multilayer filters," J. Opt. Soc. Am. 57, 1529-1533 (1967).
[CrossRef]

1965 (1)

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

1962 (1)

P. W. Baumeister, "Methods of altering the characteristics of a multilayer stack," J. Opt. Soc. Am. 52, 1149-1152 (1962).
[CrossRef]

1958 (1)

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

1951 (1)

P. J. Leurgans, "The impedance concept in thin film optics," J. Opt. Soc. Am. 41, 714-717 (1951).
[CrossRef]

1950 (1)

F. Abelès, "Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces," Ann. Phys. (Paris) 5, 596-640, 706-782 (1950).

van der Laan, C. J.

Abelès, F.

F. Abelès, "Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces," Ann. Phys. (Paris) 5, 596-640, 706-782 (1950).

Abelson, J. R.

Y. H. Yang and J. R. Abelson, "Spectroscopic ellipsometry of thin films on transparent substrates: a formalism for data interpretation," J. Vac. Sci. Technol. A 13, 1145-1149 (1995).
[CrossRef]

Apfel, J. H.

J. H. Apfel, "Graphics in optical coating design," Appl. Opt. 11, 1303-1312 (1972).
[CrossRef] [PubMed]

Baumeister, P.

P. Baumeister, "Simulation of a rugate filter via a stepped-index dielectric multilayer," Appl. Opt. 25, 2644-2645 (1986).
[CrossRef] [PubMed]

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

Baumeister, P. W.

P. W. Baumeister, "Methods of altering the characteristics of a multilayer stack," J. Opt. Soc. Am. 52, 1149-1152 (1962).
[CrossRef]

Bovard, B. G.

B. G. Bovard, "Rugate filter theory: an overview," Appl. Opt. 32, 5427-5442 (1993).
[CrossRef] [PubMed]

B. G. Bovard, "Fourier transform technique applied to quarterwave optical coatings," Appl. Opt. 27, 3062-3063 (1988).
[CrossRef] [PubMed]

B. G. Bovard, "Derivation of a matrix describing a rugate dielectric thin film," Appl. Opt. 27, 1998-2005 (1988).
[CrossRef] [PubMed]

Burton, R. L.

Chang, H.

H. Chang, S.-S. Lee, M. R. Chol, and S. Lim, "Inhomogeneous optical filter design with the use of a Riccati equation," Microwave Opt. Technol. Lett. 22, 140-144 (1999).
[CrossRef]

Chol, M. R.

H. Chang, S.-S. Lee, M. R. Chol, and S. Lim, "Inhomogeneous optical filter design with the use of a Riccati equation," Microwave Opt. Technol. Lett. 22, 140-144 (1999).
[CrossRef]

CIE,

CIE, Colorimetry, 3rd ed. CIE 15:2004 (Commission Internationale de l'Éclairage, 2004).

DeBell, G. W.

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Optical coating design approaches based on the needle optimization technique," Appl. Opt. 46, 704-710 (2007).
[CrossRef] [PubMed]

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

Delano, E.

E. Delano, "Fourier synthesis of multilayer filters," J. Opt. Soc. Am. 57, 1529-1533 (1967).
[CrossRef]

Dobrowolski, J. A.

J. A. Dobrowolski, "The impact of computers on the design and manufacture of optical multilayer coatings during the past 50 years," in 50th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2008), pp. 289-301.

B. T. Sullivan and J. A. Dobrowolski, "Implementation of a numerical needle method for thin-film design," Appl. Opt. 35, 5484-5492 (1996).
[CrossRef] [PubMed]

P. G. Verly and J. A. Dobrowolski, "Iterative correction process for optical thin film synthesis with the Fourier transform method," Appl. Opt. 29, 3672-3684 (1990).
[CrossRef] [PubMed]

P. G. Verly, J. A. Dobrowolski, W. J. Wild, and R. L. Burton, "Synthesis of high rejection filters with the Fourier transform method," Appl. Opt. 28, 2864-2875 (1989).
[CrossRef] [PubMed]

J. A. Dobrowolski, "Versatile computer program for absorbing optical thin film systems," Appl. Opt. 20, 74-81 (1981).
[CrossRef] [PubMed]

J. A. Dobrowolski and D. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
[CrossRef] [PubMed]

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

Frankena, H. J.

Furman, Sh. A.

Sh. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Éditions Frontières, 1992).

Garbow, B.

J. Moré, B. Garbow, and K. Hillstrom, "MINPACK," http://www.netlib.org/minpack.

Hendrix, K.

M. Tilsch and K. Hendrix, "Optical Interference Coatings design contest 2007: triple bandpass and nonpolarizing beam splitter," Appl. Opt. 47, C55-C69 (2008).
[CrossRef] [PubMed]

Hillstrom, K.

J. Moré, B. Garbow, and K. Hillstrom, "MINPACK," http://www.netlib.org/minpack.

Köházi-Kis, A.

R. Szipöcs and A. Köházi-Kis, "Theory and design of chirped dielectric laser mirrors," Appl. Phys. B 65, 115-135 (1997).
[CrossRef]

Kruschwitz, J.

J. Kruschwitz, "Software tools speed optical thin-film design," Laser Focus World 39, 153-157 (2003).

Larouche, S.

S. Larouche and L. Martinu, "Dispersion implementation in optical filter design by the Fourier transform method using correction factors," Appl. Opt. 46, 7436-7441 (2007).
[CrossRef] [PubMed]

S. Larouche and L. Martinu, "Optical filters with constant optical thickness and refined refractive indices," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. TuD8.

S. Larouche and L. Martinu, "OpenFilters: an open source software for the design and optimization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. WB6.

S. Larouche and L. Martinu, "A new step method for the synthesis of optical filters with arbitrary indices," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 305-308.

D. Poitras, S. Larouche, and L. Martinu, "Design and plasma deposition of dispersion-corrected multiband rugate filters," Appl. Opt. 41, 5249-5255 (2002).
[CrossRef] [PubMed]

Lee, S.-S.

H. Chang, S.-S. Lee, M. R. Chol, and S. Lim, "Inhomogeneous optical filter design with the use of a Riccati equation," Microwave Opt. Technol. Lett. 22, 140-144 (1999).
[CrossRef]

Leurgans, P. J.

P. J. Leurgans, "The impedance concept in thin film optics," J. Opt. Soc. Am. 41, 714-717 (1951).
[CrossRef]

Lim, S.

H. Chang, S.-S. Lee, M. R. Chol, and S. Lim, "Inhomogeneous optical filter design with the use of a Riccati equation," Microwave Opt. Technol. Lett. 22, 140-144 (1999).
[CrossRef]

Lowe, D.

J. A. Dobrowolski and D. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978).
[CrossRef] [PubMed]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publishing, 2001).
[CrossRef]

Martinu, L.

S. Larouche and L. Martinu, "Dispersion implementation in optical filter design by the Fourier transform method using correction factors," Appl. Opt. 46, 7436-7441 (2007).
[CrossRef] [PubMed]

S. Larouche and L. Martinu, "OpenFilters: an open source software for the design and optimization of optical coatings," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. WB6.

S. Larouche and L. Martinu, "Optical filters with constant optical thickness and refined refractive indices," in Optical Interference Coatings on CD-ROM (Optical Society of America, 2007), p. TuD8.

S. Larouche and L. Martinu, "A new step method for the synthesis of optical filters with arbitrary indices," in 49th Annual Technical Conference Proceedings (Society of Vacuum Coaters, 2006), pp. 305-308.

D. Poitras, S. Larouche, and L. Martinu, "Design and plasma deposition of dispersion-corrected multiband rugate filters," Appl. Opt. 41, 5249-5255 (2002).
[CrossRef] [PubMed]

Minkov, I. M.

V. V. Veremei and I. M. Minkov, "Distribution of light intensity within a dielectric mirror," Opt. Spectrosc. (USSR) 33, 1175-1178 (1972); translation, Opt. Spectrosc. 33, 640-641 (1972).

Moré, J.

J. Moré, B. Garbow, and K. Hillstrom, "MINPACK," http://www.netlib.org/minpack.

Moré, J. J.

J. J. Moré, "The Levenberg-Marquardt algorithm: implementation and theory," Lect. Notes Math. 630, 105-116 (1978).
[CrossRef]

Muller, R. H.

R. H. Muller, "Definitions and conventions in ellipsometry," Surf. Sci. 16, 14-33 (1969).
[CrossRef]

Poitras, D.

Sossi, L.

L. Sossi, "On the theory of the synthesis of multilayer dielectric light filters," Eesti NSV Teaduste Akadeemia Toimetised Füüsika, Matemaatika 25, 171-176 (1976). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI).

L. Sossi, "A method for the synthesis of multilayer dielectric interference coatings," Eesti NSV Teaduste Akadeemia Toimetised Füüsika, Matemaatika 23, 229-237 (1974). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI).

Southwell, W. H.

W. H. Southwell, "Gradient-index antireflection coatings," Opt. Lett. 8, 584-586 (1983).
[CrossRef] [PubMed]

Sullivan, B. T.

B. T. Sullivan and J. A. Dobrowolski, "Implementation of a numerical needle method for thin-film design," Appl. Opt. 35, 5484-5492 (1996).
[CrossRef] [PubMed]

Szipöcs, R.

R. Szipöcs and A. Köházi-Kis, "Theory and design of chirped dielectric laser mirrors," Appl. Phys. B 65, 115-135 (1997).
[CrossRef]

Thoeni, W. P.

W. P. Thoeni, "Deposition of optical coatings: process control and automation," Thin Solid Films 88, 385-397 (1982).
[CrossRef]

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, "Optical coating design approaches based on the needle optimization technique," Appl. Opt. 46, 704-710 (2007).
[CrossRef] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Multilayer optical filter.

Fig. 2
Fig. 2

Optical filter with backside.

Fig. 3
Fig. 3

Discretization of the refractive index profile of a graded-index filter (see text for details).

Fig. 4
Fig. 4

Schematic representation of (a) the needle method and (b) the step method.

Fig. 5
Fig. 5

(Color online) Main window of OpenFilters.

Fig. 6
Fig. 6

(Color online) Needle method dialog.

Equations (55)

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

M i = [ cos φ i ( i / η i ) sin φ i i η i sin φ i cos φ i ] ,
η i = { N i cos θ i s  polarization N i / cos θ i p  polarization
φ i = 2 π λ N i d i cos θ i
η i = { N i 2 α 2 s  polarization N i 2 / N i 2 α 2 p  polarization ,
φ i = 2 π λ N i 2 α 2 d i
M = [ m 11 m 12 m 21 m 22 ] = i = q 1 M i ,
r = η inc m 11 η ex m 22 + η inc η ex m 12 m 21 η inc m 11 + η ex m 22 + η inc η ex m 12 + m 21 ,
t = 2 η inc η inc m 11 + η ex m 22 + η inc η ex m 12 + m 21 ,
R = r r * = | r | 2 ,
T = Re N ex Re N inc t t * = Re N ex Re N inc | t | 2 ,
A = 1 R T .
ϕ r = arg r = arctan Im r Re r ,
ϕ t = arg t = arctan Im t Re t ,
GD = d ϕ d ω ,
GDD = d 2 ϕ d ω 2 ,
ρ = r p r s = tan Ψ e i Δ ,
Ψ = arctan | r p | | r s | , Δ = arg ( r p ) arg ( r s ) .
R = R F + T F T FR R B exp 4 β i 1 R FR R B exp 4 β i ,
T = T F T B exp 2 β i 1 R FR R B exp 4 β i ,
β i = Im ( 2 π λ N s u b 2 α 2 d s u b )
d j + d j + 1 = b a ,
n j d j + n j + 1 d j + 1 = a b n ( z ) d z ,
χ 2 = i = 1 m ( B i B ¯ i Δ B i ) 2 ,
d χ 2 d a k = 2 i = 1 m [ B i B ¯ i ( Δ B i ) 2 d B i d a k ] ,
d R d a k = 2 r * d r d a k ,
d T d a k = 2 Re ( N s ) Re ( N m ) t * d t d a k .
d r d a k = T r ( d M d a k ψ r ) ,
ψ r = t 2 N inc [ N inc ( 1 r ) ( 1 + r ) N inc N ex ( 1 r ) N ex ( 1 + r ) ] .
d t d a k = T r ( d M d a k ψ t ) ,
ψ t = t 2 2 N inc [ N inc 1 N inc N ex N inc ] .
d M d a k = i = q j + 1 M i d M j d a k i = j 1 1 M i .
d M j d d j = d M j d φ j d φ j d d j ,
d M j d φ j = [ sin φ j ( i / η j ) cos φ j i η j cos φ j sin φ j ] ,
d φ j d d j = 2 π λ N j 2 α 2 .
d M j d N j = d M j d φ j d φ j d N j + d M j d η j d η j d N j ,
d M j d η j = [ 0 ( i / η j 2 ) sin φ j i sin φ j 0 ] ,
d η j d N j = { N j N j 2 α 2 s  polarization N j N j 2 α 2 ( 2 N j 2 N j 2 α 2 ) p  polarization ,
d φ j d N j = 2 π λ N j N j 2 α 2 d j .
d M j d n j , 0 = d M j d N j d N j d n j , 0 ,
d R d a k = d R F d a k + T F T F R R B exp 4 β i 1 R F R R B exp 4 β i ( 1 T F d T F d a k + 1 T R d T R d a k + R B exp 4 β i 1 R F R R B exp 4 β i d R F R d a k ) ,
d T d a k = T ( 1 T F d T F d a k + R B exp 4 β i 1 R F R R B exp 4 β i d R F R d a k ) .
d M j d d n | d n = 0 = M j , 2 d M n d d n | d n = 0 M j , 1 .
d M j d d n | d n = 0 = 1 2 [ ( η j η n + η n η j ) d M j d φ j + ( η j η n η n η j ) × [ 1 0 0 1 ] d M j ( Δ φ j ) d Δ φ j ] d φ n d d n ,
d M j d Δ N j | Δ N j = 0 = 1 2 d M j , 2 d N j M j , 1 M j , 2 1 2 d M j , 1 d N j .
d M j d Δ N j | Δ N j = 0 = 1 2 [ d M j d φ j d Δ φ j d N j + ( d M j ( Δ φ j ) d η j + 1 η j ( cos φ j cos Δ φ j ) [ 1 0 0 1 ] ) d η j d N j ] ,
ln n ( x ) n m = 2 π 0 Q ( σ ) σ sin ( Ψ ( σ ) σ x ) d σ ,
n m = n m i n n m a x
x = 2 0 z n ( u ) d u
ln n ( x ) n m = i Q ¯ i sin ( 2 π x / λ i + φ i ) w ( x ) ,
Q ¯ i = 1 2 ln n m + Δ n i / 2 n m Δ n i / 2
w ( x ) = I 0 ( β 1 4 x 2 ) I 0 ( β ) Π ( x ) ,
Δ n = 2 n m sin ( π 4 Δ λ i λ i ) ,
x = Q π Q ¯ i | W 0 | / λ i ,
n ( u ) = n 1 + ( n 2 n 1 ) ( 10 u 3 15 u 4 + 6 u 5 ) ,
n ( u ) = n 1 exp [ ln 1 + ( n 2 n 1 ) n 1 ( 10 u 3 15 u 4 + 6 u 5 ) ] ,

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