Abstract

Inverse Fourier transform method has been commonly used for designing complex inhomogeneous optical coatings. Since it assumes dispersion-free optical constants, introducing real optical materials induces shifts in the position of reflectance bands in multiband inhomogeneous minus (rugate) filters. We propose a simple method for considering optical dispersion in the synthesis of multiband rugate filter designs. Model filters designed with this method were fabricated on glass and polycarbonate substrates by plasma-enhanced chemical vapor deposition of silicon oxynitrides and SiO2/TiO2 mixtures with precisely controlled composition gradients.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2000 (1)

L. Martinu, D. Poitras, “Plasma deposition of optical films and coatings: a review,” J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[CrossRef]

1999 (2)

D. Rats, D. Poitras, J. M. Soro, L. Martinu, J. von Stebut, “Mechanical properties of plasma-deposited silicon-based inhomogeneous optical coatings,” Surf. Coat. Technol. 111, 220–228 (1999).
[CrossRef]

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

1996 (1)

D. Poitras, P. Leroux, J. E. Klemberg-Sapieha, S. C. Gujrathi, L. Martinu, “Characterization of homogeneous and inhomogeneous Si-based optical coatings deposited in dual-frequency plasma,” Opt. Eng. 35, 2690–2699 (1996).
[CrossRef]

1993 (1)

1992 (2)

1990 (2)

1989 (2)

1988 (1)

1983 (1)

1978 (1)

1974 (1)

L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Izvestiya Akademii Nauk Estonskoi SSR Fizika, Matematika 23, 229–237 (1974). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI), National Research Council of Canada, 1200 Montreal Road, Building M-55, Ottawa, Ontario, K1A 0R6 Canada.

1967 (1)

1960 (1)

Amassian, A.

S. Larouche, A. Amassian, S. C. Gujrathi, J. Klemberg-Sapieha, L. Martinu, “Multilayer and inhomogeneous optical filters fabricated by PECVD using titanium dioxide and silicon dioxide,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 277–281.

Bovard, B. G.

Brandt, W.

Burton, R. L.

Chang, H.

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

Choi, M.-R.

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

Delano, E.

Dobrowolski, J. A.

Fabricius, H.

Friel, D. D.

Greenwalt, C. H.

Gujrathi, S. C.

D. Poitras, P. Leroux, J. E. Klemberg-Sapieha, S. C. Gujrathi, L. Martinu, “Characterization of homogeneous and inhomogeneous Si-based optical coatings deposited in dual-frequency plasma,” Opt. Eng. 35, 2690–2699 (1996).
[CrossRef]

S. Larouche, A. Amassian, S. C. Gujrathi, J. Klemberg-Sapieha, L. Martinu, “Multilayer and inhomogeneous optical filters fabricated by PECVD using titanium dioxide and silicon dioxide,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 277–281.

Klemberg-Sapieha, J.

S. Larouche, A. Amassian, S. C. Gujrathi, J. Klemberg-Sapieha, L. Martinu, “Multilayer and inhomogeneous optical filters fabricated by PECVD using titanium dioxide and silicon dioxide,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 277–281.

Klemberg-Sapieha, J. E.

D. Poitras, P. Leroux, J. E. Klemberg-Sapieha, S. C. Gujrathi, L. Martinu, “Characterization of homogeneous and inhomogeneous Si-based optical coatings deposited in dual-frequency plasma,” Opt. Eng. 35, 2690–2699 (1996).
[CrossRef]

M.-A. Raymond, S. Larouche, O. Zabeida, L. Martinu, J. E. Klemberg-Sapieha, “Tribological properties of PECVD optical coatings,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 301–305.

Larouche, S.

M.-A. Raymond, S. Larouche, O. Zabeida, L. Martinu, J. E. Klemberg-Sapieha, “Tribological properties of PECVD optical coatings,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 301–305.

D. Poitras, S. Larouche, L. Martinu, “Design and plasma deposition of dispersion-corrected multiband rugate filters,” in Optical Interference Coatings, Vol. 63 of OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp.MB7–1-MB7–3.

S. Larouche, A. Amassian, S. C. Gujrathi, J. Klemberg-Sapieha, L. Martinu, “Multilayer and inhomogeneous optical filters fabricated by PECVD using titanium dioxide and silicon dioxide,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 277–281.

Lee, S.-S.

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

Leroux, P.

D. Poitras, P. Leroux, J. E. Klemberg-Sapieha, S. C. Gujrathi, L. Martinu, “Characterization of homogeneous and inhomogeneous Si-based optical coatings deposited in dual-frequency plasma,” Opt. Eng. 35, 2690–2699 (1996).
[CrossRef]

Lim, S.

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

Lowe, D.

Martinu, L.

L. Martinu, D. Poitras, “Plasma deposition of optical films and coatings: a review,” J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[CrossRef]

D. Rats, D. Poitras, J. M. Soro, L. Martinu, J. von Stebut, “Mechanical properties of plasma-deposited silicon-based inhomogeneous optical coatings,” Surf. Coat. Technol. 111, 220–228 (1999).
[CrossRef]

D. Poitras, P. Leroux, J. E. Klemberg-Sapieha, S. C. Gujrathi, L. Martinu, “Characterization of homogeneous and inhomogeneous Si-based optical coatings deposited in dual-frequency plasma,” Opt. Eng. 35, 2690–2699 (1996).
[CrossRef]

S. Larouche, A. Amassian, S. C. Gujrathi, J. Klemberg-Sapieha, L. Martinu, “Multilayer and inhomogeneous optical filters fabricated by PECVD using titanium dioxide and silicon dioxide,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 277–281.

M.-A. Raymond, S. Larouche, O. Zabeida, L. Martinu, J. E. Klemberg-Sapieha, “Tribological properties of PECVD optical coatings,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 301–305.

D. Poitras, S. Larouche, L. Martinu, “Design and plasma deposition of dispersion-corrected multiband rugate filters,” in Optical Interference Coatings, Vol. 63 of OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp.MB7–1-MB7–3.

Poitras, D.

L. Martinu, D. Poitras, “Plasma deposition of optical films and coatings: a review,” J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[CrossRef]

D. Rats, D. Poitras, J. M. Soro, L. Martinu, J. von Stebut, “Mechanical properties of plasma-deposited silicon-based inhomogeneous optical coatings,” Surf. Coat. Technol. 111, 220–228 (1999).
[CrossRef]

D. Poitras, P. Leroux, J. E. Klemberg-Sapieha, S. C. Gujrathi, L. Martinu, “Characterization of homogeneous and inhomogeneous Si-based optical coatings deposited in dual-frequency plasma,” Opt. Eng. 35, 2690–2699 (1996).
[CrossRef]

D. Poitras, S. Larouche, L. Martinu, “Design and plasma deposition of dispersion-corrected multiband rugate filters,” in Optical Interference Coatings, Vol. 63 of OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp.MB7–1-MB7–3.

Rats, D.

D. Rats, D. Poitras, J. M. Soro, L. Martinu, J. von Stebut, “Mechanical properties of plasma-deposited silicon-based inhomogeneous optical coatings,” Surf. Coat. Technol. 111, 220–228 (1999).
[CrossRef]

Raymond, M.-A.

M.-A. Raymond, S. Larouche, O. Zabeida, L. Martinu, J. E. Klemberg-Sapieha, “Tribological properties of PECVD optical coatings,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 301–305.

Soro, J. M.

D. Rats, D. Poitras, J. M. Soro, L. Martinu, J. von Stebut, “Mechanical properties of plasma-deposited silicon-based inhomogeneous optical coatings,” Surf. Coat. Technol. 111, 220–228 (1999).
[CrossRef]

Sossi, L.

L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Izvestiya Akademii Nauk Estonskoi SSR Fizika, Matematika 23, 229–237 (1974). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI), National Research Council of Canada, 1200 Montreal Road, Building M-55, Ottawa, Ontario, K1A 0R6 Canada.

Southwell, W. H.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988).

Verly, P. G.

von Stebut, J.

D. Rats, D. Poitras, J. M. Soro, L. Martinu, J. von Stebut, “Mechanical properties of plasma-deposited silicon-based inhomogeneous optical coatings,” Surf. Coat. Technol. 111, 220–228 (1999).
[CrossRef]

Wild, W. J.

Willey, R. R.

Zabeida, O.

M.-A. Raymond, S. Larouche, O. Zabeida, L. Martinu, J. E. Klemberg-Sapieha, “Tribological properties of PECVD optical coatings,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 301–305.

Appl. Opt. (9)

Izvestiya Akademii Nauk Estonskoi SSR Fizika, Matematika (1)

L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Izvestiya Akademii Nauk Estonskoi SSR Fizika, Matematika 23, 229–237 (1974). English translation available from the Translation Services of the Canada Institute for Scientific and Technical Information (CISTI), National Research Council of Canada, 1200 Montreal Road, Building M-55, Ottawa, Ontario, K1A 0R6 Canada.

J. Opt. Soc. Am. (2)

J. Vac. Sci. Technol. A (1)

L. Martinu, D. Poitras, “Plasma deposition of optical films and coatings: a review,” J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

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

Opt. Eng. (1)

D. Poitras, P. Leroux, J. E. Klemberg-Sapieha, S. C. Gujrathi, L. Martinu, “Characterization of homogeneous and inhomogeneous Si-based optical coatings deposited in dual-frequency plasma,” Opt. Eng. 35, 2690–2699 (1996).
[CrossRef]

Opt. Lett. (1)

Surf. Coat. Technol. (1)

D. Rats, D. Poitras, J. M. Soro, L. Martinu, J. von Stebut, “Mechanical properties of plasma-deposited silicon-based inhomogeneous optical coatings,” Surf. Coat. Technol. 111, 220–228 (1999).
[CrossRef]

Other (4)

M.-A. Raymond, S. Larouche, O. Zabeida, L. Martinu, J. E. Klemberg-Sapieha, “Tribological properties of PECVD optical coatings,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 301–305.

S. Larouche, A. Amassian, S. C. Gujrathi, J. Klemberg-Sapieha, L. Martinu, “Multilayer and inhomogeneous optical filters fabricated by PECVD using titanium dioxide and silicon dioxide,” in Proceedings of the Forty-Fourth Annual Technical Conference of the Society of Vacuum Coaters (Society of Vacuum Coaters, Albuquerque, N. Mex., 2001), pp. 277–281.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988).

D. Poitras, S. Larouche, L. Martinu, “Design and plasma deposition of dispersion-corrected multiband rugate filters,” in Optical Interference Coatings, Vol. 63 of OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp.MB7–1-MB7–3.

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Figures (7)

Fig. 1
Fig. 1

Variation of the refractive-index dispersion as a function of working gas composition during the plasma deposition of (a) SiO x N y and (b) SiO2/TiO2.

Fig. 2
Fig. 2

Deposition rate as a function of working gas composition during the plasma deposition of (a) SiO x N y and (b) SiO2/TiO2.

Fig. 3
Fig. 3

Calculated reflectance spectra of an inhomogeneous optical filter designed with the inverse Fourier transform method, with nondispersive (solid line) and dispersive (dotted line) optical constants; the index profile is defined at 800 nm.

Fig. 4
Fig. 4

Schematic representation of the design n(x) of a two-band rugate filter: 1, separate designs are generated for every band; 2, designs are all expressed at a common wavelength λ0; 3, designs are multiplied and normalized.

Fig. 5
Fig. 5

Example of the application of the design approach described in Fig. 4 applied to a triple-band rugate filter, with a SiO2/TiO2 mixture, with bands at 450, 600, and 750 nm: (a) refractive-index depth profile n(z) at λ0 = 600 nm and (b) refection spectra (solid line) compared with the results of Eq. 6 (dotted line).

Fig. 6
Fig. 6

Example of plasma-deposited, dispersion-corrected, double-band rugate filters with SiO x N y with bands at 450 and 633 nm: (a) design index profile, (b) design variation of the gas flows during the fabrication, (c) measured transmission spectra of the filter deposited on glass (solid line) compared with calculated spectra (dotted line), (d) measured transmission spectra of the filter deposited on polycarbonate.

Fig. 7
Fig. 7

Example of plasma-deposited, dispersion-corrected, triple-band rugate filter fabricated on glass with SiO2/TiO2 mixtures with bands at 600, 800, and 1100 nm: (a) design index profile and (b) measured transmission spectra (solid line) compared with calculated spectra (dotted line).

Equations (13)

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

nAx=nA0expQ¯AπxAσA|W0|sin2πσAx+ϕA-sinϕAwx,
Q¯A=12ln1+RA1-RA
xA=2Q¯AπσA lnnmax/nmin|W0|
wKx=I0β1-4x21/2I0β Πx,
WK0=sinh ββI0β.
nx=i=1m ni0expQ¯iπxλiσi|Wi0|sin2πσix+ϕi-sinϕiwix.
xλi=x0=2π lnnmax/nmini=1mQ¯iσi|Wi0|,
nx=K i=1m nixλ0, λ0,
Qλexpiϕλ=i=1m Qiλexpiϕiλ.
Rλi=1m Riλ.
ncorrx=anxb,
b=lnnmax/nminlnmaxnx/minnx,
a=nmaxbmaxnx.

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