Abstract

The possibility of converting the continuous refractive-index profile into a two-index solution is shown. The technique of conversion that is developed makes it possible to take dispersion into account. This ensures that it is possible to achieve a good agreement between theory and practice in a broad spectral range. Several gradient-index filters have been developed and produced, and measuring results are presented.

© 1992 Optical Society of America

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References

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  1. L. Sossi, P. Kard, “On the theory of the reflection and transmission of light by a thin inhomogeneous dielectric film,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 17, 41–48(1968). An English translation is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario K1A 0S2, Canada.
  2. L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation is available (see Ref. 1).
  3. L. Sossi, “On the theory of the synthesis of multilayer dielectric light filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171–176 (1976). An English translation is available (see Ref. 1).
  4. J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
    [CrossRef] [PubMed]
  5. J. A. Dobrowolski, “Design of optical multilayer coatings at NRCC,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 48–56 (1986).
  6. B. G. Bovard, “Derivation of a matrix describing a rugate dielectric thin film,” Appl. Opt. 27, 1998–2005 (1988).
    [CrossRef] [PubMed]
  7. H. Fabricius, “Gradient-index filters: designing filters with steep skirts, high reflection, and quintic matching layers,” Appl. Opt. 31, (August1992).
    [CrossRef] [PubMed]
  8. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef] [PubMed]
  9. H. A. Macleod, Thin-Film Optical Filters (Hilger, London, 1986), Chap. 2, pp. 11–48.

1992 (1)

H. Fabricius, “Gradient-index filters: designing filters with steep skirts, high reflection, and quintic matching layers,” Appl. Opt. 31, (August1992).
[CrossRef] [PubMed]

1988 (1)

1985 (1)

1978 (1)

1976 (1)

L. Sossi, “On the theory of the synthesis of multilayer dielectric light filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171–176 (1976). An English translation is available (see Ref. 1).

1974 (1)

L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation is available (see Ref. 1).

1968 (1)

L. Sossi, P. Kard, “On the theory of the reflection and transmission of light by a thin inhomogeneous dielectric film,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 17, 41–48(1968). An English translation is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario K1A 0S2, Canada.

Bovard, B. G.

Dobrowolski, J. A.

J. A. Dobrowolski, 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, “Design of optical multilayer coatings at NRCC,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 48–56 (1986).

Fabricius, H.

H. Fabricius, “Gradient-index filters: designing filters with steep skirts, high reflection, and quintic matching layers,” Appl. Opt. 31, (August1992).
[CrossRef] [PubMed]

Kard, P.

L. Sossi, P. Kard, “On the theory of the reflection and transmission of light by a thin inhomogeneous dielectric film,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 17, 41–48(1968). An English translation is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario K1A 0S2, Canada.

Lowe, D.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Hilger, London, 1986), Chap. 2, pp. 11–48.

Sossi, L.

L. Sossi, “On the theory of the synthesis of multilayer dielectric light filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171–176 (1976). An English translation is available (see Ref. 1).

L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation is available (see Ref. 1).

L. Sossi, P. Kard, “On the theory of the reflection and transmission of light by a thin inhomogeneous dielectric film,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 17, 41–48(1968). An English translation is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario K1A 0S2, Canada.

Southwell, W. H.

Appl. Opt. (4)

Eesti NSV Tead. Akad. Toim. Fuus. Mat. (3)

L. Sossi, P. Kard, “On the theory of the reflection and transmission of light by a thin inhomogeneous dielectric film,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 17, 41–48(1968). An English translation is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council, Ottawa, Ontario K1A 0S2, Canada.

L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229–237 (1974). An English translation is available (see Ref. 1).

L. Sossi, “On the theory of the synthesis of multilayer dielectric light filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171–176 (1976). An English translation is available (see Ref. 1).

Other (2)

J. A. Dobrowolski, “Design of optical multilayer coatings at NRCC,” in Thin Film Technologies II, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 48–56 (1986).

H. A. Macleod, Thin-Film Optical Filters (Hilger, London, 1986), Chap. 2, pp. 11–48.

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Figures (7)

Fig. 1
Fig. 1

Spectral performance of a GIF predicted by calculations that do not take into account dispersion (see the dotted curve). The fixed refractive indices correspond to the real ones of ZnS and Misch-Flouride at a wavelength of 500 nm. When dispersion is taken into account, the transmission curve is compressed toward the fixing point at 500 nm (see the solid curve).

Fig. 2
Fig. 2

Example of a chromatic filter.

Fig. 3
Fig. 3

Result of the first Fourier calculation when a material-dependent synthetic dispersion is included, as described in Eqs. (12) and (13). It is seen that the transmission curve is compressed around λ0 as a result of dispersion.

Fig. 4
Fig. 4

New input to the calculation when the described initial correction has been performed upon the desired transmission curve in Fig. 20 = λc = 500 nm).

Fig. 5
Fig. 5

Result of the first Fourier calculation when used upon the corrected desired transmission curve. When comparing Figs. 3 and 5, one sees that it is much more realistic to achieve a good solution by further refinements when the initial correction is used.

Fig. 6
Fig. 6

Theoretically predicted spectral characteristic (dotted curve) and the obtained spectral characteristic (solid curve) of a real GIF. (The surfaces are not antireflection coated.) It is believed that deviations between the predicted and the obtained transmission curve can be reduced by further optimization of the process parameters.

Fig. 7
Fig. 7

Theoretically predicted spectral characteristic (dotted curve) and the obtained spectral characteristic (solid curve) of a real GIF for the linearization of a system containing a halogen lamp and a silicon photodiode. (The surfaces are not antireflection coated.)

Equations (15)

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M = [ cos Φ i sin Φ / n ( x ) i n ( x ) sin Φ cos Φ ] ,
Φ = 2 π / λ O T = 2 π / λ n ( x ) t ( x ) ,
t ( x ) = O T tot / [ ( N - 1 ) n ( x ) ] ,
O T = n ( x ) t ( x ) λ ,
M = [ 1 i 2 π / λ t ( x ) i 2 π / λ n 2 ( x ) t ( x ) 1 ] .
M = [ 1 i 2 π / λ [ t H ( x ) + t L ( x ) ] i 2 π / λ [ n H 2 t H ( x ) + n L 2 t L ( x ) ] 1 ] .
t H ( x ) = n 2 ( x ) - n L 2 n H 2 - n L 2 t ( x ) ,
t L ( x ) = t ( x ) - t H ( x ) .
t H ( x ) = n 2 ( x ) - n L 2 ( λ c ) n H 2 ( λ c ) - n L 2 ( λ c ) t ( x ) ,
t L ( x ) = t ( x ) - t H ( x ) .
n ( x , λ ) = { n H 2 ( λ ) [ t H ( x ) / t ( x ) ] + n L 2 ( λ ) [ t L ( x ) / t ( x ) } 1 / 2 .
n ( x , λ ) = [ A ( x ) n H 2 ( λ ) + [ 1 - A ( x ) ] n L 2 ( λ ) ] 1 / 2 ,
A ( x ) = n 2 ( x ) - n L 2 ( λ c ) n H 2 ( λ c ) - n L 2 ( λ c ) .
λ * λ = n ( λ 0 ) n ( λ ) .
λ * λ = α H L 1 + α H L n H ( λ 0 ) n H ( λ ) + 1 1 + α H L n L ( λ 0 ) n L ( λ ) ,

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