Abstract

A starting design for a prototype bandpass is modeled as a periodic structure, following the teachings of Thelen. A sample prototype bandpass contains twenty-one cavities and, after computer optimization, manifests a quasi-Chebyshev transmissive response in its passband. When the prototype is converted to a thin film multilayer bandpass, its spectral bandwidth is 12.70 nm at the -0.5 dB transmittance level and 12.99 nm at the -25 dB level.

© 2001 Optical Society of America

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References

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  1. Philip Baumeister, “Transmissive spectral slope of a bandpass for WDM,” post-deadline paper TuB8 presented at the Topical Meeting on Optical Interference Coatings under the auspices of the Optical Society of America, July 17, 2001.
  2. George Matthaei, Leo Young, and E. M. T. Jones, Microwave filters, impedance matching networks, and coupling structures (McGraw-Hill, New York, 1964) §6.03.
  3. A. J. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1538 (1966).
    [CrossRef]
  4. A. J. Thelen, Design of optical interference coatings (McGraw-Hill, New York, 1989).
  5. H. A. Macleod, Thin film optical filters (Macmillan, New York, 1986).
    [CrossRef]
  6. Sh. A. Furman and A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif -sur-Yvette, France1992).
  7. Philip Baumeister, “Bandpass filters for wavelength division multiplexing—modification of the spectral bandwidth,” Appl. Opt. 37, 6609–6614 (1998).
    [CrossRef]
  8. TFCalc, An optical coating design code marketed by Software Spectra, Portland, Oregon, USA.
  9. Florin Abelès, “Remarque sur l’influence de la dispersion dans les systèm de couches minces diélectriques,” J. Phys. Radium 1 9, 327–334 (1958).
    [CrossRef]
  10. Francis Jenkins and Philip Baumeister, “Dispersion of the phase change for dielectric multilayers—application to the interference filter,” J. Opt. Soc. Am. 47, 57–61 (1957).
    [CrossRef]

1998 (1)

1966 (1)

1958 (1)

Florin Abelès, “Remarque sur l’influence de la dispersion dans les systèm de couches minces diélectriques,” J. Phys. Radium 1 9, 327–334 (1958).
[CrossRef]

1957 (1)

Abelès, Florin

Florin Abelès, “Remarque sur l’influence de la dispersion dans les systèm de couches minces diélectriques,” J. Phys. Radium 1 9, 327–334 (1958).
[CrossRef]

Baumeister, Philip

Furman, Sh. A.

Sh. A. Furman and A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif -sur-Yvette, France1992).

Jenkins, Francis

Jones, E. M. T.

George Matthaei, Leo Young, and E. M. T. Jones, Microwave filters, impedance matching networks, and coupling structures (McGraw-Hill, New York, 1964) §6.03.

Macleod, H. A.

H. A. Macleod, Thin film optical filters (Macmillan, New York, 1986).
[CrossRef]

Matthaei, George

George Matthaei, Leo Young, and E. M. T. Jones, Microwave filters, impedance matching networks, and coupling structures (McGraw-Hill, New York, 1964) §6.03.

Thelen, A. J.

A. J. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1538 (1966).
[CrossRef]

A. J. Thelen, Design of optical interference coatings (McGraw-Hill, New York, 1989).

Tikhonravov, A. V.

Sh. A. Furman and A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif -sur-Yvette, France1992).

Young, Leo

George Matthaei, Leo Young, and E. M. T. Jones, Microwave filters, impedance matching networks, and coupling structures (McGraw-Hill, New York, 1964) §6.03.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Phys. Radium (1)

Florin Abelès, “Remarque sur l’influence de la dispersion dans les systèm de couches minces diélectriques,” J. Phys. Radium 1 9, 327–334 (1958).
[CrossRef]

Other (6)

A. J. Thelen, Design of optical interference coatings (McGraw-Hill, New York, 1989).

H. A. Macleod, Thin film optical filters (Macmillan, New York, 1986).
[CrossRef]

Sh. A. Furman and A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif -sur-Yvette, France1992).

TFCalc, An optical coating design code marketed by Software Spectra, Portland, Oregon, USA.

Philip Baumeister, “Transmissive spectral slope of a bandpass for WDM,” post-deadline paper TuB8 presented at the Topical Meeting on Optical Interference Coatings under the auspices of the Optical Society of America, July 17, 2001.

George Matthaei, Leo Young, and E. M. T. Jones, Microwave filters, impedance matching networks, and coupling structures (McGraw-Hill, New York, 1964) §6.03.

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Figures (5)

Fig. 1.
Fig. 1.

Versus optical thickness in waves, refractive index (on log scale) of a starting design for a prototype bandpass. The antireflection layers are arrowed.

Fig. 2.
Fig. 2.

Versus normalized frequency, transmittance of the prototype bandpass whose design appears in Fig. 1. At a frequency of 2.0, each layer is a halfwave in optical thickness.

Fig. 3.
Fig. 3.

Versus normalized frequency, transmittance of design air A B C D E F G H J K L K J H G F E D C B A air, where the refractive indices of A, B, C, D, E, F, G, H, J, K and L are 0.05775, 32.935, 0.02422, 41.093, 0.02223, 42.815, 0.02174, 43.375, 0.02157, 43.568 and 0.02153, respectively. At a frequency of 2.0, each layer is a halfwave in optical thickness.

Fig. 4.
Fig. 4.

Versus optical thickness in waves, refractive index (on log scale) of an optimized design for a prototype bandpass. Its design is captioned in Fig. 3.

Fig. 5.
Fig. 5.

Transmittance of the coating described in the section “Twenty-one cavity bandpass design.” The scale of the ordinate changes from linear to log at 0.9.

Equations (9)

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V = 1 + R 1 R
f 1 = 1 + 2 π arcsin ( V 1 V + 1 )
BW = ( 2 f 1 ) = 1 2 π arcsin ( V 1 V + 1 ) .
V = 1 + cos ( π 2 BW ) 1 cos ( π 2 BW ) .
V = 17.3 = n E 2 n L 7 n H 6 ( 1.00 3 ) 1 .
V = 570 = n E 2 n L 18 n H 20 .
d δ d σ π λ 0 n 0 n H n L
Δ σ = F ( R ) ( π λ 0 d δ / ) 1
Δσ = F ( R ) ( π λ 0 ) 1 [ 1 + n L / ( n H n L ) 1 .

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