Abstract

Dispersion of the phase shift upon reflection of the reflectors is used to narrow the spectral bandwidth of an all-dielectric bandpass filter for wavelength division multiplexing. The bandwidth is altered by the shifting of the order numbers of the spacer layers (of multiple half-wave optical thicknesses).

© 1998 Optical Society of America

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References

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  1. G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.
  2. Ref. 1, p. 258.
  3. An illustration is Fig. 9.07-1 in Ref. 1.
  4. Ref. 1, p. 285.
  5. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).
  6. F. A. Jenkins, P. W. Baumeister, “Dispersion of the phase change for dielectric multilayers—application to the interference filter,” J. Opt. Soc. Am. 47, 57–61 (1957).
    [CrossRef]
  7. P. Baumeister, “Simplified equations for maximally flat all-dielectric bandpass design,” App. Opt. 22, 1960–1961 (1983).
    [CrossRef]
  8. Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif-sur-Yvette, France1992), p. 79.
  9. Ref. 5, p. 41.
  10. P. W. Baumeister, “Bandpass design—applications to nonnormal incidence,” Appl. Opt. 31, 504–512 (1992).
    [CrossRef] [PubMed]
  11. J. Minowa, Y. Fujii, “High performance bandpass filter for WDM transmission,” App. Opt. 23, 193–194 (1984).
    [CrossRef]
  12. L. Young, “Prediction of the absorption loss in multilayer interference filters,” J. Opt. Soc. Am. 51, 753–761 (1961).

1992

1984

J. Minowa, Y. Fujii, “High performance bandpass filter for WDM transmission,” App. Opt. 23, 193–194 (1984).
[CrossRef]

1983

P. Baumeister, “Simplified equations for maximally flat all-dielectric bandpass design,” App. Opt. 22, 1960–1961 (1983).
[CrossRef]

1961

L. Young, “Prediction of the absorption loss in multilayer interference filters,” J. Opt. Soc. Am. 51, 753–761 (1961).

1957

Baumeister, P.

P. Baumeister, “Simplified equations for maximally flat all-dielectric bandpass design,” App. Opt. 22, 1960–1961 (1983).
[CrossRef]

Baumeister, P. W.

Fujii, Y.

J. Minowa, Y. Fujii, “High performance bandpass filter for WDM transmission,” App. Opt. 23, 193–194 (1984).
[CrossRef]

Furman, Sh. A.

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif-sur-Yvette, France1992), p. 79.

Jenkins, F. A.

Jones, E. M. T.

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

Matthaei, G.

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

Minowa, J.

J. Minowa, Y. Fujii, “High performance bandpass filter for WDM transmission,” App. Opt. 23, 193–194 (1984).
[CrossRef]

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).

Tikhonravov, A. V.

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif-sur-Yvette, France1992), p. 79.

Young, L.

L. Young, “Prediction of the absorption loss in multilayer interference filters,” J. Opt. Soc. Am. 51, 753–761 (1961).

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

App. Opt.

P. Baumeister, “Simplified equations for maximally flat all-dielectric bandpass design,” App. Opt. 22, 1960–1961 (1983).
[CrossRef]

J. Minowa, Y. Fujii, “High performance bandpass filter for WDM transmission,” App. Opt. 23, 193–194 (1984).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

F. A. Jenkins, P. W. Baumeister, “Dispersion of the phase change for dielectric multilayers—application to the interference filter,” J. Opt. Soc. Am. 47, 57–61 (1957).
[CrossRef]

L. Young, “Prediction of the absorption loss in multilayer interference filters,” J. Opt. Soc. Am. 51, 753–761 (1961).

Other

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, Gif-sur-Yvette, France1992), p. 79.

Ref. 5, p. 41.

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

Ref. 1, p. 258.

An illustration is Fig. 9.07-1 in Ref. 1.

Ref. 1, p. 285.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).

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Figures (13)

Fig. 1
Fig. 1

Spectral transmittance of a three-cavity BP (dashed curve), glass 0.257H 0.47L 0.257H L (H L)2 H 3L 3H L L 3H (L H)7 L H L L H L H (L H)6 L 3H L L 3H 3L H L H L 0.327L 0.332H 0.327L air, and a six-cavity bandpass (solid curve), glass H L 0.174L 0.638H 0.174L L H 16L H (L H)5 16L (H L)3 0.16L 0.666H 0.16L (L H)3 16L H (L H)6 16L (H L)3 0.16L 0.666H 0.16L (L H)3 16L H (L H)5 16L H L 0.411L 0.170H 0.411L L H air, where the refractive indices of glass, L, and H are 1.51, 1.46, and 2.02, respectively. The optical thickness of L and H is λ0/4 at λ0 of 1.552 μm. The scale of the ordinate changes from linear to log at 0.40.

Fig. 2
Fig. 2

Shape factors (defined in the text) of BP’s whose spectral transmittances are given by Eq. (2), with F ≫ 1.

Fig. 3
Fig. 3

Construction of a four-cavity BP consisting of five reflectors and four spacers, showing the incident medium (Incdt) and emergent medium (Sub).

Fig. 4
Fig. 4

Radiant reflectance R 0 of the outer reflector is measured by considering the incident medium as a pseudosubstrate and the contiguous spacer as a pseudoincident medium.

Fig. 5
Fig. 5

Radiant reflectance R 1 of an inner reflector is measured by considering one of the contiguous spacers as a pseudosubstrate and the other contiguous spacer as a pseudoincident medium.

Fig. 6
Fig. 6

Phase shift on reflection versus wavelength of the stack (solid curve): incident (H L)5 F air, and (dashed curve): incident 3H 3L (H L)4 F air, where H, F, and L represent layers of optical thickness λ0/4 at λ0 of 1552 nm. The refractive indices of incident, H, F, L, and air are 1.46, 2.02, 1.67, 1.46, and 1.0003, respectively.

Fig. 7
Fig. 7

Spectral transmittance of a bandpass of the design: air 0.360L 0.268H 1.360L H (L H)3 L H 2L H L (H L)4 H 1.313L 0.358H 1.313L H (L H)5 L H 2L H L (H L)12 H L H 2L H L (H L)4 H 1.313L 0.358H 1.313L H (L H)5 L H 2L H L (H L)3 H 1.451L 0.563H 0.902L 0.563H 0.451L glass, where H and L represent layers of optical thickness λ0/4 at λ0 of 1552 nm. The refractive indices of glass, L, and H are 1.50, 1.46, and 2.02, respectively. The scale of the ordinate changes from linear to log at 0.80.

Fig. 8
Fig. 8

Spectral transmittance (on an absorbance scale) of (dotted- dashed curve): air 0.360L 0.268H 1.360L H (L H)3 L′ H′ 2L H′ L′ (H L)4 H 1.313L 0.358H 1.313L H (L H)5 L′ H′ 2L H′ L′ (H L)12 H L′ H′ 2L H′ L′ (H L)4 H 1.313L 0.358H 1.313L H (L H)5 L′ H′ 2L H′ L′ (H L)3 H 1.451L 0.563H 0.902L 0.563H 0.451L glass, where H, H′, L, and L′ represent layers of optical thickness λ0/4 at λ0 of 1552 nm. The refractive indices of glass, H, H′, L, and L′ are 1.50, 2.02, 2.02, 1.46, and 1.46, respectively. Each H′ layer is replaced with 3H (solid curve). Each 2L layer is replaced with 6L (dashed curve).

Fig. 9
Fig. 9

Spectral transmittance (on an absorbance scale) of air 0.360L 0.268H 1.360L H (L H)3 L′ H′ 2L H′ L′ (H L)4 H 1.313L 0.358H 1.313L H (L H)5 L′ H′ 2L H′ L′ (H L)12 H L′ H′ 2L H′ L′ (H L)4 H 1.313L 0.358H 1.313L H (L H)5 L′ H′ 2L H′ L′ (H L)3 H 1.451L 0.563H 0.902L 0.563H 0.451L glass, where H, H′, L, and L′ represent layers of optical thickness λ0/4 at λ0 of 1552 nm. The refractive indices of glass, H, H′, L, and L′ are 1.50, 2.02, 2.02, 1.46, and 1.46, respectively. Each H′ layer is replaced with 3H (solid curve). Each H′ and L′ layer is replaced with 3H and 3L, respectively (dashed curve). Each 2L layer is replaced with 10L (dotted-dashed curve).

Fig. 10
Fig. 10

Spectral transmittance of a six-cavity bandpass: glass H L 0.174L 0.638H 0.174L L H 22L H (L H)5 10L (H L)3 0.16L 0.666H 0.16L (L H)3 16L H (L H)6 16L (H L)3 0.16L 0.666H 0.16L (L H)3 10L H (L H)5 22L H L 0.411L 0.170H 0.411L L H air, where H and L represent layers of optical thickness λ0/4 at λ0 of 1552 nm. The refractive indices of glass, H, and L are 1.51, 2.02, and 1.46, respectively.

Fig. 11
Fig. 11

Spectral transmittance of a six-cavity BP (solid curve): glass H L 0.174L 0.638H 0.174L L H 16L H (L H)5 16L (H L)3 0.16L 0.666H 0.16L (L H)3 16L H (L H)6 16L (H L)3 0.16L 0.666H 0.16L (L H)3 16L H (L H)5 16L H L 0.411L 0.170H 0.411L L H air, and (dashed curve): glass H L H 22L (H L)2 0.327L 0.332H 0.327L L (H L)2 H 10L (H L)3 H L (H L)2 H 16L (H L)3 0.188L 0.608H 0.188L L (H L)2 H 16L (H L)3 1.461H 0.073L 1.461H L (H L)2 H 10L (H L)2 0.271L 0.442H 0.271L L (H L)2 H 22L H 0.313L 0.358H 0.313L H air, where H and L represent layers of optical thickness λ0/4 at λ0 of 1552 nm. The refractive indices of glass, H, and L are 1.51, 2.02, and 1,46, respectively. The scale of the ordinate changes from linear to log at 0.10.

Fig. 12
Fig. 12

Spectral transmittance of a five-cavity BP with spacers of unequal order (solid curve): glass H L H 2L H L H L H L H 4L H L H L H L H 6L H L H L H L H 4L H L H L H L H 2L H L H glass, and a five-cavity BP with spacers of equal order (dashed curve): glass H L H 6L H L H L H L H 6L H L H L H L H 6L H L H L H L H 6L H L H L H L H 6L H L H glass, where H and L represent layers of optical thickness λ0/4 at λ0 of 1330 nm. The refractive indices of glass, H, and L are 1.51, 2.20, and 1.45, respectively.

Fig. 13
Fig. 13

Spectral transmittance of a five-cavity BP (solid curve): glass 0.306L 0.364H 0.306L L H 6L H L H 0.396H 0.192L 0.396H H L H 6L H L H 0.118H 0.746L 0.118H H L H 6L H L H 0.118H 0.746L 0.118H H L H 6L H L H 0.396H 0.192L 0.396H H L H 6L H L 0.306L 0.364H 0.306L glass, and (dashed curve): glass H L H 2L H L H L H L H 4L H L H L H L H 6L H L H L H L H 4L H L H L H L H 2L H L H glass, where H and L represent layers of optical thickness λ0/4 and λ0 of 1330 nm. The refractive indices of glass, H, and L are 1.51, 2.20, and 1.45, respectively. The scale of the ordinate changes from linear to log at 0.80.

Equations (17)

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S 3 Δ λ 3 / B W ,
T β = 1 + F   sin 2 q β - 1 ,
β = 2 π nh / λ ,
incident   H   L 5   F   air ,
incident   3 H   3 L   H   L 4   F   air .
V 0 = V 4     0.682   10 0.1225 η ,
V 1 = V 3     10 0.250 η ,
V 2     2.147   10 0.255 η ,
incident   H   L 14   H   emergent
V 2 = n H 30 n L - 30 = 2.02 30 1.46 - 30 = 16901 ,
incident   H   L 13   F   emergent ,   or
incident   H   L 6   F   L   H   L 6   H   emergent .
V 1 = V 3 = n H 26 n L - 28 n F 2 = 2.02 26 1.46 - 28 1.743 2 = 6605
incident   H   L 5   E   emergent
V 0 = n H 10 n L - 11 n E 2 = 2.02 10 1.46 - 11 1.69 2 = 50.3 .
incident   H   L 5   G   substrate ,
V 4 = n H 10 n L - 11 n G 2 n s - 1 = 2.02 10 1.46 - 11 2.08 2 1.50 - 1 = 50.8 .

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