Abstract

An automated approach to the design of wavelength-division multiplexing (WDM) filters is based on the combination of ideas from classical design approaches with an integer optimization technique. This approach turns out to be extremely efficient from a computational point of view and makes it possible to construct a set of significantly different filter designs with nearly equivalent spectral properties. The sensitivity of WDM filters is analyzed by a computer simulation of the deposition process with turning-point optical monitoring. This analysis enables the designer to compare feasibility properties of various filter designs.

© 2002 Optical Society of America

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References

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  1. H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 19, 1–28 (1972).
    [CrossRef]
  2. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
    [CrossRef]
  3. S. A. Furman, Thin-Film Optical Coatings (Mashinosroenie, Leningrad, 1977) (in Russian).
  4. S. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).
  5. A. V. Tikhonravov, M. K. Trubetskov, G. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
    [CrossRef] [PubMed]
  6. G. Mathaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964).
  7. P. Baumeister, “Design of a WDM bandpass with quasi-Chebyshev spectral shape,” Appl. Opt. 40, 1132–1137 (2001).
    [CrossRef]
  8. A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1538 (1966).
    [CrossRef]
  9. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988).
  10. P. Baumeister, Optical Coating Technology (1998), book used at a five-day short course, Engineering 823.17, University of California at Los Angeles, Department of Engineering, Information Systems and Technical Management, 12–16 January, 1998.
  11. M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Applied Mathematics Series 55 (National Bureau of Standards, Gaithersburg, Md., 1964).
  12. I. V. Sergienko, Mathematical Models and Methods for Solution of Discrete Optimization Problems (Naukova Dumka, Kiev, 1988) (in Russian).
  13. A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston-Wiley, New York, 1977).

2001 (1)

1996 (1)

1972 (2)

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 19, 1–28 (1972).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

1966 (1)

Arsenin, V. Y.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston-Wiley, New York, 1977).

Baumeister, P.

P. Baumeister, “Design of a WDM bandpass with quasi-Chebyshev spectral shape,” Appl. Opt. 40, 1132–1137 (2001).
[CrossRef]

P. Baumeister, Optical Coating Technology (1998), book used at a five-day short course, Engineering 823.17, University of California at Los Angeles, Department of Engineering, Information Systems and Technical Management, 12–16 January, 1998.

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

DeBell, G.

Fornier, A.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Furman, S.

S. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

Furman, S. A.

S. A. Furman, Thin-Film Optical Coatings (Mashinosroenie, Leningrad, 1977) (in Russian).

Jones, E. M. T.

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

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Macleod, H. A.

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 19, 1–28 (1972).
[CrossRef]

Mathaei, G.

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

Pelletier, E.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Roche, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Sergienko, I. V.

I. V. Sergienko, Mathematical Models and Methods for Solution of Discrete Optimization Problems (Naukova Dumka, Kiev, 1988) (in Russian).

Thelen, A.

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

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

Tikhonov, A. N.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston-Wiley, New York, 1977).

Tikhonravov, A. V.

Trubetskov, M. K.

Young, L.

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

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 19, 1–28 (1972).
[CrossRef]

Thin Solid Films (1)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, “Optical filters: monitoring process allowing the auto-correction of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Other (8)

S. A. Furman, Thin-Film Optical Coatings (Mashinosroenie, Leningrad, 1977) (in Russian).

S. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

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

P. Baumeister, Optical Coating Technology (1998), book used at a five-day short course, Engineering 823.17, University of California at Los Angeles, Department of Engineering, Information Systems and Technical Management, 12–16 January, 1998.

M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Applied Mathematics Series 55 (National Bureau of Standards, Gaithersburg, Md., 1964).

I. V. Sergienko, Mathematical Models and Methods for Solution of Discrete Optimization Problems (Naukova Dumka, Kiev, 1988) (in Russian).

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston-Wiley, New York, 1977).

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

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Figures (6)

Fig. 1
Fig. 1

General schematic of WDM filters: M 1, M 2, … are multilayer mirrors; S 1, S 2, … are spacer layers.

Fig. 2
Fig. 2

Typical WDM filter specifications: λ0 is the filter central wavelength, Δλ p is the bandwidth at the transmittance level of 89.12% (-0.5 dB), Δλ r is the bandwidth at the transmittance level of 0.1% (-30 dB).

Fig. 3
Fig. 3

Transmittances of three filter prototypes with different spacer orders and numbers of mirror layers.

Fig. 4
Fig. 4

Transmittances of three filters obtained by use of the prototypes with transmittances shown in Fig. 2. (Transmittances of Filters 2 and 3 are very close).

Fig. 5
Fig. 5

Transmittance of filter 1 from Table 1 (solid curve); transmittance of this filter with +5% thickness error in layer 13 (dotted curve); and transmittance of this filter with +5% thickness error in layer 13 compensated by -2% thickness error in layer 16 and -2.1% thickness error in layer 17 (dashed curve): the nearby spacer layer is layer 15.

Fig. 6
Fig. 6

Bars representing relative sensitivities of WDM filter spectral properties to the errors in thicknesses of individual filter layers for filter 3 from Table 1; arrows mark spacer layers.

Tables (2)

Tables Icon

Table 1 Parameters of Three Filter Prototypes and Three Final Designsa

Tables Icon

Table 2 Simulated Production Yields (%) for the Three WDM Filters from Table 1

Equations (21)

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ϕλ=ϕlλ+ϕrλ-2πsλ0/λ.
Tλ=1+ρTq2η cosπ2λ0λ-1.
η cosπ2λ0λ0±Δλp/2=±1.
πηΔλp/4λ0 =1.
1+ρ-1=0.8913
ρTq2η cosπ2λ0λ0+Δλr/2  103.
η cosπ2λ0λ0+Δλr/2  πηΔλr4λ0.
S=Δλr/Δλp.
TqS  100.
ns | Equiv. layer 1 | Equiv. layer 2 |  | Equiv. layer 2 | Equiv. layer 1 | ns.
N12=nsN2.
ϕlλ0+ϕrλ0-4πnd/λ0=0mod 2π
Fj=i=j-kjTi-ati-b2,
a=2T/d2r2,
at+bj=0
T0s=1, T1s=s.
Tjs=2sTj-1s-Tj-2s.
T0=1.0,T1=1.714286,T2=4.877553,T3=15.00876,T4=46.58105,T5=144.69771.
T=TlTr1+RlRr-2RlRrcosϕl+ϕr-4πnd/λ.
T=TlTr1-RlRr2+4RlRrsin2ϕλ0/2,
ϕλ0=ϕlλ0+ϕrλ0-4πnd/λ0.

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