Abstract

The thermal shift of dense-wavelength-division-multiplexing (DWDM) filters that is caused by nonconstant temperature during fabrication invokes a spectrum shift and an error in the optical thickness of the layer before the matching layer. The relation between the thermal shift and the optical thickness of the layer before the matching layer was calculated. Five kinds of narrow-bandpass filters were fabricated, and their thermal shifts were measured and compared with the theoretical model. By using this technique, we were able to predict the thermal shift of DWDM filters from the abnormal behavior of the layer before the matching layer during deposition.

© 2006 Optical Society of America

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  1. H. A. Macleod, 'Tutorial on the design of telecommunication filters,' presented at the Eighth Optical Interference Coatings Conference, Banff, Alberta, Canada July 15-20, 2001, paper WC1.
  2. C. Grezes-Besset, R. Richier, and E. Pelletier, 'Layer uniformity obtained by vacuum evaporation: application to Fabry-Perot filters,' Appl. Opt. 28, 2960-2964 (1989).
    [CrossRef] [PubMed]
  3. C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).
  4. C. C. Lee and S. H. Chen, 'Influence of deposition parameters for the fabrication of a large area narrow band-pass filter with bandwidth in subnanometer scale,' Vacuum 74, 577-583 (2004).
    [CrossRef]
  5. J. C. Hsu, C. C. Lee, C. C. Kuo, S. H. Chen, J. Y. Wu, H. L. Chen, and C. Y. Wei, 'Coating uniformity improvement for a dense-wavelength-division-multiplexing filter by use of the etching effect,' Appl. Opt. 44, 4402-4407 (2005).
    [CrossRef] [PubMed]
  6. H. Takashashi, 'Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,' Appl. Opt. 34, 667-675 (1995).
    [CrossRef] [PubMed]
  7. E. Drouard, P. Huguet-Chantome, L. Escoubas, and F. Flory, 'delta⁢n/delta⁢T measurements performed with guided waves and their application to the temperature sensitivity of wavelength-division multiplexing filters,' Appl. Opt. 41, 3132-3136 (2002).
    [CrossRef] [PubMed]
  8. S. H. Kim and C. K. Hwangbo, 'Derivation of the center-wavelength shift of narrow-band passfilters under temperature change,' Opt. Express 12, 5634-5639 (2004).
    [CrossRef] [PubMed]
  9. K. Zhang, J. Wang, E. Schwendeman, D. Dawson-Elli, R. Faber, and R. Sharps, 'Group delay and chromatic dispersion of thin-film-based, narrow bandpass filters used in dense wavelength-division-multiplexed systems,' Appl. Opt. 41, 3172-3175 (2002).
    [CrossRef] [PubMed]
  10. P. Bousquet, A. Fornier, R. Kowalczak, E. Pelletier, and P. Roche, 'Optical filters: monitoring process allowing the auto-correction of thickness errors,' Thin Solid Films 13, 285-290 (1972).
    [CrossRef]
  11. H. A. Macleod and E. Pelletier, 'Error compensation mechanisms in some thin-film monitoring systems,' Opt. Acta 24, 907-930 (1977).
    [CrossRef]
  12. Bellcore, 'GR-2883, Generic requirements for fiber optic filters,' Sec. 4.1 Optical Criteria (Bell Communications Research, Inc., 1995).
  13. C.-C. Lee, Thin Film Optics and Coating Technologies, 4th ed. (Yi Hsien Publishing, 2004), Chap. 12.

2005

2004

C. C. Lee and S. H. Chen, 'Influence of deposition parameters for the fabrication of a large area narrow band-pass filter with bandwidth in subnanometer scale,' Vacuum 74, 577-583 (2004).
[CrossRef]

S. H. Kim and C. K. Hwangbo, 'Derivation of the center-wavelength shift of narrow-band passfilters under temperature change,' Opt. Express 12, 5634-5639 (2004).
[CrossRef] [PubMed]

2003

C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).

2002

1995

H. Takashashi, 'Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,' Appl. Opt. 34, 667-675 (1995).
[CrossRef] [PubMed]

Bellcore, 'GR-2883, Generic requirements for fiber optic filters,' Sec. 4.1 Optical Criteria (Bell Communications Research, Inc., 1995).

1989

1977

H. A. Macleod and E. Pelletier, 'Error compensation mechanisms in some thin-film monitoring systems,' Opt. Acta 24, 907-930 (1977).
[CrossRef]

1972

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

Bousquet, P.

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

Chen, H. L.

Chen, S. H.

J. C. Hsu, C. C. Lee, C. C. Kuo, S. H. Chen, J. Y. Wu, H. L. Chen, and C. Y. Wei, 'Coating uniformity improvement for a dense-wavelength-division-multiplexing filter by use of the etching effect,' Appl. Opt. 44, 4402-4407 (2005).
[CrossRef] [PubMed]

C. C. Lee and S. H. Chen, 'Influence of deposition parameters for the fabrication of a large area narrow band-pass filter with bandwidth in subnanometer scale,' Vacuum 74, 577-583 (2004).
[CrossRef]

C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).

Dawson-Elli, D.

Drouard, E.

Escoubas, L.

Faber, R.

Flory, F.

Fornier, A.

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

Grezes-Besset, C.

Hsu, J. C.

J. C. Hsu, C. C. Lee, C. C. Kuo, S. H. Chen, J. Y. Wu, H. L. Chen, and C. Y. Wei, 'Coating uniformity improvement for a dense-wavelength-division-multiplexing filter by use of the etching effect,' Appl. Opt. 44, 4402-4407 (2005).
[CrossRef] [PubMed]

C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).

Huguet-Chantome, P.

Hwangbo, C. K.

Kim, S. H.

Kowalczak, R.

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

Kuo, C. C.

J. C. Hsu, C. C. Lee, C. C. Kuo, S. H. Chen, J. Y. Wu, H. L. Chen, and C. Y. Wei, 'Coating uniformity improvement for a dense-wavelength-division-multiplexing filter by use of the etching effect,' Appl. Opt. 44, 4402-4407 (2005).
[CrossRef] [PubMed]

C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).

Lee, C. C.

J. C. Hsu, C. C. Lee, C. C. Kuo, S. H. Chen, J. Y. Wu, H. L. Chen, and C. Y. Wei, 'Coating uniformity improvement for a dense-wavelength-division-multiplexing filter by use of the etching effect,' Appl. Opt. 44, 4402-4407 (2005).
[CrossRef] [PubMed]

C. C. Lee and S. H. Chen, 'Influence of deposition parameters for the fabrication of a large area narrow band-pass filter with bandwidth in subnanometer scale,' Vacuum 74, 577-583 (2004).
[CrossRef]

C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).

Lee, C.-C.

C.-C. Lee, Thin Film Optics and Coating Technologies, 4th ed. (Yi Hsien Publishing, 2004), Chap. 12.

Macleod, H. A.

H. A. Macleod and E. Pelletier, 'Error compensation mechanisms in some thin-film monitoring systems,' Opt. Acta 24, 907-930 (1977).
[CrossRef]

H. A. Macleod, 'Tutorial on the design of telecommunication filters,' presented at the Eighth Optical Interference Coatings Conference, Banff, Alberta, Canada July 15-20, 2001, paper WC1.

Pelletier, E.

C. Grezes-Besset, R. Richier, and E. Pelletier, 'Layer uniformity obtained by vacuum evaporation: application to Fabry-Perot filters,' Appl. Opt. 28, 2960-2964 (1989).
[CrossRef] [PubMed]

H. A. Macleod and E. Pelletier, 'Error compensation mechanisms in some thin-film monitoring systems,' Opt. Acta 24, 907-930 (1977).
[CrossRef]

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

Richier, R.

Roche, P.

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

Schwendeman, E.

Sharps, R.

Takashashi, H.

Wang, J.

Wei, C. Y.

J. C. Hsu, C. C. Lee, C. C. Kuo, S. H. Chen, J. Y. Wu, H. L. Chen, and C. Y. Wei, 'Coating uniformity improvement for a dense-wavelength-division-multiplexing filter by use of the etching effect,' Appl. Opt. 44, 4402-4407 (2005).
[CrossRef] [PubMed]

C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).

Wu, J. Y.

Zhang, K.

Appl. Opt.

Opt. Acta

H. A. Macleod and E. Pelletier, 'Error compensation mechanisms in some thin-film monitoring systems,' Opt. Acta 24, 907-930 (1977).
[CrossRef]

Opt. Express

Thin Solid Films

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

Vacuum

C. C. Lee and S. H. Chen, 'Influence of deposition parameters for the fabrication of a large area narrow band-pass filter with bandwidth in subnanometer scale,' Vacuum 74, 577-583 (2004).
[CrossRef]

Vacuum Coating Technol. October

C. C. Lee, S. H. Chen, J. C. Hsu, C. C. Kuo, and C. Y. Wei, 'Improving the uniformity of the coating of DWDM filters,' Vacuum Coating Technol. October , 46-51 (2003).

Other

H. A. Macleod, 'Tutorial on the design of telecommunication filters,' presented at the Eighth Optical Interference Coatings Conference, Banff, Alberta, Canada July 15-20, 2001, paper WC1.

Bellcore, 'GR-2883, Generic requirements for fiber optic filters,' Sec. 4.1 Optical Criteria (Bell Communications Research, Inc., 1995).

C.-C. Lee, Thin Film Optics and Coating Technologies, 4th ed. (Yi Hsien Publishing, 2004), Chap. 12.

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Figures (5)

Fig. 1
Fig. 1

Surface temperature curve of the substrate during DWDM filter fabrication, measured by an IR thermal detector aimed at the front of the substrate.

Fig. 2
Fig. 2

Experimental results of the thicknesses of the layers in the first cavity in all five designs.

Fig. 3
Fig. 3

Relation between the abnormal optical thicknesses of the first cavities and the thermal shifts of the filters. Solid line, theoretical prediction; diamonds, experimental results (numbers 1–5 denote the designs).

Fig. 4
Fig. 4

Admittance curves of the first cavity of design 1. Re, real; Im, imaginary.

Fig. 5
Fig. 5

Admittance curves of the abnormal layers and matching layers of design 1 without thermal shift (dashed curve) and with positive thermal shift (solid curve). Re, real; Im, imaginary.

Tables (3)

Tables Icon

Table 1 Calculated Result of the Thermal Shift and the Quarter-Wavelength Optical Thickness of the Abnormal Layer

Tables Icon

Table 2 Design Parameters and Bandwidths of Five Kinds of DWDM Filters and Their Different Spacer Materials, Coating Materials, and Substrates

Tables Icon

Table 3 Abnormal Optical Thicknesses, Predicted Thermal Shifts, and Measured Thermal Shifts of the Five Designs

Equations (16)

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substrate / / [ ( HL ) m ( 2 L ) n H ( LH ) m L ] or  [ ( HL ) m ( 2 H ) n ( LH ) m L ] / / air ,
[ M j ] = [ cos δ j ( i sin δ j ) / n j i n j sin δ j cos δ j ] ,
δ j = 2 π λ n j d j ,
ρ = λ λ j f T j T f .
λ j f = λ ρ ( T j T f ) = λ ρ Δ T j .
δ j = 2 π λ n j d j = 2 π λ j f n j f d j f = π 2 ,
n j f d j f = n j d j ( 1 ρ Δ T j λ ) .
δ j f = 2 π λ n j f d j f = 2 π λ n j d j ( 1 ρ Δ T j λ ) = π 2 π 2 ρ Δ T j λ .
[ M j f ] = [ πρ Δ T j / 2 λ i / n j f i n j f πρ Δ T j / 2 λ ] [ πρ Δ T j / 2 λ i / n 0 i n 0 πρ Δ T j / 2 λ ] .
[ M f ] = [ M 1 ] [ M 2 ] [ M 3 ] [ M i ] = [ M 11 i M 12 i M 21 M 22 ] ,
[ M i ] = [ ε i / n 0 i n 0 ε ] ,
Y = C / B ,
[ B C ] = [ M f ] [ 1 n S ] ,
M 11 M 21 n s     2 M 12 M 22 = 0.
substrate//L [ ( HL ) m −1 ( n H ) ( LH ) m −1 L ] [ ( HL ) m ( n H ) ( LH ) m L ] 3 [ ( HL ) m 1 ( n H ) H ( LH ) m L ] //air, or
substrate//L [ ( HL ) m 1 H ( n L ) H ( LH ) m - 1 L ] [ ( HL ) m H ( n L ) H ( LH ) m L ] 3 [ ( HL ) m 1 H ( n L ) H ( LH ) m 1 L ] //air.

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