Abstract

By adjusting the coating parameters to vary the refractive index of the thin film material, we are able to fine tune the bandwidth of a narrow bandpass filter to an arbitrary value. The relation between the varied index Δn and the maximum arbitrary bandwidth was analyzed. A 4-skip-0 bandpass filter for a 100 GHz DWDM system was designed and fabricated. In addition, the relation between the tolerance of the index and the bandwidth was also analyzed to avoid broadening or narrowing the bandwidth. The final results showed that the arbitrary bandwidth met the requirements very well.

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References

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1. C. C. Lee, S. H. Chen, and C. C. Kuo, “Fabrication of dense wavelength division multiplexing filters with large useful area,” Proc. SPIE 6286, 62860E (2006).
[Crossref]
2. H. A. Macleod, “Tutorial on the design of telecommunication filters,” in Conference on Optical Interference Coatings, Technical Digest (CD) (Optical Society of America, 2001) paper PWC1.
3. P. Baumeister, “Bandpass Filters for Wavelength Division Multiplexing-Modification of the Spectral Bandwidth,” Appl. Opt. 37, 6609–6614 (1998).
[Crossref]
4. R R. Willey, “Achieving narrow bandpass filters which meet the requirements for DWDM,” Thin Solid Films 398, 1–9 (2001).
[Crossref]
5. P. Baumeister, “Design of a wavelength-division multiplexing bandpass with quasi-Chebyshev spectral shape,” Appl. Opt. 40, 1132–1137 (2001).
[Crossref]
6. H. A. Macleod, Thin-Film Optical Filters, 3rd Ed., (Institute of Physics Publishing, 2001), Chap. 7.2.2.
[Crossref]

2006 (1)

C. C. Lee, S. H. Chen, and C. C. Kuo, “Fabrication of dense wavelength division multiplexing filters with large useful area,” Proc. SPIE 6286, 62860E (2006).
[Crossref]

2001 (2)

R R. Willey, “Achieving narrow bandpass filters which meet the requirements for DWDM,” Thin Solid Films 398, 1–9 (2001).
[Crossref]

Chen, S. H.

C. C. Lee, S. H. Chen, and C. C. Kuo, “Fabrication of dense wavelength division multiplexing filters with large useful area,” Proc. SPIE 6286, 62860E (2006).
[Crossref]

Kuo, C. C.

C. C. Lee, S. H. Chen, and C. C. Kuo, “Fabrication of dense wavelength division multiplexing filters with large useful area,” Proc. SPIE 6286, 62860E (2006).
[Crossref]

Lee, C. C.

C. C. Lee, S. H. Chen, and C. C. Kuo, “Fabrication of dense wavelength division multiplexing filters with large useful area,” Proc. SPIE 6286, 62860E (2006).
[Crossref]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd Ed., (Institute of Physics Publishing, 2001), Chap. 7.2.2.
[Crossref]

H. A. Macleod, “Tutorial on the design of telecommunication filters,” in Conference on Optical Interference Coatings, Technical Digest (CD) (Optical Society of America, 2001) paper PWC1.

Willey, R R.

R R. Willey, “Achieving narrow bandpass filters which meet the requirements for DWDM,” Thin Solid Films 398, 1–9 (2001).
[Crossref]

Proc. SPIE (1)

C. C. Lee, S. H. Chen, and C. C. Kuo, “Fabrication of dense wavelength division multiplexing filters with large useful area,” Proc. SPIE 6286, 62860E (2006).
[Crossref]

Thin Solid Films (1)

R R. Willey, “Achieving narrow bandpass filters which meet the requirements for DWDM,” Thin Solid Films 398, 1–9 (2001).
[Crossref]

Other (2)

H. A. Macleod, Thin-Film Optical Filters, 3rd Ed., (Institute of Physics Publishing, 2001), Chap. 7.2.2.
[Crossref]

H. A. Macleod, “Tutorial on the design of telecommunication filters,” in Conference on Optical Interference Coatings, Technical Digest (CD) (Optical Society of America, 2001) paper PWC1.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Figures (5)

Fig. 1. Solutions of pass bandwidths for different spacer materials, orders m and x
Fig. 2. Relation between the variation of the index Δn and the maximum arbitrary bandwidth
Fig. 3. Sketch of the 4-skip-0 bandpass filter with 100GHz DWDM filters
Fig. 4 Relation between the Ar flow rate in an ion source and the index of Nb2O5
Fig. 5 Fabrication result for a 4-skip-0 bandpass filter

Tables (1) Table 1. Requirements and designs of a 4-skip-0 bandpass filter

Equations (17)

$T = ( 1 − R a ) ( 1 − R b ) [ 1 − ( R a R b ) 1 2 ] 2 ∙ [ 1 1 + F sin 2 ϕ ] ,$
$BW H ( m , x ) = 1 m ( n L n H ) 2 x 4 n S π n H λ c ( n H − n L n H − n L + n L m ) ( for the high− index spacer ) ,$
$BW L ( m , x ) = 1 m ( n L n H ) 2 x 4 n S π n L λ c ( n H − n L n H − n L + n L m ) ( for the low− index spacer ) ,$
$BW H − ΔH ( m , x ) = BW L ( m , x )$
$BW L − ΔH ( m , x ) = BW H ( m , x − 1 )$
$1 m ( n L n H − ΔH ) 2 x 4 n S π n H − ΔH λ c ( n H−ΔH − n L n H−ΔH − n L + n L m ) = 1 m ( n L n H ) 2 x 4 n S π n L λ c ( n H − n L n H − n L + n L m )$
$1 m ( n L n H − ΔH ) 2 x 4 n S π n L λ c ( n H−ΔH − n L n H−ΔH − n L + n L m ) = 1 m ( n L n H ) 2 x − 2 4 n S π n H λ c ( n H − n L n H − n L + n L m ) .$
$Δn ≈ n H [ 1 − ( n L n H ) 1 2 x + 1 ]$
$Δn ≈ n H [ 1 − ( n L n H ) 1 2 x ] .$
$BW H − ΔH ( m , x ) = BW L ( m , x )$
$BW L − ΔH ( m , x ) = BW H ( m − 1 , x )$
$1 m ( n L n H − ΔH ) 2 x 4 n S π n H − ΔH λ c ( n H−ΔH − n L n H−ΔH − n L + n L m ) = 1 m ( n L n H ) 2 x 4 n S π n L λ c ( n H − n L n H − n L + n L m )$
$1 m ( n L n H − ΔH ) 2 x 4 n S π n L λ c ( n H−ΔH − n L n H−ΔH − n L + n L m ) = 1 m − 1 ( n L n H ) 2 x 4 n S π n H λ c ( n H − n L n H − n L + n L m ) .$
$Δn ≈ n H [ 1 − ( n L n H ) 1 2 x + 1 ]$
$Δn ≈ n H [ 1 − ( m − 1 m ∙ n H n L ) 1 2 x ]$
$BW max ( Δn ) ≈ ( n L n H ) 2 x − 1 4 n S π n H λ c ( n H − n L n H − n L + n L m ) , where x = ln ( n L n H ) 2 ∙ ln ( 1 − Δn n H ) ,$
$BW’ = BW ( 1 + 2 xΔ n H )$
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