Abstract

The use of asymmetrical dual-cavity (ADC) filters with two transmittance peaks is proposed for a simultaneous monitoring of the thickness uniformities of high- and low-index materials. The method described works independently of the manufacturing technique used, and can detect non-uniformities of refractive indices. The properties of these ADC filters are studied using Smith’s concept of effective interfaces, and admittance diagrams. An experimental application of this method is demonstrated, which can be used for increasing the yield of manufactured optical filters.

© 2003 Optical Society of America

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References

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  1. J. A. Dobrowolski, S. Browning, M. Jacobson, and M. Nadal, �??2001 Optical Society of America Topical Meeting on Optical Coatings: Manufacturing Problem,�?? Appl. Opt. 41, 1�??14 (2002).
    [CrossRef]
  2. S. D. Smith, �??Design of Multilayer Filters by Considering Two Effective Interfaces,�?? J. Opt. Soc. Am. 48, 43�??50 (1958).
    [CrossRef]
  3. H. A. Macleod, Thin-film optical filters (Institute of Physics, Bristol, 2001).
    [CrossRef]
  4. D. Poitras, T. Cassidy, and S. Guétré, �??Asymmetrical Dual-Cavity Filters: Theory and Application,�?? in Optical Interference Coatings, OSA Technical Digest, pp. MD3�??1�??3 (Optical Society of America, Washington D.C., 2001).
  5. D. I. Pearson, P. Luff, M. Davis, and A. T. Howe, �??Use of asymmetric dual-cavity filters to track small H and L variations as a tool to increase yield of DWDM filters,�?? in Photonic Integrated Systems, L. A. Eldada, A. R. Pirich, P. L. Repak, R. T. Chen and J. C. Chon, eds., Proc. SPIE 4998, 178�??185 (2003).
    [CrossRef]

Appl. Opt.

J. A. Dobrowolski, S. Browning, M. Jacobson, and M. Nadal, �??2001 Optical Society of America Topical Meeting on Optical Coatings: Manufacturing Problem,�?? Appl. Opt. 41, 1�??14 (2002).
[CrossRef]

J. Opt. Soc. Am.

Optical Interference Coatings 2001

D. Poitras, T. Cassidy, and S. Guétré, �??Asymmetrical Dual-Cavity Filters: Theory and Application,�?? in Optical Interference Coatings, OSA Technical Digest, pp. MD3�??1�??3 (Optical Society of America, Washington D.C., 2001).

Proc. SPIE

D. I. Pearson, P. Luff, M. Davis, and A. T. Howe, �??Use of asymmetric dual-cavity filters to track small H and L variations as a tool to increase yield of DWDM filters,�?? in Photonic Integrated Systems, L. A. Eldada, A. R. Pirich, P. L. Repak, R. T. Chen and J. C. Chon, eds., Proc. SPIE 4998, 178�??185 (2003).
[CrossRef]

Other

H. A. Macleod, Thin-film optical filters (Institute of Physics, Bristol, 2001).
[CrossRef]

Supplementary Material (1)

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Figures (10)

Fig. 1.
Fig. 1.

Demonstration of the effect of having different material thickness uniformities on the spectra of three types of filters: (column 1) Single-cavity Fabry-Perot, (column 2) Bow Lake problem, and (column 3) asymmetrical dual-cavity filter. The spectra in rows a to d correspond to an increase of the discrepancy between low- and high-index materials thickness errors, compared to the design values (see Eq. (2)).

Fig. 2.
Fig. 2.

(a) Schematic representation of Smith’s concept of effective interfaces applied to an ADC filter design. R 1,2(λ), T 1,2(λ) and ϕ 1,2(λ) are the reflectances, transmittances and phase-changes on reflection for the two effective interfaces surrounding a spacer with a thickness of ds =0 (exceptionally) (b) Typical transmission spectrum of an ADC filter with ideal thickness uniformity for both high- and low-index materials. The parameters used in the text for describing the properties of the ADC filters are shown.

Fig. 3.
Fig. 3.

(row a) Variation of T (solid line), TSmith (dotted line, given by Eq. (4)) spectra when multiplying every H- or L-layers by a factor, multH or multL , close to unity (H:TiO2, L:SiO2); (row b) Corresponding phase changes ϕ 1+ϕ 2 (solid line); (row c) Corresponding R 1 and R 2 spectra.

Fig. 4.
Fig. 4.

Dependency of (a) multL/multH relative to Tleft/Tright , and of (b) the total optical thickness OT relative to the central wavelength λcenter .

Fig. 5.
Fig. 5.

Effect of varying the refractive indices on T and TSmith spectra: Variation of (a) the thicknesses, dHdetuned =0.9×dHdesign [identical to Fig. 3(a6)], and (b) the refractive indices, nHdetuned =0.9×nHdesign (in both cases multL/multH =0.9).

Fig. 6.
Fig. 6.

Admittance diagrams of an ADC filter with multH =multL =1. Rows a–c correspond to different wavelengths, identified by dotted lines in the transmittance spectra of column 1. The thin- and thick-lines in the admittance diagrams correspond to H- and Llayers, respectively. The open-circle symbols indicate the admittance values on top of the structures, which are the starting values for the next column’s admittance loci.

Fig. 7.
Fig. 7.

Admittance diagrams of an ADC filter with multH =1/multL =0.98.

Fig. 8.
Fig. 8.

(568 KB) Movie of the variation of transmittance spectra measured at different locations on an ADC filter. The color contour map in (a) shows the variation of λ center along the surface of the filter; the transmittance spectra given in (b) were measured at the positions on the sample indicated by small open squares in (a).

Fig. 9.
Fig. 9.

Example of data extracted from the central position λ center and the peak ratio values measured after a transmittance scan over the length Y of a ADC sample (with X=2.2 cm). The several zones A–F are interpreted in Table 1.

Fig. 10.
Fig. 10.

Calculated multL/multH ratio, total optical thickness, and center peak position (the former two being normalized to the monitoring position value), before and after a uniformity mask iteration.

Tables (1)

Tables Icon

Table 1. Interpretation of the curves shown in Fig. 9.

Equations (5)

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( HL ) a d 2 H ( LH ) b e 2 L ( HL ) c H ,
mult H , L = ( n H , L d H , L ) detuned ( n H , L d H , L ) design ,
ϕ 1 ( λ i ) + ϕ 2 ( λ i ) 2 2 π λ i n s ( λ i ) d s = m π
T Smith ( λ i ) = T 1 ( λ i ) T 2 ( λ i ) [ 1 R 1 ( λ i ) R 2 ( λ i ) ] 2
R ( λ 0 ) = Y ( z , λ 0 ) Y 0 Y ( z , λ 0 ) + Y 0 2 .

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