Abstract

An apodized thickness design method for discrete layer notch filters is presented. The method produces error tolerant designs with low ripple in the passband regions without any additional numerical optimization. Several apodization functions including Gaussian, cosine squared, as well as quintic are considered. Theoretical and experimental results from ion beam deposited sample designs for single-notch as well as multinotch filters are presented. Good agreement is observed between the theoretical design and the experimental measurement even when the deposition process is only controlled on time. This demonstrates the low layer error sensitivity of the apodized designs.

© 2013 Optical Society of America

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References

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  1. L. Young, “Multilayer interference filters with narrow stop bands,” Appl. Opt. 6, 297–315 (1967).
    [CrossRef]
  2. A. Thelen, “Design of optical minus filters,” J. Opt. Soc. Am. 61, 365–369 (1971).
    [CrossRef]
  3. W. H. Southwell, “Spectral response calculation of rugate filters using coupled-wave theory,” J. Opt. Soc. Am. A 5, 1558–1564 (1988).
    [CrossRef]
  4. C.-C. Lee, C.-J. Tang, J.-Y. Wu, “Rugate filter made with composite thin films by ion-beam sputtering,” Appl. Opt. 45, 1333–1337 (2006).
    [CrossRef]
  5. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989).
    [CrossRef]
  6. P. W. Baumeister, Optical Coating Technology (SPIE, 2004).
  7. H. A. Macleod, Thin-Film Optical Filters, 4th ed. (CRC Press, 2010).
  8. B. E. Perilloux, Thin-Film Design: Modulated Thickness and Other Stopband Design Methods (SPIE, 2002).

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Figures (11)

Fig. 1.
Fig. 1.

QW thickness of high index and low index layers for a 301 layer Gaussian apodized design with a = 0.1 and FWHM = 215 .

Fig. 2.
Fig. 2.

Modeled transmission and optical density (OD) spectra for the 301 layer design shown in Fig. 1 immersed in fused silica and centered at 532 nm using Ta 2 O 5 / SiO 2 .

Fig. 3.
Fig. 3.

Modeled transmission and OD spectra for a 100 layer design immersed in fused silica with a = 1 and FWHM = 53 centered at 690 nm using Ta 2 O 5 / SiO 2 .

Fig. 4.
Fig. 4.

Optical thickness in QWs for a design with the apodization applied over 101 layers with a = 0.1 and FWHM = 63 . An additional 210 layers with a = 0.1 are inserted in the middle of the design.

Fig. 5.
Fig. 5.

Modeled transmission and OD spectra for the 311 layer design shown in Fig. 4 immersed in fused silica and centered at 532 nm using Ta 2 O 5 / SiO 2 .

Fig. 6.
Fig. 6.

QW thickness of high index and low index layers for a 301 layer Gaussian apodized design with a = 0.1 and FWHM = 215 .

Fig. 7.
Fig. 7.

Modeled transmission and OD spectra for a 301 layer Ta 2 O 5 / SiO 2 design with a = 0.1 and FWHM = 215 centered at 532 nm immersed in fused silica using quintic, cosine-squared, and Gaussian apodization.

Fig. 8.
Fig. 8.

Modeled transmission (solid line) and OD (dashed line) spectra for a 85 layer multinotch design immersed in the high-index material referenced at 464 nm using Gaussian apodization and Ta 2 O 5 / SiO 2 as the coating materials.

Fig. 9.
Fig. 9.

Measured transmission spectrum for a 301 layer 532 nm notch filter. The solid line is measured as an immersed coating, while the dotted line is for a coated sample in air.

Fig. 10.
Fig. 10.

Measured and modeled transmission spectra for a 100 layer design immersed in glass with a = 1 and FWHM = 53 centered at 690 nm using Ta 2 O 5 / SiO 2 .

Fig. 11.
Fig. 11.

Measured (solid line) and modeled (dashed line) transmission spectra for a 92 layer multinotch design referenced at 460 nm using Gaussian apodization and Ta 2 O 5 / SiO 2 as the coating materials.

Equations (12)

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[ a H ( 2 a ) L ] N 1 2 a H ,
T H = a · e [ n N 2 ] 2 / 2 · C 2 ,
T L = 2 T H ( n ) ,
C = FWHM [ 2 · 2 ln ( 2 ) ] .
T H = a [ 10 ( 1 x ) 3 15 ( 1 x ) 4 + 6 ( 1 x ) 5 ] , n N 2 = [ 10 ( 1 + x ) 3 15 ( 1 + x ) 4 + 6 ( 1 + x ) 5 ] , n > N 2 ,
x = C · ( 1 2 n N ) T L = 2 T H ,
C = N 2 · FWHM .
T H = a · cos 2 [ C · ( 1 2 n N ) · π 2 ] ,
T L = 2 T H ,
C = N 2 · FWHM .
{ b L [ 8 b ] H 0.75 b L [ 9 0.75 b ] H } i ,
b = a · e [ n N 2 ] 2 / 2 · C 2 .

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