Abstract

For costly optical coatings, a precise monitoring method is necessary. A new monitoring method based on the selection of the most sensitive monitor wavelength is proposed. The most sensitive monitor wavelength is easy to find by a numerical analysis. The equation for the thickness compensation when a layer is over-shot or under-shot was derived. Several examples, including narrow-band pass filters, have been given to demonstrate that this new method is superior to the turning point method in the coating process.

© 2005 Optical Society of America

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References

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  1. H. A. Macleod, �??Monitoring of optical coatings,�?? Appl. Opt. 20, 82-89 (1981)
    [CrossRef] [PubMed]
  2. Cheng Zang, Yongtain Wang, and Weiqiang Lu, �??A single-wavelength monitoring method for optical thin-film coatings,�?? Opt. Eng. 43, 1439-1443 (2004).
    [CrossRef]
  3. B. Vidal, A. Fornier and E Pelletier, �??Wideband optical monitoring of nonquarter wave multilayer filter�??, Appl. Opt. 18, 3851-3856 (1979).
    [PubMed]
  4. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IoP, Bristal, 2001).
    [CrossRef]
  5. Y. R. Chen, Monitoring of film growth by admittance diagram, Master Thesis of the National Central University, Taiwan (2004).
  6. H. A. Macleod and E Pelletier, �??Error compensation mechanisms in some thin film monitoring systems,�?? Opt. Acta 24, 907-930 (1977)
    [CrossRef]
  7. H. A. Macleod, �??Turning value monitoring of narrow-band all-dielectric thin-film optical filters,�?? Opt. Acta, 19, 1-28 (1972).
    [CrossRef]

Appl. Opt. (2)

Opt. Acta (2)

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, �??Turning value monitoring of narrow-band all-dielectric thin-film optical filters,�?? Opt. Acta, 19, 1-28 (1972).
[CrossRef]

Opt. Eng. (1)

Cheng Zang, Yongtain Wang, and Weiqiang Lu, �??A single-wavelength monitoring method for optical thin-film coatings,�?? Opt. Eng. 43, 1439-1443 (2004).
[CrossRef]

Other (2)

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (IoP, Bristal, 2001).
[CrossRef]

Y. R. Chen, Monitoring of film growth by admittance diagram, Master Thesis of the National Central University, Taiwan (2004).

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Figures (12)

Fig. 1.
Fig. 1.

Sensitivity of reference wavelength at different high refractive index layer “H”.

Fig. 2.
Fig. 2.

Sensitivity of monitor wavelengths on cutting points in high refractive index layer “H”.

Fig. 3.
Fig. 3.

Sensitivity of monitor wavelengths on cutting points for low refractive index layer “L”.

Fig. 4.
Fig. 4.

Comparison of the sensitivity of the cutting point in the seventh layer: dark line, each layer in quarter-wave stack; grey line, each layer not in exact quarter-wave stack.

Fig. 5.
Fig. 5.

Comparison of the sensitivity on the cutting point in the seventh layer: dark line, nH=2.3; grey line, nH=2.25.

Fig. 6.
Fig. 6.

Admittance loci of 1550nm of the first two layers.

Fig. 7.
Fig. 7.

Admittance loci of 1194nm of the first two layers.

Fig. 8.
Fig. 8.

Spectrum of reflectors monitored by different methods with a 1 % standard deviation error.

Fig. 9.
Fig. 9.

Comparison of 1-cavity narrow-band pass filter performance between two monitoring methods.

Fig. 10.
Fig. 10.

Comparison of 2-cavity narrow-band pass filter performance between two monitoring methods.

Fig. 11.
Fig. 11.

Comparison of 3-cavity narrow-band pass filter performance between two monitoring methods.

Fig. 12.
Fig. 12.

The first, second and third cavities of the filters monitored by turning point method shown in Fig. 10 and Fig. 11.

Tables (1)

Tables Icon

Table 1. Result optical thickness of the filters monitored by two methods under a 0.3% standard deviation of transmittance error and the monitor wavelength used by the SSMW method

Equations (17)

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[ B ' C ' ] = [ cos δ i n sin δ in sin δ cos δ ] [ 1 n E ]
T = 4 Re ( n E ) ( B + C ) ( B + C ) * = 4 Re ( n E ) ( cos δ + in sin δ + i n E n sin δ + n E cos δ ) ( cos δ + in sin δ + i n E n sin δ + n E cos δ ) *
Sensitivity = Δ T Δ nd = π T 2 χ λ Re ( n E )
χ = { [ 1 + Re ( n E ) ] sin δ + Im ( n E n ) cos δ } { [ 1 + Re ( n E ) ] cos δ Im ( n E n ) sin δ }
{ [ n + Re ( n E n ) ] cos δ Im ( n E ) sin δ } { [ n + Re ( n E n ) ] sin δ + Im ( n E ) cos δ }
Y = { ( 1 + R ) ( 1 R ) ( The valley point of the transmittance curve in runsheet ) ( 1 R ) ( 1 + R ) ( The peak point of the transmittance curve in runsheet )
[ B C ] = [ cos δ B i sin δ B n B in B sin δ B cos δ B ] [ cos δ A i sin δ A n A in A sin δ A cos δ A ] [ 1 n ]
Y = C B = n ( cos δ A cos δ B n B n A sin δ A sin δ B ) + i ( n A sin δ A sin δ B + n B cos δ A sin δ B ) ( cos δ A cos δ B n A n B sin δ A sin δ B ) + in ( sin δ A cos δ B n A + cos δ A sin δ B n B )
Im { Y } = ( cos δ A cos δ B n A n B sin δ A sin δ B ) ( n B cos δ A sin δ A + n A sin δ A cos δ B )
n 2 ( cos δ B cos δ A n B n A sin δ A sin δ B ) ( sin δ A cos δ B n A + cos δ A sin δ B n B ) = 0
Re { Y } =
[ n ( cos 2 δ A cos 2 δ B + sin 2 δ A sin 2 δ B { n B n A + n A n B } cos δ A sin δ A cos δ B sin δ B ) +
n ( { n B n A + n A n B } cos δ A sin δ A cos δ B sin δ B + cos 2 δ A sin 2 δ B + sin 2 δ A cos 2 δ B ) ] ÷
[ ( cos δ A cos δ B n A n B sin δ A sin δ B ) 2 + n 2 ( sin δ A cos δ B n A + sin δ B cos δ A n B ) 2 ]
n sin δ c cos δ c β sin 2 δ c + β cos 2 δ c β 2 n sin δ c cos δ c α 2 sin δ c cos δ c n = 0
δ c = tan 1 ( 1 2 β n ( n 2 β 2 α 2 ± ( n 4 + 2 β 2 n 2 2 n 2 α 2 + β 4 + 2 β 2 α 2 + α 4 ) 1 2 ) )
δ B = tan 1 ( ± n B ( ( Y n A 2 n B 2 n A 2 α Y 2 n B 4 α + Y β 2 n B 2 + Y β 2 n B 2 ) ( α n B 2 + Y n A 2 + Y α 2 + Y β 2 α Y 2 ) ) 1 2 ( Y n A 2 n B 2 n A 2 α Y 2 n B 4 α + Y β 2 n B 2 + Y α 2 n B 2 ) )

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