Abstract

We proposed an analytical method to design optical minus filters by the thickness modulation of discrete, homogeneous thin-film layers of a two-material multilayer coating. The main stack provides the narrow, second-order rejection band, and the correct thickness–modulation apodization and match layers can effectively suppress the sidelobes of the passband. Using this approach, we can design minus filters with layer thicknesses close to half-wave of the rejection wavelength, making this method well suited for accurate monitoring during the deposition.

© 2013 Optical Society of America

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References

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  1. J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, vol. IV (McGraw-Hill, 2010), pp. 7.15–7.53.
  2. B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990).
    [CrossRef]
  3. W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949–2951(1989).
    [CrossRef]
  4. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989).
    [CrossRef]
  5. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Wilbrandt, and D. Gabler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515–1524 (2006).
    [CrossRef]
  6. X. Cheng, B. Fan, J. A. Dobrowolski, L. Wang, and Z. Wang, “Gradient-index optical filter synthesis with controllable and predictable refractive index profiles,” Opt. Express 16, 2315–2321 (2008).
    [CrossRef]
  7. M. Lappschies, B. Gortz, and D. Ristau, “Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering,” Appl. Opt. 45, 1502–1506 (2006).
    [CrossRef]
  8. C. Lee, C. Tang, and J. Wu, “Rugate filter made with composite thin films by ion-beam sputtering,” Appl. Opt. 45, 1333–1337 (2006).
    [CrossRef]
  9. J. Zhang, M. Fang, Y. Jin, and H. He, “Narrow line-width filters based on rugate structure and antireflection coating,” Thin Solid Films 520, 5447–5450 (2012).
    [CrossRef]
  10. A. Thelen, “Design of optical minus filter,” J. Opt. Soc. Am. 61, 365–369 (1971).
    [CrossRef]
  11. L. Young, “Multilayer interference filters with narrow stop bands,” Appl. Opt. 6, 297–315 (1967).
    [CrossRef]
  12. V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: two-material technology versus rugate,” Appl. Opt. 46, 1190–1193 (2007).
    [CrossRef]
  13. U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturing of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
    [CrossRef]
  14. T. I. Oh, “Infrared minus-filter coatings: design and production,” Appl. Opt. 30, 4565–4573 (1991).
    [CrossRef]
  15. T. V. Amotchkina, “Analytical estimations for the reflectance wavelength reflectance and width of high-reflection zone of two-material periodic multilayers,” Appl. Opt. 52, 4590–4595 (2013).
    [CrossRef]
  16. B. H. Ibrahim, R. Botha, J. E. Bouree, P. Bulkin, and B. Drevillon, “Correlation of sidelobe suppression between rugate filters and multilayer mirrors,” Appl. Opt. 46, 7776–7779 (2007).
    [CrossRef]
  17. B. E. Perilloux, “Discrete thin-film layer thickness modulation,” Appl. Opt. 37, 3527–3532 (1998).
    [CrossRef]
  18. A. V. Tikhonravov and M. K. Trubetskov, Optilayer Thin Film Software, http://www.optilayer.com .

2013 (1)

2012 (1)

J. Zhang, M. Fang, Y. Jin, and H. He, “Narrow line-width filters based on rugate structure and antireflection coating,” Thin Solid Films 520, 5447–5450 (2012).
[CrossRef]

2010 (1)

U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturing of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
[CrossRef]

2008 (1)

2007 (2)

2006 (3)

1998 (1)

1991 (1)

1990 (1)

1989 (2)

1971 (1)

1967 (1)

Amotchkina, T. V.

Apolonski, A.

Botha, R.

Bouree, J. E.

Bovard, B. G.

Bulkin, P.

Cheng, X.

Dobrowolski, J. A.

Drevillon, B.

Fan, B.

Fang, M.

J. Zhang, M. Fang, Y. Jin, and H. He, “Narrow line-width filters based on rugate structure and antireflection coating,” Thin Solid Films 520, 5447–5450 (2012).
[CrossRef]

Gabler, D.

Gortz, B.

Hall, R. L.

He, H.

J. Zhang, M. Fang, Y. Jin, and H. He, “Narrow line-width filters based on rugate structure and antireflection coating,” Thin Solid Films 520, 5447–5450 (2012).
[CrossRef]

Ibrahim, B. H.

Jakobs, S.

U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturing of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
[CrossRef]

Jin, Y.

J. Zhang, M. Fang, Y. Jin, and H. He, “Narrow line-width filters based on rugate structure and antireflection coating,” Thin Solid Films 520, 5447–5450 (2012).
[CrossRef]

Kaiser, N.

Kokarev, M. A.

Krausz, F.

Lappschies, M.

U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturing of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
[CrossRef]

M. Lappschies, B. Gortz, and D. Ristau, “Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering,” Appl. Opt. 45, 1502–1506 (2006).
[CrossRef]

Lee, C.

Oh, T. I.

Perilloux, B. E.

Pervak, V.

Pistner, J.

Ploss, B.

U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturing of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
[CrossRef]

Ristau, D.

Schallenberg, U.

U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturing of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
[CrossRef]

Southwell, W. H.

Stenzel, O.

Tang, C.

Thelen, A.

Tikhonravov, A. V.

Trubetskov, M. K.

Wang, L.

Wang, Z.

Wilbrandt, S.

Wu, J.

Young, L.

Zhang, J.

J. Zhang, M. Fang, Y. Jin, and H. He, “Narrow line-width filters based on rugate structure and antireflection coating,” Thin Solid Films 520, 5447–5450 (2012).
[CrossRef]

Appl. Opt. (12)

B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990).
[CrossRef]

W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949–2951(1989).
[CrossRef]

W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, M. A. Kokarev, N. Kaiser, O. Stenzel, S. Wilbrandt, and D. Gabler, “New optimization algorithm for the synthesis of rugate optical coatings,” Appl. Opt. 45, 1515–1524 (2006).
[CrossRef]

M. Lappschies, B. Gortz, and D. Ristau, “Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering,” Appl. Opt. 45, 1502–1506 (2006).
[CrossRef]

C. Lee, C. Tang, and J. Wu, “Rugate filter made with composite thin films by ion-beam sputtering,” Appl. Opt. 45, 1333–1337 (2006).
[CrossRef]

T. I. Oh, “Infrared minus-filter coatings: design and production,” Appl. Opt. 30, 4565–4573 (1991).
[CrossRef]

T. V. Amotchkina, “Analytical estimations for the reflectance wavelength reflectance and width of high-reflection zone of two-material periodic multilayers,” Appl. Opt. 52, 4590–4595 (2013).
[CrossRef]

B. H. Ibrahim, R. Botha, J. E. Bouree, P. Bulkin, and B. Drevillon, “Correlation of sidelobe suppression between rugate filters and multilayer mirrors,” Appl. Opt. 46, 7776–7779 (2007).
[CrossRef]

B. E. Perilloux, “Discrete thin-film layer thickness modulation,” Appl. Opt. 37, 3527–3532 (1998).
[CrossRef]

L. Young, “Multilayer interference filters with narrow stop bands,” Appl. Opt. 6, 297–315 (1967).
[CrossRef]

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, J. Pistner, F. Krausz, and A. Apolonski, “Band filters: two-material technology versus rugate,” Appl. Opt. 46, 1190–1193 (2007).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (1)

Proc. SPIE (1)

U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturing of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
[CrossRef]

Thin Solid Films (1)

J. Zhang, M. Fang, Y. Jin, and H. He, “Narrow line-width filters based on rugate structure and antireflection coating,” Thin Solid Films 520, 5447–5450 (2012).
[CrossRef]

Other (2)

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, vol. IV (McGraw-Hill, 2010), pp. 7.15–7.53.

A. V. Tikhonravov and M. K. Trubetskov, Optilayer Thin Film Software, http://www.optilayer.com .

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Figures (8)

Fig. 1.
Fig. 1.

Layer-thickness profile (a) and transmittance (b) of the multilayer sub/(0.4L1.2H0.4L)23/air. Notice the sidelobes near the stopband are very high. The purple dots represent the spectral target.

Fig. 2.
Fig. 2.

Equivalent index of the symmetrical structures with different thickness ratios.

Fig. 3.
Fig. 3.

Transmittance of the coatings Sub/H0.5L/air at the incident angle of 0 deg.

Fig. 4.
Fig. 4.

Layer-thickness profile (a) and the spectral response (b) of a minus filter with linear modulation.

Fig. 5.
Fig. 5.

Layer-thickness profile (a) and the spectral response (b) of a minus filter with sine-wave modulation. Notice the reduced sidelobes near and far from the stopband.

Fig. 6.
Fig. 6.

Layer-thickness profile (a) and the spectral response (b) for a quintic-enveloped minus filter.

Fig. 7.
Fig. 7.

Layer-thickness profile (a) and spectral response (b) for a sine-envelope minus filter with more match layers.

Fig. 8.
Fig. 8.

Layer-thickness profile (a) and spectral response (b) for a sine-envelope multilayer with a HR range of 35 nm.

Equations (7)

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Δλ0=2πC21sin(πp)[(C+1)(14p)2(C1)cos(2πp)]λ0,
R(λ)=a112(nans)2+a2(nansα+1)2a122a112(na+ns)2+a2(1nansα)2a122and
a11=0.5[(1+αa)n+(1αa)n],a12=0.5[(1αa)n(1+αa)n]/(αa),
λ1=λ/3+2/9λsin1((nhnl)/(nh+nl))/πandλ2=λ2λsin1((nhnl)/(nh+nl))/π.
T=ta+0.5*tp*A(l)*sin(π*l+ϕ),
A(l)=10t315t4+6t5,
t=2l/sforls/2,=2(sl)/sforl>s/2.

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