Abstract

Periodic multilayer structures of quarterwave and multiple quarterwave stacks with shifted ratios of high and low index layers in the half-wave pairs are considered. Analytical dependencies of the reference wavelength reflectance and the width of high reflectance zone on the number of layers, fraction quarterwave and layer refractive indices are obtained. The structures are used as starting designs for notch filters. Obtained dependencies allow one to estimate in advance parameters required to achieve target spectral characteristics.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).
  2. L. Young, “Multilayer interference filters with narrow stop bands,” Appl. Opt. 6, 297–316 (1967).
    [CrossRef]
  3. M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
    [CrossRef]
  4. K. D. Hendrix, C. Hulse, G. J. Ockenfuss, and R. Sargent, “Demonstration of narrowband notch and multi-notch filters,” Proc. SPIE 7067, 706702 (2008).
    [CrossRef]
  5. U. Schallenberg, B. Ploss, M. Lappschies, and S. Jakobs, “Design and manufacturability of high performance notch filters,” Proc. SPIE 7739, 77391X (2010).
    [CrossRef]
  6. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989).
    [CrossRef]
  7. M. Lappschies, B. Görtz, and D. Ristau, “Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering,” Appl. Opt. 45, 1502–1506 (2006).
    [CrossRef]
  8. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Application of constrained optimization to the design of quasi-rugate optical coatings,” Appl. Opt. 47, 5103–5109 (2008).
    [CrossRef]
  9. P. G. Verly, J. A. Dobrowolski, W. Wild, and R. Burton, “Synthesis of high rejection filters with the fourier transform method,” Appl. Opt. 28, 2864–2875 (1989).
    [CrossRef]
  10. P. W. Baumeister, Optical Coating Technology (SPIE, 2004).
  11. A. Zöller, M. Boos, H. Hagedorn, and B. Romanov, “Computer simulation of coating processes with monochromatic monitoring,” Proc. SPIE 7101, 71010G (2008).
    [CrossRef]
  12. H. Dwight, Tables of Integrals and Other Mathematical Data (Macmillan Company, 1957).
  13. Sh. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).
  14. A. V. Tikhonravov and M. K. Trubetskov, OptiLayer thin film software, http://www.optilayer.com .

2010 (1)

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

2008 (4)

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

K. D. Hendrix, C. Hulse, G. J. Ockenfuss, and R. Sargent, “Demonstration of narrowband notch and multi-notch filters,” Proc. SPIE 7067, 706702 (2008).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Application of constrained optimization to the design of quasi-rugate optical coatings,” Appl. Opt. 47, 5103–5109 (2008).
[CrossRef]

A. Zöller, M. Boos, H. Hagedorn, and B. Romanov, “Computer simulation of coating processes with monochromatic monitoring,” Proc. SPIE 7101, 71010G (2008).
[CrossRef]

2006 (1)

1989 (2)

1967 (1)

Amotchkina, T. V.

Baumeister, P. W.

P. W. Baumeister, Optical Coating Technology (SPIE, 2004).

Boos, M.

A. Zöller, M. Boos, H. Hagedorn, and B. Romanov, “Computer simulation of coating processes with monochromatic monitoring,” Proc. SPIE 7101, 71010G (2008).
[CrossRef]

Burton, R.

Dobrowolski, J. A.

Dwight, H.

H. Dwight, Tables of Integrals and Other Mathematical Data (Macmillan Company, 1957).

Furman, Sh.

Sh. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

Görtz, B.

Hagedorn, H.

A. Zöller, M. Boos, H. Hagedorn, and B. Romanov, “Computer simulation of coating processes with monochromatic monitoring,” Proc. SPIE 7101, 71010G (2008).
[CrossRef]

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

Hendrix, K. D.

K. D. Hendrix, C. Hulse, G. J. Ockenfuss, and R. Sargent, “Demonstration of narrowband notch and multi-notch filters,” Proc. SPIE 7067, 706702 (2008).
[CrossRef]

Hulse, C.

K. D. Hendrix, C. Hulse, G. J. Ockenfuss, and R. Sargent, “Demonstration of narrowband notch and multi-notch filters,” Proc. SPIE 7067, 706702 (2008).
[CrossRef]

Jakobs, S.

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

Lappschies, M.

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

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

Lehnert, W.

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

Ockenfuss, G. J.

K. D. Hendrix, C. Hulse, G. J. Ockenfuss, and R. Sargent, “Demonstration of narrowband notch and multi-notch filters,” Proc. SPIE 7067, 706702 (2008).
[CrossRef]

Ploss, B.

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

Ristau, D.

Romanov, B.

A. Zöller, M. Boos, H. Hagedorn, and B. Romanov, “Computer simulation of coating processes with monochromatic monitoring,” Proc. SPIE 7101, 71010G (2008).
[CrossRef]

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

Sargent, R.

K. D. Hendrix, C. Hulse, G. J. Ockenfuss, and R. Sargent, “Demonstration of narrowband notch and multi-notch filters,” Proc. SPIE 7067, 706702 (2008).
[CrossRef]

Schallenberg, U.

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

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

Scherer, M.

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

Southwell, W. H.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

Tikhonravov, A. V.

Trubetskov, M. K.

Verly, P. G.

Wild, W.

Young, L.

Zöller, A.

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

A. Zöller, M. Boos, H. Hagedorn, and B. Romanov, “Computer simulation of coating processes with monochromatic monitoring,” Proc. SPIE 7101, 71010G (2008).
[CrossRef]

Appl. Opt. (5)

Proc. SPIE (4)

M. Scherer, U. Schallenberg, H. Hagedorn, W. Lehnert, B. Romanov, and A. Zöller, “High performance notch filter coatings produced with piad and magnetron sputtering,” Proc. SPIE 7101, 71010I (2008).
[CrossRef]

K. D. Hendrix, C. Hulse, G. J. Ockenfuss, and R. Sargent, “Demonstration of narrowband notch and multi-notch filters,” Proc. SPIE 7067, 706702 (2008).
[CrossRef]

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

A. Zöller, M. Boos, H. Hagedorn, and B. Romanov, “Computer simulation of coating processes with monochromatic monitoring,” Proc. SPIE 7101, 71010G (2008).
[CrossRef]

Other (5)

H. Dwight, Tables of Integrals and Other Mathematical Data (Macmillan Company, 1957).

Sh. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette, 1992).

A. V. Tikhonravov and M. K. Trubetskov, OptiLayer thin film software, http://www.optilayer.com .

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1988).

P. W. Baumeister, Optical Coating Technology (SPIE, 2004).

Cited By

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

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Comparison of exact (markers) and predicted (solid curves) dependencies of the reference wavelength reflectance R(λ0) on the fraction of the quarterwave p.

Fig. 2.
Fig. 2.

Comparison of exact (markers) and predicted (solid curves) dependencies of the reference wavelength reflectance R(λ0) on the number of layer pairs n.

Fig. 3.
Fig. 3.

Comparison of exact (markers) and estimated (solid curves) dependencies of the width of HR zone on the fraction quarterwave p.

Fig. 4.
Fig. 4.

Comparison of exact (markers) and predicted (solid curves) dependencies of the width of HR zone Δλ0 on the ratio of high and low refractive indices n1/n2.

Fig. 5.
Fig. 5.

Refractive index profile of the 140-layer design obtained with the help of OptiLayer software.

Fig. 6.
Fig. 6.

Reflectance of the 140-layer design obtained with the help of OptiLayer software.

Tables (2)

Tables Icon

Table 1. Expressions for a11

Tables Icon

Table 2. Expressions for a12

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

M=(cosφ1cosφ2n2n1sinφ1sinφ2in1sinφ1cosφ2+in2cosφ1sinφ2in1sinφ1cosφ2+in2cosφ1sinφ2cosφ1cosφ2n1n2sinφ1sinφ2),
M=(cos2ϵn2n1sin2ϵi2(1n11n2)sin2ϵi2(n1n2)sin2ϵcos2ϵn1n2sin2ϵ),
M(1iαaia1),
Mr=(a11iαaa12iaa12a11),
(1+x)n=1nx+n(n+1)2!x2n(n+1)(n+2)3!x3++(1)r(n+r1)!(n1)!r!xr+,(1x)n=1+nx+n(n+1)2!x2+n(n+1)(n+2)3!x3++(n+r1)!(n1)!r!xr+.
1+n(n+1)2!x2+n(n+1)(n+2)(n+3)4!x4+0.5[(1+x)n+(1x)n],nx+n(n+1)(n+2)3!x3+n(n+1)(n+2)(n+3)(n+4)5!x5+0.5[(1x)n(1+x)n].
a11=0.5[(1+α|a|)n+(1α|a|)n],a12=0.5[(1α|a|)n(1+α|a|)n]/(α|a|).
R(λ0)=a112(nans)2+a2(nansα1)2a122a112(na+ns)2+a2(nansα+1)2a122,
b(λ)=cosφ1cosφ212(n1n2+n2n1)sinφ1sinφ2.
b(λ)=12cos(πλ0λ)(1+C)+12(1C)cos(πλ0λ(1p)),C=12(n1n2+n2n1).
12(C+1)cosπy+12(1C)cos(πyπpy)=1.
Δ=y1y2=4πC21sin(πp/2)[C+1(1p)2(C1)cos(πp)].
Δλ0=2·λ0Δ(1+Δ21)λ0Δ.
Δλ0=4λ0πC21sin(πp/2)[C+1(1p)2(C1)cos(πp)].
b(λ)=C+12cos(2πy(λ))+1C2cos(πy(λ)(2p)),
Δ=y1y2=2λ0πC21sin(πp/2)[(C+1)(12p)2(C1)cos(πp)].

Metrics