Abstract

Recent investigations have added to and refined the understanding of the behavior of broadband antireflection coating designs and provided further guidance for achieving more nearly optimal designs. The ability to optimize designs wherein the overall optical thickness of the design is constrained to a specific value has allowed this investigation. A broader bandwidth than previously reported has been studied and statistically fit more precisely by a polynomial equation, and also two linear equations for routine approximations have been derived. It has also been found that the optimal number of layers in the design can be predicted as a function of the bandwidth.

© 2011 Optical Society of America

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References

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  1. R. R. Willey, “Broadband antireflection coating design performance estimation,” Society of Vacuum Coaters Annual Technical Conference Proceedings (1991), Vol.  34, pp. 205–208.
  2. R. R. Willey, “Predicting achievable design performance of broadband antireflection coatings,” Appl. Opt. 32, 5447–5451(1993).
    [CrossRef] [PubMed]
  3. R. R. Willey, “Refined criteria for estimating limits of broadband AR coatings,” Proc. SPIE 5250, 393–399 (2004).
    [CrossRef]
  4. R. R. Willey, “Broadband antireflection coating design recommendations,” Society of Vacuum Coaters Annual Technical Conference Proceedings ( 2004), Vol.  47, pp. 16–21.
  5. R. R. Willey, Practical Design of Optical Thin Films, 2nd ed. (Willey Optical, 2007), pp. 139–158.
  6. R. R. Willey, Practical Design of Optical Thin Films, 2nd ed. (Willey Optical, 2007), Appendix C.
  7. R. R. Willey, “Looking outside the box for broadband AR coating designs,” in Optical Interference Coatings (OIC) (Optical Society of America, June 2010).
  8. R. R. Willey, “Expanded viewpoint for broadband AR coating designs,” Appl. Opt. 50, C86–C89 (2011).
    [CrossRef] [PubMed]
  9. F. T. Goldstein, FilmStar, FTG Software Associates, P.O. Box 579, Princeton, N.J. 08542.
  10. A. Tikhonravov, M. Trubetskov, and T. Amotchkina, “Application of constrained optimization to the design of quasi-rugate optical coatings,” Appl. Opt. 47, 5103–5109(2008).
    [CrossRef] [PubMed]
  11. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, Brian T. Sullivan, and P. G. Verly, “Optimal single-band normal-incidence antireflection coatings,” Appl. Opt. 35, 644–658(1996).
    [CrossRef] [PubMed]
  12. T. Amotchkina, “Empirical expression for the minimum residual reflectance of normal- and oblique-incidence antireflection coatings,” Appl. Opt. 47, 3109–3113(2008).
    [CrossRef] [PubMed]
  13. Numerical Optimization Library, DSNL Version 2.0, Technologix Corporation, 12020 113th Avenue NE, Kirkland, Wash. 98034-6938.
  14. A. Tikhonravov, M. Trubetskov, T. Amotchkina, and J. Dobrowolski, “Estimation of the average residual reflectance of broadband antireflection coatings,” Appl. Opt. 47, C124–C130 (2008).
    [CrossRef] [PubMed]
  15. DOE KISS 2007 Software, SigmaZone.com and Air Academy Associates, LLC, 1650 Telstar Drive, Suite 110, Colorado Springs, Colo. 80920.

2011

2008

2004

R. R. Willey, “Refined criteria for estimating limits of broadband AR coatings,” Proc. SPIE 5250, 393–399 (2004).
[CrossRef]

1996

1993

Amotchkina, T.

Dobrowolski, J.

Dobrowolski, J. A.

Goldstein, F. T.

F. T. Goldstein, FilmStar, FTG Software Associates, P.O. Box 579, Princeton, N.J. 08542.

Sullivan, Brian T.

Tikhonravov, A.

Tikhonravov, A. V.

Trubetskov, M.

Trubetskov, M. K.

Verly, P. G.

Willey, R. R.

R. R. Willey, “Expanded viewpoint for broadband AR coating designs,” Appl. Opt. 50, C86–C89 (2011).
[CrossRef] [PubMed]

R. R. Willey, “Refined criteria for estimating limits of broadband AR coatings,” Proc. SPIE 5250, 393–399 (2004).
[CrossRef]

R. R. Willey, “Predicting achievable design performance of broadband antireflection coatings,” Appl. Opt. 32, 5447–5451(1993).
[CrossRef] [PubMed]

R. R. Willey, Practical Design of Optical Thin Films, 2nd ed. (Willey Optical, 2007), Appendix C.

R. R. Willey, Practical Design of Optical Thin Films, 2nd ed. (Willey Optical, 2007), pp. 139–158.

R. R. Willey, “Broadband antireflection coating design recommendations,” Society of Vacuum Coaters Annual Technical Conference Proceedings ( 2004), Vol.  47, pp. 16–21.

R. R. Willey, “Looking outside the box for broadband AR coating designs,” in Optical Interference Coatings (OIC) (Optical Society of America, June 2010).

R. R. Willey, “Broadband antireflection coating design performance estimation,” Society of Vacuum Coaters Annual Technical Conference Proceedings (1991), Vol.  34, pp. 205–208.

Appl. Opt.

Proc. SPIE

R. R. Willey, “Refined criteria for estimating limits of broadband AR coatings,” Proc. SPIE 5250, 393–399 (2004).
[CrossRef]

Other

R. R. Willey, “Broadband antireflection coating design recommendations,” Society of Vacuum Coaters Annual Technical Conference Proceedings ( 2004), Vol.  47, pp. 16–21.

R. R. Willey, Practical Design of Optical Thin Films, 2nd ed. (Willey Optical, 2007), pp. 139–158.

R. R. Willey, Practical Design of Optical Thin Films, 2nd ed. (Willey Optical, 2007), Appendix C.

R. R. Willey, “Looking outside the box for broadband AR coating designs,” in Optical Interference Coatings (OIC) (Optical Society of America, June 2010).

R. R. Willey, “Broadband antireflection coating design performance estimation,” Society of Vacuum Coaters Annual Technical Conference Proceedings (1991), Vol.  34, pp. 205–208.

F. T. Goldstein, FilmStar, FTG Software Associates, P.O. Box 579, Princeton, N.J. 08542.

Numerical Optimization Library, DSNL Version 2.0, Technologix Corporation, 12020 113th Avenue NE, Kirkland, Wash. 98034-6938.

DOE KISS 2007 Software, SigmaZone.com and Air Academy Associates, LLC, 1650 Telstar Drive, Suite 110, Colorado Springs, Colo. 80920.

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Figures (6)

Fig. 1
Fig. 1

Patterns of the minimum Rave in the AR band versus the overall OT of designs for B values of 4.0, 4.5, and 5.0, where the QWOT thicknesses were each constrained. This illustrates that the best Rave depends on the specific thickness of the design.

Fig. 2
Fig. 2

Rave versus B for L = 1.46 and 1.38 ( C = 1 ). The dots are actual designs, solid lines are from statistical polynomial curve fits to these results, and dashed lines are from linear fit equations.

Fig. 3
Fig. 3

Comparison of previous estimation equation (OLD FIT) with the actual data and the statistical polynomial equation (NEW FIT).

Fig. 4
Fig. 4

Overall OT of various optimal designs versus Rave in band as a function of number of layers. The bandwidth is shown to the right of each associated point.

Fig. 5
Fig. 5

Thickness of various optimal designs versus bandwidth and number of layers.

Fig. 6
Fig. 6

Fifteen minima (ripples) in the AR band of a B = 4.0 ( C = 3 ) design with 30 layers. The 61 targets at a value of 0.1 % T are shown on the bottom of the plot. Rave was calculated for approximately 400 equally spaced values over the band.

Equations (4)

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Rave = 3.99569 8.95463 × B + 7.40513 × B 2 2.89893 × B 3 + 0.60833 × B 4 0.06582 × B 5 + 0.00288 × B 6 .
( 6.447 / D ) × ( L 1 ) 2.55 ,
Rave = ( 6.447 / D ) × ( a × B + c ) × ( L 1 ) 2.55 ,
minimum   #   layers needed = 0.3725 × B 0.907 maximum   #   layers needed = 0.3725 × B 0.162

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