Abstract

A novel robust optimization algorithm is demonstrated that is largely deterministic, and yet it attempts to account for statistical variations in coating. Through Monte Carlo simulations of manufacturing, we compare the performance of a proof-of-concept antireflection (AR) coating designed with our robust optimization to that of a conventionally optimized AR coating. We find that the robust algorithm produces an AR coating with a significantly improved yield.

© 2011 Optical Society of America

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References

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2010 (1)

D. Bertsimas, O. Nohadani, and K. M. Teo, “Robust nonconvex optimization for simulation-based problems,” Oper. Res. 58, 161 (2010).
[CrossRef]

2008 (1)

2005 (1)

2002 (1)

1996 (2)

1992 (1)

Amotchkina, T. V.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “On the reliability of computational estimations used for choosing the most manufacturable design,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper TuA3.

Bertsimas, D.

D. Bertsimas, O. Nohadani, and K. M. Teo, “Robust nonconvex optimization for simulation-based problems,” Oper. Res. 58, 161 (2010).
[CrossRef]

Bertsimas, D. J.

Birge, J. R.

DeBell, G.

Dobrowolski, J.

Kärtner, F. X.

Nohadani, O.

D. Bertsimas, O. Nohadani, and K. M. Teo, “Robust nonconvex optimization for simulation-based problems,” Oper. Res. 58, 161 (2010).
[CrossRef]

O. Nohadani, J. R. Birge, F. X. Kärtner, and D. J. Bertsimas, “Robust chirped mirrors,” Appl. Opt. 47, 2630–2636 (2008).
[CrossRef] [PubMed]

Sullivan, B.

Tempea, G.

Teo, K. M.

D. Bertsimas, O. Nohadani, and K. M. Teo, “Robust nonconvex optimization for simulation-based problems,” Oper. Res. 58, 161 (2010).
[CrossRef]

Tikhonravov, A.

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “On the reliability of computational estimations used for choosing the most manufacturable design,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper TuA3.

Trubetskov, M.

Trubetskov, M. K.

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “On the reliability of computational estimations used for choosing the most manufacturable design,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper TuA3.

Verly, P.

Yakovlev, V.

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Figures (5)

Fig. 1
Fig. 1

Two-dimensional illustration of the neighborhood. For a design x ^ , all possible implementation errors Δ x U are contained in the shaded circle. The bold arrow d shows apossible descent direction, and thin arrows Δ x i * represent worst errors.

Fig. 2
Fig. 2

Reflectances of the nominal- and robust-optimized AR coatings. The nominal design has an average reflectance of roughly 0.1%, and the robust design has a reflectance of around 0.2%.

Fig. 3
Fig. 3

Layer thicknesses of nominal-optimized (top) and robust-optimized (bottom) designs.

Fig. 4
Fig. 4

Yield as a function of the final postoptimization from the robust point to the nominal optimum, parameterized by iteration number. The last stage of our robust optimization routine is to search this function for the maximum yield point typically found relatively close to the robust optimum despite having a significantly better yield.

Fig. 5
Fig. 5

Manufacturing yield of both robust- and nominal- optimized designs as a function of performance cutoff, assuming layer thickness errors of 2.5 nm rms. At the design cutoff of 1%, the robust design has a yield of 74% versus 36% for the nominally optimized design we started with.

Equations (2)

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min x g ( x ) min x max Δ x U f ( x + Δ x ) .
minimize     β d , β subject to     d 2 1 d · Δ x * β     Δ x * U * ( x ^ ) β ϵ ,

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