Abstract

Many existing well-known multilayer design methods are based on so-called greedy algorithms. New deep search algorithms developed for needle optimization, gradual evolution, and design cleaner methods are presented. The algorithms possess machine learning features. The advantages of the deep search methods are demonstrated on a set of examples including the OIC Design Contest 2019.

© 2019 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  10. W. H. Southwell, “Flip-flop coating synthesis revisited,” Appl. Opt. 53, A179–A185 (2014).
    [Crossref]
  11. J.-M. Yang and C.-Y. Kao, “Efficient evolutionary algorithm for the thin-film synthesis of inhomogeneous optical coatings,” Appl. Opt. 40, 3256–3267 (2001).
    [Crossref]
  12. J.-M. Yang and C.-Y. Kao, “An evolutionary algorithm for the synthesis of multilayer coatings at oblique light incidence,” J. Lightwave Technol. 19, 559–570 (2001).
    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (1)

2014 (3)

2012 (1)

2010 (2)

2007 (2)

2001 (2)

1996 (1)

1995 (1)

1993 (1)

1985 (1)

1958 (1)

Baltz, E.

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Baumeister, P.

Bolshakov, I.

Cui, W. K.

DeBell, G. W.

Deliwala, A.

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Gerig, Z.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Gill, P. E.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Gu, P.

Guo, S.

Guo, X.

Hendrix, K.

Kao, C.-Y.

Keck, J.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Kotlikov, E. N.

Kruschwitz, J. D. T.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Lemarchand, F.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Liu, X.

Luan, X. X.

Luo, Z.

Ma, Y. F.

Martin, S.

Murray, W.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Nocedal, J.

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

Pellicori, S.

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Pervak, V.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Rivory, J.

Sato, K.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Schoenauer, M.

Shalin, V. B.

Shen, W.

Shi, L.

Southwell, W.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Southwell, W. H.

Sugiura, M.

Tikhonravov, A. V.

Tilsch, M.

Tropin, A. N.

Trubeskov, M.

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Trubetskov, M.

Trubetskov, M. K.

Wright, M. H.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

Wright, S. J.

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

Xia, C.

Yang, J.-M.

Yano, K.

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Yuan, W.

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

Zhou, H. Y.

Appl. Opt. (10)

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[Crossref]

A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993).
[Crossref]

S. Martin, J. Rivory, and M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt. 34, 2247–2254 (1995).
[Crossref]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Application of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[Crossref]

J.-M. Yang and C.-Y. Kao, “Efficient evolutionary algorithm for the thin-film synthesis of inhomogeneous optical coatings,” Appl. Opt. 40, 3256–3267 (2001).
[Crossref]

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46, 704–710 (2007).
[Crossref]

M. Tilsch and K. Hendrix, “Optical interference coatings design contest 2007: triple bandpass filter and nonpolarizing beam splitter,” Appl. Opt. 47, C55–C69 (2007).
[Crossref]

A. V. Tikhonravov and M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51, 7319–7332 (2012).
[Crossref]

W. H. Southwell, “Flip-flop coating synthesis revisited,” Appl. Opt. 53, A179–A185 (2014).
[Crossref]

J. D. T. Kruschwitz, V. Pervak, J. Keck, I. Bolshakov, Z. Gerig, F. Lemarchand, K. Sato, W. Southwell, M. Sugiura, M. Trubetskov, and W. Yuan, “Optical interference coating design contest 2016: a dispersive mirror and coating uniformity challenge,” Appl. Opt. 56, C151–C162 (2017).
[Crossref]

Chin. Opt. Lett. (2)

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Opt. Technol. (1)

Opt. Express (1)

Other (4)

J. D. T. Kruschwitz, V. Pervak, J. Keck, E. Baltz, A. Deliwala, Z. Gerig, F. Lemarchand, S. Pellicori, K. Sato, W. Southwell, M. Trubeskov, K. Yano, and W. Yuan, “Optical interference coating design contest 2019: a non-polarizing beamsplitter and a color-mixing challenge,” Appl. Opt. (to be published).

T. H. Cormen, ed., Introduction to Algorithms, 3rd ed. (MIT, 2009).

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1981).

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

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Figures (13)

Fig. 1.
Fig. 1. Block diagram of the needle optimization with deep search modification.
Fig. 2.
Fig. 2. $P$ function for different materials and needle insertions for the greedy algorithm and the deep search algorithms.
Fig. 3.
Fig. 3. Three-line filter target (magenta crosses) and spectral performance of classical and deep search designs (two black lines, indistinguishable in this resolution).
Fig. 4.
Fig. 4. Layer thicknesses of the three-line filter obtained with the classical approach (top) and with the deep search methods (bottom).
Fig. 5.
Fig. 5. Evolution of MF values as a function of design total optical thickness in classical and deep search variants of the synthesis procedure.
Fig. 6.
Fig. 6. Target of OIC 2016 Contest B [17] (magenta crosses) and the deep search result reflectance (the black curve).
Fig. 7.
Fig. 7. Evolution of the deep search (light-blue circles) and standard (green crosses) gradual evolution methods; the obtained results fulfilling the contest restriction of a maximum of 50 layers are shown with markers.
Fig. 8.
Fig. 8. Reflectance and GDD of one-octave 68-layer dispersive mirror [18] (dashed curves) and of the 62-layer design obtained with the deep search approach (solid lines).
Fig. 9.
Fig. 9. Layer thicknesses of the 62-layer design obtained with the deep search methods.
Fig. 10.
Fig. 10. Reflectance (top) and differential phase shifts on reflectance and transmittance (bottom) at 45° incidence for the winning design (bandwidth 63.932 nm) with the intermediate material with refractive index $n = 1.65$. Target requirements are shown by dark yellow and by magenta crosses.
Fig. 11.
Fig. 11. Reflectances (top) and differential phase shifts on reflectance and transmittance (bottom) at 45° incidence for the design with the intermediate material with refractive index $n = 1.8$ (bandwidth 63.732 nm). Target requirements are shown by dark yellow and by magenta crosses.
Fig. 12.
Fig. 12. Overview of the results for the same plane of incidence light mixing system subproblem. The MF of the winning result is shown by the red bar. Colors are different for the different selections of the light source at the direct path position. Source positions are shown by labels from bottom (direct path position A) to top (position D).
Fig. 13.
Fig. 13. Overview of the results for the orthogonal plane of incidence light mixing system subproblem. The MF of the winning result is shown by the red bar. Colors are different for the different selections of the light source at the direct path position. Source positions are shown by labels from bottom (direct path position A) to top (position D).

Equations (1)

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δ M F = P ( n ^ , z ) δ z + o ( δ z ) .

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