Abstract

The flip-flop synthesis method is robust with rapid convergence, but the solutions are often not the best. Modifications to the flip-flop algorithm have been developed, one of which puts it on par with needle synthesis.

© 2013 Optical Society of America

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References

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  1. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef]
  2. J. A. Dobrowolski, “Comparison of the Fourier transform and flip-flop synthesis methods,” Appl. Opt. 25, 1966–1972 (1986).
    [CrossRef]
  3. T. Skettrup, “Three-layer approximation of dielectric thin films systems,” Appl. Opt. 28, 2860–2863 (1989).
    [CrossRef]
  4. J. A. Dobrowolski and R. A. Kemp, “Flip-flop thin-film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
    [CrossRef]
  5. L. Li and J. A. Dobrowolski, “Computational speeds of different optical thin-film synthesis methods,” Appl. Opt. 31, 3790–3799 (1992).
    [CrossRef]
  6. J. A. Dobrowolski and R. A. Kemp, “Interface design methods for two-material optical multilayer coatings,” Appl. Opt. 31, 6747–6756 (1992).
    [CrossRef]
  7. J. Hrdina, “A technologically acceptable coating synthesis based on the flip-flop synthesis method,” J. Mod. Opt. 36, 111–118 (1989).
    [CrossRef]
  8. H. Arabshahi and M. Asmari, “Optimum designing of thin film filter layers of SiO2 and SnTe based on optical particle swarm optimizer,” Int. J. Phys. Sci. 5, 57–61 (2010).
  9. J. Baedi, H. Arabshahi, M. Gordi Armak, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).
  10. P. W. Baumeister, Optical Coating Technology (SPIE, 2004).
  11. H. A. Macleod, ed., Thin-Film Optical Filters, 4th ed. (CRC Press, 2010).
  12. R. R. Willey, Practical Design of Optical Thin Films (Willey Optical, 2011).
  13. FilmStar and Film Wizard list Flip-Flop as an option but this list may be incomplete.
  14. A. V. Tikhonravov and M. K. Trubetskov, Optilayer Thin Film Software, http://www.optilayer.com .

2010 (2)

H. Arabshahi and M. Asmari, “Optimum designing of thin film filter layers of SiO2 and SnTe based on optical particle swarm optimizer,” Int. J. Phys. Sci. 5, 57–61 (2010).

J. Baedi, H. Arabshahi, M. Gordi Armak, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

1992 (3)

1989 (2)

J. Hrdina, “A technologically acceptable coating synthesis based on the flip-flop synthesis method,” J. Mod. Opt. 36, 111–118 (1989).
[CrossRef]

T. Skettrup, “Three-layer approximation of dielectric thin films systems,” Appl. Opt. 28, 2860–2863 (1989).
[CrossRef]

1986 (1)

1985 (1)

Arabshahi, H.

H. Arabshahi and M. Asmari, “Optimum designing of thin film filter layers of SiO2 and SnTe based on optical particle swarm optimizer,” Int. J. Phys. Sci. 5, 57–61 (2010).

J. Baedi, H. Arabshahi, M. Gordi Armak, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Asmari, M.

H. Arabshahi and M. Asmari, “Optimum designing of thin film filter layers of SiO2 and SnTe based on optical particle swarm optimizer,” Int. J. Phys. Sci. 5, 57–61 (2010).

Baedi, J.

J. Baedi, H. Arabshahi, M. Gordi Armak, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Baumeister, P. W.

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

Dobrowolski, J. A.

Gordi Armak, M.

J. Baedi, H. Arabshahi, M. Gordi Armak, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Hosseini, E.

J. Baedi, H. Arabshahi, M. Gordi Armak, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Hrdina, J.

J. Hrdina, “A technologically acceptable coating synthesis based on the flip-flop synthesis method,” J. Mod. Opt. 36, 111–118 (1989).
[CrossRef]

Kemp, R. A.

Li, L.

Skettrup, T.

Southwell, W. H.

Willey, R. R.

R. R. Willey, Practical Design of Optical Thin Films (Willey Optical, 2011).

Appl. Opt. (6)

Int. J. Phys. Sci. (1)

H. Arabshahi and M. Asmari, “Optimum designing of thin film filter layers of SiO2 and SnTe based on optical particle swarm optimizer,” Int. J. Phys. Sci. 5, 57–61 (2010).

J. Mod. Opt. (1)

J. Hrdina, “A technologically acceptable coating synthesis based on the flip-flop synthesis method,” J. Mod. Opt. 36, 111–118 (1989).
[CrossRef]

Res. J. Appl. Sci. Eng. Technol. (1)

J. Baedi, H. Arabshahi, M. Gordi Armak, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Other (5)

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

H. A. Macleod, ed., Thin-Film Optical Filters, 4th ed. (CRC Press, 2010).

R. R. Willey, Practical Design of Optical Thin Films (Willey Optical, 2011).

FilmStar and Film Wizard list Flip-Flop as an option but this list may be incomplete.

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

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Figures (16)

Fig. 1.
Fig. 1.

Some flip-flop strategies.

Fig. 2.
Fig. 2.

Edge filter using flip-flop from the incident side with all low index. This converged after 10 passes. The merit function is 6.335.

Fig. 3.
Fig. 3.

Only three or four matrix multiplication are needed to compute the spectra from M=BVF, including the matrix updates to the base and front matrices.

Fig. 4.
Fig. 4.

Algorithm for the flip-flop method.

Fig. 5.
Fig. 5.

Use of Boolean array to describe the flip-flop stack.

Fig. 6.
Fig. 6.

Merit function as a function of layer refractive index and its quadratic fit where the layer favors the high index. The R in the figure is a measure of the goodness of fit to the quadratic function.

Fig. 7.
Fig. 7.

Merit function as a function of layer refractive index and its quadratic fit where the layer favors an intermediate index. The R’s in the figure are a measure of the goodness of fit to the quadratic function. Note the actual merit function is not a perfect quadratic, but hopefully close enough to locate its minimum.

Fig. 8.
Fig. 8.

Convergence history for implementations of the Vary_n method. The flip-flop method is given for comparison, but it is complete at six passes.

Fig. 9.
Fig. 9.

Convergence history showing that the Vary_n method can result in better solutions than the flip-flop method.

Fig. 10.
Fig. 10.

Results after 100 passes of the Vary_n method with ndif=0.125(nHnL), starting from the substrate with all low index. The merit function is 5.898.

Fig. 11.
Fig. 11.

Results of the flip-flop method, starting from the substrate with all low index. The merit function is 6.911. This converged in seven passes.

Fig. 12.
Fig. 12.

AR coating designed with flip-flop from incidence and using all low index to start. MF=0.518%, which is the average reflectance.

Fig. 13.
Fig. 13.

AR with Vary_n with ndiff=0.05(nHnL) from incidence and using all low index to start. MF=0.241%.

Fig. 14.
Fig. 14.

Design generated with the Vary_t method starting with 400 layers of alternating high and low index each 5 nm physical thickness. Near-zero thickness layers were removed and the adjacent layers combined.

Fig. 15.
Fig. 15.

Design using the flip-flop method followed by the Vary_t method on the combined layers. The merit function is 5.837.

Fig. 16.
Fig. 16.

Flip-flop Q-function (solid line) for the first pass of the edge filter example. The needle P-function (dashed line) for the same case is shown for comparison.

Equations (8)

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

M=j=1NlayersVj=(M11iM12iM21M22),
V=(cosφisinφ/nsinφcosφ),
(BC)=(M11iM12iM21M22)(1nsub),
r=(nincBC)/(nincB+C),
R=r*r.
MF=k=1NWavelengths(RkRtk)2,
F=a+bx+cx2,
xmin=b/(2c),

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