Abstract

Two design problems were posed: a high-temperature solar-selective coating, and a near to mid-infrared Fabry–Perot etalon. A total of 50 submissions were received, 42 for problem A and eight for problem B. The submissions were created through a wide spectrum of design approaches and optimization strategies. Michael Trubetskov and Fabien Lemarchand won the first contest by submitting the design with the highest overall merit function, and the fewest layer/thinnest solar-selective design, respectively. Michael Trubetskov also won the second contest by submitting the thinnest Fabry–Perot etalon design, with a free spectral range standard deviation of 0. Vladimir Pervak and Bill Southwell received second-place finishes. The submitted designs are described and evaluated.

© 2011 Optical Society of America

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References

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  1. C. E. Kennedy, “Advances in concentrating solar power collectors: mirrors and solar-selective coatings,” Vac. Tech. & Coating 9(6), 44–55 (2008).
  2. C. E. Kennedy, “Progress to develop an advanced solar-selective coating,” 2008 14th Biennial CSP SolarPACES (Solar Power and Chemical Energy Systems) Symposium, Las Vegas, Nevada, 4–7 March 2008, (CD-ROM) (NREL/CD-550-42709).
  3. E.D.Palik, ed., Handbook of Optical Constants of Solids(Academic, 1985).
  4. E.D.Palik, ed., Handbook of Optical Constants of Solids II (Academic, 1991).
  5. E.D.Palik, ed., Handbook of Optical Constants of Solids III (Academic, 1998).
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  7. A. P. Lenham and D. M. Treherne, “Optical constants of transition metals in the infrared,” J. Opt. Soc. Am. 56, 1137–1138 (1966).
    [CrossRef]
  8. A. P. Lenham and D. M. Treherne, “Optical constants of transition metals in the infrared,” presented at the International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, France, 13–16 September 1965.
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    [CrossRef] [PubMed]
  10. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321(2004).
    [CrossRef]
  11. M. Tilsch and K. Hendrix, “Optical interference coatings design contest 2007: triple bandpass filter and nonpolarizing beam splitter,” Appl. Opt. 47, C55–C69 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010

2008

C. E. Kennedy, “Advances in concentrating solar power collectors: mirrors and solar-selective coatings,” Vac. Tech. & Coating 9(6), 44–55 (2008).

M. Tilsch and K. Hendrix, “Optical interference coatings design contest 2007: triple bandpass filter and nonpolarizing beam splitter,” Appl. Opt. 47, C55–C69 (2008).
[CrossRef] [PubMed]

2004

V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321(2004).
[CrossRef]

2003

2001

1998

J. F. Mulligan, “Who were Fabry and Perot?,” Am. J. Phys. 66, 797–802(1998).
[CrossRef]

1994

1986

1966

Amotchkina, T. V.

V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321(2004).
[CrossRef]

Dobrowolski, J. A.

Ferencz, K.

Garmire, E.

Gu, P. F.

Harasaki, A.

Hendrix, K.

Kennedy, C. E.

C. E. Kennedy, “Advances in concentrating solar power collectors: mirrors and solar-selective coatings,” Vac. Tech. & Coating 9(6), 44–55 (2008).

C. E. Kennedy, “Progress to develop an advanced solar-selective coating,” 2008 14th Biennial CSP SolarPACES (Solar Power and Chemical Energy Systems) Symposium, Las Vegas, Nevada, 4–7 March 2008, (CD-ROM) (NREL/CD-550-42709).

Kokarev, M. A.

V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321(2004).
[CrossRef]

Krausz, F.

Lenham, A. P.

A. P. Lenham and D. M. Treherne, “Optical constants of transition metals in the infrared,” J. Opt. Soc. Am. 56, 1137–1138 (1966).
[CrossRef]

A. P. Lenham and D. M. Treherne, “Optical constants of transition metals in the infrared,” presented at the International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, France, 13–16 September 1965.

Liu, X.

Luo, Z. Y.

Macleod, H. Angus

H. Angus Macleod, Thin Film Optical Filters (McGraw-Hill, 1989), p. 159.

Mulligan, J. F.

J. F. Mulligan, “Who were Fabry and Perot?,” Am. J. Phys. 66, 797–802(1998).
[CrossRef]

Ribbing, C.-G.

C.-G. Ribbing, Division of Solid State Physics, Angstrom Laboratory, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden (personal communication, 2009).

Schmit, J.

Shen, W. D.

Spielmann, C.

Szipocs, R.

Tikhonravov, V.

V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321(2004).
[CrossRef]

Tilsch, M.

Treherne, D. M.

A. P. Lenham and D. M. Treherne, “Optical constants of transition metals in the infrared,” J. Opt. Soc. Am. 56, 1137–1138 (1966).
[CrossRef]

A. P. Lenham and D. M. Treherne, “Optical constants of transition metals in the infrared,” presented at the International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, France, 13–16 September 1965.

Trubetskov, M. K.

V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321(2004).
[CrossRef]

Wyant, J.

Xia, C.

Am. J. Phys.

J. F. Mulligan, “Who were Fabry and Perot?,” Am. J. Phys. 66, 797–802(1998).
[CrossRef]

Appl. Opt.

Chin. Opt. Lett.

J. Opt. Soc. Am.

Opt. Lett.

Proc. SPIE

V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and M. A. Kokarev, “Key role of the coating total optical thickness in solving design problems,” Proc. SPIE 5250, 312–321(2004).
[CrossRef]

Vac. Tech. & Coating

C. E. Kennedy, “Advances in concentrating solar power collectors: mirrors and solar-selective coatings,” Vac. Tech. & Coating 9(6), 44–55 (2008).

Other

C. E. Kennedy, “Progress to develop an advanced solar-selective coating,” 2008 14th Biennial CSP SolarPACES (Solar Power and Chemical Energy Systems) Symposium, Las Vegas, Nevada, 4–7 March 2008, (CD-ROM) (NREL/CD-550-42709).

E.D.Palik, ed., Handbook of Optical Constants of Solids(Academic, 1985).

E.D.Palik, ed., Handbook of Optical Constants of Solids II (Academic, 1991).

E.D.Palik, ed., Handbook of Optical Constants of Solids III (Academic, 1998).

C.-G. Ribbing, Division of Solid State Physics, Angstrom Laboratory, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden (personal communication, 2009).

A. P. Lenham and D. M. Treherne, “Optical constants of transition metals in the infrared,” presented at the International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, France, 13–16 September 1965.

H. Angus Macleod, Thin Film Optical Filters (McGraw-Hill, 1989), p. 159.

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Figures (21)

Fig. 1
Fig. 1

Theoretical absorptance of a solar absorptive design. The normalized solar spectrum is the solid curve; the normalized 450 ° C blackbody spectrum is the dashed curve. For this example, the solar absorptance is 94.28% and the emittance for the 450 ° C blackbody is 9.96%.

Fig. 2
Fig. 2

Evaluation software for solar absorber designs. Calculation of the solar absorptance and blackbody emittance verifies that the design meets problem specifications, determines the overall merit function and summarizes the design.

Fig. 3
Fig. 3

42 submissions for problem A, sorted alphabetically by designer. The total thickness, number of layers, and materials used in each design are shown. The thicker designs shown tend to focus on achieving the maximum overall merit function, in response to the first goal for problem A. Many of the designs target the fewest layers at a minimum merit function, in response to the second design goal.

Fig. 4
Fig. 4

Correlation of the achieved merit function with the (a) number of layers and (b) overall coating thickness. As expected, those designs with greater complexity and overall coating thickness perform much better. The grouping of thin designs target the fewest-layers design goal.

Fig. 5
Fig. 5

Solar absorptance of the various submissions varied over the range of 94–98%, leading to minimal benefit in merit function. Those designs achieving very high merit functions significantly suppressed the 450 ° C blackbody emittance, since there was greater variation in the performance realized.

Fig. 6
Fig. 6

Transmittance of the three designs having the highest merit functions. Note that these designs are all somewhat transmissive for the blackbody radiation, with the coatings acting as dichroic filters with the edge positioned between the solar and blackbody spectra.

Fig. 7
Fig. 7

Sketch of Fabry–Perot Etalon with mirror coatings a and b on substrates, separated by an air gap, d s [15].

Fig. 8
Fig. 8

Theoretical transmittance of an ideal Fabry–Perot etalon with 10 μm air gap and equal reflectors of 88.83%. The reflectors are assumed to have zero reflected phase. The FWHM of each order is 20 cm 1 and the FSR is 500 cm 1 .

Fig. 9
Fig. 9

Screen capture of evaluation software GUI applied to problem B, a sample solution is shown. See text for details.

Fig. 10
Fig. 10

TrubetB1: 23 layers, Th = 4960 nm , Air gap = 5784 nm (see text for discussion).

Fig. 11
Fig. 11

PervakB1: 23 layers, Th = 4984 nm , Air gap = 4468 nm (see text for discussion).

Fig. 12
Fig. 12

PervakB3: 23 layers, Th = 4993 nm , Air gap = 4475 nm (see text for discussion).

Fig. 13
Fig. 13

PervakB2: 25 layers, Th = 5012 nm , Air gap = 4581 nm (see text for discussion).

Fig. 14
Fig. 14

Reflectance (black) plotted to the left scale and reflected phase (gray) plotted to the right scale of the QW stack ( H L ) 3 centered at 5263 cm 1 .

Fig. 15
Fig. 15

Reflectance of designs with two QW stacks, ( H L ) 3 ( H L ) 3 , centered at 5263 cm 1 and 2778 cm 1 . The heavy black and gray curves are reflectance plotted to the left scale and the thin black and gray curves are reflected phase (gray) plotted to the right scale. The black curves are for the design with the 5263 cm 1 stack near air and the gray curves are for the design with the 2778 cm 1 near air.

Fig. 16
Fig. 16

Possible configurations for a starting design for the Fabry–Perot mirrors (see text).

Fig. 17
Fig. 17

Sum of the mirror reflected phases ( ϕ a + ϕ b ) , for the Fabry–Perot configurations shown in Fig. 16. The light gray curve is for the upper configuration, the dark gray curve is for the middle configuration, and the black curve is for the lower configuration.

Fig. 18
Fig. 18

Reflectance and reflected phase of the mirrors of design TrubetB1. The heavy black and gray lines are reflectance plotted to the left scale and the thin black and gray curves are reflected phases ϕ a and ϕ b (gray) plotted to the right scale. The thin, light gray curve is ( ϕ a + ϕ b ) .

Fig. 19
Fig. 19

Similar plot to Fig. 18, but for design PervakB1. The open circles plotted on the ( ϕ a + ϕ b ) curve indicate the locations of the peaks.

Fig. 20
Fig. 20

Similar plot to Fig. 18, but for design SouthwB1. The open circles plotted on the reflectance curves indicate the locations of the peaks.

Fig. 21
Fig. 21

Similar plot to Fig. 18, but for design ZhangB1.

Tables (3)

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Table 1 Winning Solutions to the Two Design Goals for Problem A a

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Table 2 Design Submissions for Problem B a

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Table 3 Eight Solutions to Problem B Sorted by Standard Deviation of the FSR and the Tiebreaker Condition of Total Coating Thickness a

Equations (7)

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Solar absorptance= σ i Abs ( σ i ) ASTM 173 ( σ i ) σ i 2 σ i ASTM 173 ( σ i ) σ i 2 , σ i = ( 2480 , 2520 , 2560 , , 35720 cm 1 ,
450 ° C blackbody emittance = σ i Abs ( σ i ) BB 450 C ( σ i ) σ i 2 σ i BB 450 C ( σ i ) σ i 2 , σ i = ( 400 , 440 , 480 , , 35720 cm 1 ) ,
Merit function = Solar absorptance 450 ° C blackbody emittance.
CWN = ( HPP upper + HPP lower ) 2 ,
FWHM = HPP upper HPP lower .
FSR n = CWN n + 1 CWN n ( n = 1 to 11 , for orders ) .
T = T a T b [ 1 ( R a R b + ) 1 / 2 ] 2 [ 1 + 4 ( R a R b + ) 1 / 2 [ 1 ( R a R b + ) 1 / 2 ] 2 sin 2 ( ϕ a + ϕ b 2 δ ) ] 1 δ = 2 π n s d s cos θ s / λ ,

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