Abstract

Photonic crystals with slowly varying lattice period are responsible for broadband light reflectance in many biological contexts, ranging from the coatings of shiny beetles to the eye shine of butterflies. We utilize a quantum scattering analogy to obtain an approximate but closed-form expression for the reflectance of these adiabatically chirped photonic crystals (ACPCs). This expression allows us to devise a method for designing ACPCs with tailored reflectance spectra and obtain an estimate for the minimal number of layers required to exceed a given reflectance threshold. Comparison against the number of layers found in ACPCs throughout nature gives a quantitative measure of the optimality of chirped biological reflectors. Together, these results elucidate the design of chirped reflectors in nature and their possible application to future optical technologies.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Chirality in Rhomborhina Gigantea beetle

Suet Ying Ching, Guixin Li, Hoi Lam Tam, David T. P. Goh, Joseph K. L. Goh, and Kok Wai Cheah
Opt. Mater. Express 4(11) 2340-2345 (2014)

Visible light reflection spectra from cuticle layered materials

Cristian Campos-Fernández, Daniel E. Azofeifa, Marcela Hernández-Jiménez, Adams Ruiz-Ruiz, and William E. Vargas
Opt. Mater. Express 1(1) 85-100 (2011)

Retrieval of relevant parameters of natural multilayer systems by means of bio-inspired optimization strategies

Demetrio Macías, Ana Luna, Diana Skigin, Marina Inchaussandague, Alexandre Vial, and Daniel Schinca
Appl. Opt. 52(11) 2511-2520 (2013)

References

  • View by:
  • |
  • |
  • |

  1. S. Johnsen, The Optics of Life: A Biologist’s Guide to Light in Nature (Princeton University, 2012).
  2. S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, 2008).
  3. M. F. Land, Prog. Biophys. Mol. Biol. 24, 75 (1972).
    [Crossref]
  4. P. Vukusic and J. R. Sambles, Nature 424, 852 (2003).
    [Crossref]
  5. L. Biró and J. Vigneron, Laser Photon. Rev. 5, 27 (2011).
    [Crossref]
  6. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).
  7. D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, Philos. Trans. R. Soc. Lond. B 366, 709 (2011).
    [Crossref]
  8. A. Amir and P. Vukusic, Am. J. Phys. 81, 253 (2013).
    [Crossref]
  9. A. R. Parker, D. R. McKenzie, and M. C. Large, J. Exp. Biol. 201, 1307 (1998).
  10. D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
    [Crossref]
  11. W. H. Miller and G. D. Bernard, J. Ultrastruct. Res. 24, 286 (1968).
    [Crossref]
  12. T. Labhart, F. Baumann, and G. D. Bernard, Cell Tissue Res. 338, 391 (2009).
    [Crossref]
  13. D. G. Stavenga, J. Exp. Biol. 205, 1077 (2002).
  14. C. Campos-Fernández, D. E. Azofeifa, M. Hernández-Jiménez, A. Ruiz-Ruiz, and W. E. Vargas, Opt. Mater. Express 1, 85 (2011).
    [Crossref]
  15. S. Nishida, S. Ohtsuka, and A. R. Parker, Mar. Ecol. Prog. Ser. 227, 157 (2002).
    [Crossref]
  16. K. Yu, T. Fan, S. Lou, and D. Zhang, Prog. Mater. Sci. 58, 825 (2013).
    [Crossref]
  17. N. Matuschek, F. X. Kartner, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 197 (1998).
    [Crossref]
  18. T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
    [Crossref]
  19. F. Abelés, Ann. Phys. 5, 596 (1950).
  20. B. D. Wilts, T. M. Trzeciak, P. Vukusic, and D. G. Stavenga, J. Exp. Biol. 215, 796 (2012).
    [Crossref]
  21. S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
    [Crossref]
  22. S. Caveney, Proc. R. Soc. Lond. B 178, 205 (1971).
  23. E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
    [Crossref]
  24. M. Arildsen and A. Amir, “Chiral broadband reflectors in biology,” in preparation.
  25. R. B. Dingle and G. J. Morgan, Appl. Sci. Res. 18, 221 (1968).
    [Crossref]
  26. E. Merzbacher, Quantum Mechanics, 3rd ed. (Wiley, 1998).
  27. A. R. Parker, in Proceedings of the Fourth International Crustacean Congress (1999), pp. 879–887.
  28. A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
    [Crossref]
  29. S. Yoshioka and S. Kinoshita, Phys. Rev. E 83, 051917 (2011).
    [Crossref]

2015 (1)

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

2014 (1)

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

2013 (2)

A. Amir and P. Vukusic, Am. J. Phys. 81, 253 (2013).
[Crossref]

K. Yu, T. Fan, S. Lou, and D. Zhang, Prog. Mater. Sci. 58, 825 (2013).
[Crossref]

2012 (2)

B. D. Wilts, T. M. Trzeciak, P. Vukusic, and D. G. Stavenga, J. Exp. Biol. 215, 796 (2012).
[Crossref]

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

2011 (4)

S. Yoshioka and S. Kinoshita, Phys. Rev. E 83, 051917 (2011).
[Crossref]

C. Campos-Fernández, D. E. Azofeifa, M. Hernández-Jiménez, A. Ruiz-Ruiz, and W. E. Vargas, Opt. Mater. Express 1, 85 (2011).
[Crossref]

L. Biró and J. Vigneron, Laser Photon. Rev. 5, 27 (2011).
[Crossref]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, Philos. Trans. R. Soc. Lond. B 366, 709 (2011).
[Crossref]

2009 (1)

T. Labhart, F. Baumann, and G. D. Bernard, Cell Tissue Res. 338, 391 (2009).
[Crossref]

2003 (2)

P. Vukusic and J. R. Sambles, Nature 424, 852 (2003).
[Crossref]

A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
[Crossref]

2002 (2)

D. G. Stavenga, J. Exp. Biol. 205, 1077 (2002).

S. Nishida, S. Ohtsuka, and A. R. Parker, Mar. Ecol. Prog. Ser. 227, 157 (2002).
[Crossref]

1998 (2)

N. Matuschek, F. X. Kartner, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 197 (1998).
[Crossref]

A. R. Parker, D. R. McKenzie, and M. C. Large, J. Exp. Biol. 201, 1307 (1998).

1997 (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[Crossref]

1972 (1)

M. F. Land, Prog. Biophys. Mol. Biol. 24, 75 (1972).
[Crossref]

1971 (1)

S. Caveney, Proc. R. Soc. Lond. B 178, 205 (1971).

1968 (2)

R. B. Dingle and G. J. Morgan, Appl. Sci. Res. 18, 221 (1968).
[Crossref]

W. H. Miller and G. D. Bernard, J. Ultrastruct. Res. 24, 286 (1968).
[Crossref]

1950 (1)

F. Abelés, Ann. Phys. 5, 596 (1950).

Abelés, F.

F. Abelés, Ann. Phys. 5, 596 (1950).

Amir, A.

A. Amir and P. Vukusic, Am. J. Phys. 81, 253 (2013).
[Crossref]

M. Arildsen and A. Amir, “Chiral broadband reflectors in biology,” in preparation.

Arce-Marenco, L.

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

Arildsen, M.

M. Arildsen and A. Amir, “Chiral broadband reflectors in biology,” in preparation.

Azofeifa, D. E.

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

C. Campos-Fernández, D. E. Azofeifa, M. Hernández-Jiménez, A. Ruiz-Ruiz, and W. E. Vargas, Opt. Mater. Express 1, 85 (2011).
[Crossref]

Barboza-Aguilar, C.

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

Baumann, F.

T. Labhart, F. Baumann, and G. D. Bernard, Cell Tissue Res. 338, 391 (2009).
[Crossref]

Baumberg, J. J.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Bernard, G. D.

T. Labhart, F. Baumann, and G. D. Bernard, Cell Tissue Res. 338, 391 (2009).
[Crossref]

A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
[Crossref]

W. H. Miller and G. D. Bernard, J. Ultrastruct. Res. 24, 286 (1968).
[Crossref]

Biró, L.

L. Biró and J. Vigneron, Laser Photon. Rev. 5, 27 (2011).
[Crossref]

Briscoe, A. D.

A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
[Crossref]

Campos-Fernández, C.

Caveney, S.

S. Caveney, Proc. R. Soc. Lond. B 178, 205 (1971).

Dingle, R. B.

R. B. Dingle and G. J. Morgan, Appl. Sci. Res. 18, 221 (1968).
[Crossref]

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[Crossref]

Faden, R. B.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Fan, T.

K. Yu, T. Fan, S. Lou, and D. Zhang, Prog. Mater. Sci. 58, 825 (2013).
[Crossref]

García-Aguilar, I.

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

Glover, B. J.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Hariyama, T.

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, Philos. Trans. R. Soc. Lond. B 366, 709 (2011).
[Crossref]

Hernández, A.

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

Hernández-Jiménez, M.

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

C. Campos-Fernández, D. E. Azofeifa, M. Hernández-Jiménez, A. Ruiz-Ruiz, and W. E. Vargas, Opt. Mater. Express 1, 85 (2011).
[Crossref]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Johnsen, S.

S. Johnsen, The Optics of Life: A Biologist’s Guide to Light in Nature (Princeton University, 2012).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Kartner, F. X.

N. Matuschek, F. X. Kartner, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 197 (1998).
[Crossref]

Keller, U.

N. Matuschek, F. X. Kartner, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 197 (1998).
[Crossref]

Kinoshita, S.

S. Yoshioka and S. Kinoshita, Phys. Rev. E 83, 051917 (2011).
[Crossref]

S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, 2008).

Labhart, T.

T. Labhart, F. Baumann, and G. D. Bernard, Cell Tissue Res. 338, 391 (2009).
[Crossref]

Land, M. F.

M. F. Land, Prog. Biophys. Mol. Biol. 24, 75 (1972).
[Crossref]

Large, M. C.

A. R. Parker, D. R. McKenzie, and M. C. Large, J. Exp. Biol. 201, 1307 (1998).

Leertouwer, H. L.

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, Philos. Trans. R. Soc. Lond. B 366, 709 (2011).
[Crossref]

Libby, E.

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

Lou, S.

K. Yu, T. Fan, S. Lou, and D. Zhang, Prog. Mater. Sci. 58, 825 (2013).
[Crossref]

Matuschek, N.

N. Matuschek, F. X. Kartner, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 197 (1998).
[Crossref]

McKenzie, D. R.

A. R. Parker, D. R. McKenzie, and M. C. Large, J. Exp. Biol. 201, 1307 (1998).

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Merzbacher, E.

E. Merzbacher, Quantum Mechanics, 3rd ed. (Wiley, 1998).

Miller, W. H.

W. H. Miller and G. D. Bernard, J. Ultrastruct. Res. 24, 286 (1968).
[Crossref]

Morgan, G. J.

R. B. Dingle and G. J. Morgan, Appl. Sci. Res. 18, 221 (1968).
[Crossref]

Moyroud, E.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Nagy, L. M.

A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
[Crossref]

Nishida, S.

S. Nishida, S. Ohtsuka, and A. R. Parker, Mar. Ecol. Prog. Ser. 227, 157 (2002).
[Crossref]

Ohtsuka, S.

S. Nishida, S. Ohtsuka, and A. R. Parker, Mar. Ecol. Prog. Ser. 227, 157 (2002).
[Crossref]

Parker, A. R.

S. Nishida, S. Ohtsuka, and A. R. Parker, Mar. Ecol. Prog. Ser. 227, 157 (2002).
[Crossref]

A. R. Parker, D. R. McKenzie, and M. C. Large, J. Exp. Biol. 201, 1307 (1998).

A. R. Parker, in Proceedings of the Fourth International Crustacean Congress (1999), pp. 879–887.

Reed, A.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Rowland, A. V.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Rudall, P. J.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Ruiz-Ruiz, A.

Sambles, J. R.

P. Vukusic and J. R. Sambles, Nature 424, 852 (2003).
[Crossref]

Solís, A.

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

Sols, A.

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

Stavenga, D. G.

B. D. Wilts, T. M. Trzeciak, P. Vukusic, and D. G. Stavenga, J. Exp. Biol. 215, 796 (2012).
[Crossref]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, Philos. Trans. R. Soc. Lond. B 366, 709 (2011).
[Crossref]

D. G. Stavenga, J. Exp. Biol. 205, 1077 (2002).

Steiner, U.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Szeto, A. S.

A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
[Crossref]

Trzeciak, T. M.

B. D. Wilts, T. M. Trzeciak, P. Vukusic, and D. G. Stavenga, J. Exp. Biol. 215, 796 (2012).
[Crossref]

Vargas, W. E.

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

C. Campos-Fernández, D. E. Azofeifa, M. Hernández-Jiménez, A. Ruiz-Ruiz, and W. E. Vargas, Opt. Mater. Express 1, 85 (2011).
[Crossref]

Vigneron, J.

L. Biró and J. Vigneron, Laser Photon. Rev. 5, 27 (2011).
[Crossref]

Vignolini, S.

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Vukusic, P.

A. Amir and P. Vukusic, Am. J. Phys. 81, 253 (2013).
[Crossref]

B. D. Wilts, T. M. Trzeciak, P. Vukusic, and D. G. Stavenga, J. Exp. Biol. 215, 796 (2012).
[Crossref]

P. Vukusic and J. R. Sambles, Nature 424, 852 (2003).
[Crossref]

White, R. H.

A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
[Crossref]

Wilts, B. D.

B. D. Wilts, T. M. Trzeciak, P. Vukusic, and D. G. Stavenga, J. Exp. Biol. 215, 796 (2012).
[Crossref]

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, Philos. Trans. R. Soc. Lond. B 366, 709 (2011).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Yoshioka, S.

S. Yoshioka and S. Kinoshita, Phys. Rev. E 83, 051917 (2011).
[Crossref]

Yu, K.

K. Yu, T. Fan, S. Lou, and D. Zhang, Prog. Mater. Sci. 58, 825 (2013).
[Crossref]

Zhang, D.

K. Yu, T. Fan, S. Lou, and D. Zhang, Prog. Mater. Sci. 58, 825 (2013).
[Crossref]

Am. J. Phys. (1)

A. Amir and P. Vukusic, Am. J. Phys. 81, 253 (2013).
[Crossref]

Ann. Phys. (1)

F. Abelés, Ann. Phys. 5, 596 (1950).

Appl. Sci. Res. (1)

R. B. Dingle and G. J. Morgan, Appl. Sci. Res. 18, 221 (1968).
[Crossref]

Cell Tissue Res. (1)

T. Labhart, F. Baumann, and G. D. Bernard, Cell Tissue Res. 338, 391 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

N. Matuschek, F. X. Kartner, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 197 (1998).
[Crossref]

J. Comp. Neurol. (1)

A. D. Briscoe, G. D. Bernard, A. S. Szeto, L. M. Nagy, and R. H. White, J. Comp. Neurol. 458, 334 (2003).
[Crossref]

J. Exp. Biol. (3)

B. D. Wilts, T. M. Trzeciak, P. Vukusic, and D. G. Stavenga, J. Exp. Biol. 215, 796 (2012).
[Crossref]

D. G. Stavenga, J. Exp. Biol. 205, 1077 (2002).

A. R. Parker, D. R. McKenzie, and M. C. Large, J. Exp. Biol. 201, 1307 (1998).

J. Lightwave Technol. (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[Crossref]

J. Opt. (1)

E. Libby, D. E. Azofeifa, M. Hernández-Jiménez, C. Barboza-Aguilar, A. Solís, I. García-Aguilar, L. Arce-Marenco, A. Hernández, and W. E. Vargas, J. Opt. 16, 082001 (2014).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

D. E. Azofeifa, M. Hernández-Jiménez, E. Libby, A. Sols, C. Barboza-Aguilar, and W. E. Vargas, J. Quant. Spectrosc. Radiat. Transfer 160, 63 (2015).
[Crossref]

J. Ultrastruct. Res. (1)

W. H. Miller and G. D. Bernard, J. Ultrastruct. Res. 24, 286 (1968).
[Crossref]

Laser Photon. Rev. (1)

L. Biró and J. Vigneron, Laser Photon. Rev. 5, 27 (2011).
[Crossref]

Mar. Ecol. Prog. Ser. (1)

S. Nishida, S. Ohtsuka, and A. R. Parker, Mar. Ecol. Prog. Ser. 227, 157 (2002).
[Crossref]

Nature (1)

P. Vukusic and J. R. Sambles, Nature 424, 852 (2003).
[Crossref]

Opt. Mater. Express (1)

Philos. Trans. R. Soc. Lond. B (1)

D. G. Stavenga, B. D. Wilts, H. L. Leertouwer, and T. Hariyama, Philos. Trans. R. Soc. Lond. B 366, 709 (2011).
[Crossref]

Phys. Rev. E (1)

S. Yoshioka and S. Kinoshita, Phys. Rev. E 83, 051917 (2011).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

S. Vignolini, P. J. Rudall, A. V. Rowland, A. Reed, E. Moyroud, R. B. Faden, J. J. Baumberg, B. J. Glover, and U. Steiner, Proc. Natl. Acad. Sci. USA 109, 15712 (2012).
[Crossref]

Proc. R. Soc. Lond. B (1)

S. Caveney, Proc. R. Soc. Lond. B 178, 205 (1971).

Prog. Biophys. Mol. Biol. (1)

M. F. Land, Prog. Biophys. Mol. Biol. 24, 75 (1972).
[Crossref]

Prog. Mater. Sci. (1)

K. Yu, T. Fan, S. Lou, and D. Zhang, Prog. Mater. Sci. 58, 825 (2013).
[Crossref]

Other (6)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

S. Johnsen, The Optics of Life: A Biologist’s Guide to Light in Nature (Princeton University, 2012).

S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, 2008).

M. Arildsen and A. Amir, “Chiral broadband reflectors in biology,” in preparation.

E. Merzbacher, Quantum Mechanics, 3rd ed. (Wiley, 1998).

A. R. Parker, in Proceedings of the Fourth International Crustacean Congress (1999), pp. 879–887.

Supplementary Material (1)

NameDescription
» Supplement 1: PDF (803 KB)      Supplementary Materials

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. C. limbata (left) and C. aurigans (right) displaying brilliant silver and gold color, respectively, due to reflection from ACPCs in their elytra. Figure adapted from Ref. [14].
Fig. 2.
Fig. 2. Top: TEM image of an ACPC in the eye of the crustacean C. refulgens, taken from Ref. [15]. Stained regions show layers, each on the order of 100 nm thick, of differing refractive index. Bottom: Our model ACPC. Adiabatic chirp requires that the optical thicknesses m vary slowly. The forward- and backward-propagating fields E m ± are also shown, with a light-scattering and absorptive layer at the back enforcing E N = 0 .
Fig. 3.
Fig. 3. Plot of the stopband potential Tr [ F ( x ) ] 2 and its quadratic expansion about x = Ξ = 1 and ρ = 0 in the quantum scattering analogy (detailed in Section 2 of Supplement 1). The regions of validity for various approximate expressions for E m ± are sketched. The WKB matching formulae (derived in Section 3 of Supplement 1) relate the pre-stopband coefficients A , B and the post-stopband coefficients F , G in the mBloch wave solution [Eq. (3)].
Fig. 4.
Fig. 4. Exponentially chirped multilayer with n L = 1.34 , n H = 1.54 , and Ξ = 1 . A comparison between the numerically exact transfer matrix (red), first-order WKB [Supplement 1, Eq. (S18), blue], and zeroth-order WKB [Eq. (6), dashed] spectra is shown.
Fig. 5.
Fig. 5. An ACPC with a designed average reflectance spectrum. The desired spectrum (red) is put into the chirp differential equation (7) with n H = 1.54 and n L = 1.34 , which is solved numerically to give the chirp function m plotted in the inset (green). The resulting exact reflectance (blue) of the computed chirp m is then found numerically via transfer matrices and plotted against the desired spectrum.

Tables (1)

Tables Icon

Table 1. Comparison Between the Bilayer Number N Found in Biological ACPCs and Our Predicted Minimal Number (8)a

Equations (8)

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

E m = F m ( λ )    E m + 1 .
F ( x ) = 1 1 ρ 2 [ e i π x ρ 2 e i π ( 1 Ξ 1 + Ξ ) x 2 i ρ e i π ( Ξ 1 + Ξ ) x 2 i ρ e i π ( Ξ 1 + Ξ ) x e i π x ρ 2 e i π ( 1 Ξ 1 + Ξ ) x ] ,
E m = C + exp [ i m m t ϕ k d k ] w m + + C exp [ i m t m ϕ k d k ] w m ,
E m + 1 ± Tr ( F m ) E m ± E m 1 ± ,
γ ( λ ) = m 1 ( λ ) m 2 ( λ ) cosh 1 { Tr [ F m ( λ ) ] 2 } d m λ q ( λ ) sin 2 ( π 1 + Ξ ) ρ 2 + O ( ρ 3 ) ,
R ˜ ( λ ) = 1 exp [ 2 γ ( λ ) ] ,
d d m = 4 ρ 2 sin 2 ( π 1 + Ξ ) log [ 1 R ˜ ( λ = 2 ( 1 + Ξ ) ) ] .
N = log ( 1 1 R ˜ ) 4 ρ 2 sin 2 ( π 1 + Ξ ) × { log ( λ max / λ min ) , ( exponential ) λ max / λ min 1 , ( linear ) .

Metrics