Abstract

By using the notion of wavelength- and angle-averaged reflectance, we assess in a systematic way the performance of finite omnidirectional reflectors. We put forward how this concept can be employed to optimize omnidirectional capabilities. We also apply it to give an alternative meaningful characterization of the bandwidth of these systems.

© 2007 Optical Society of America

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References

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  1. J. P. Dowling, "Photonic and sonic band-gap bibliography," http://baton.phys.lsu.edu/ jdowling/pbgbib.html.
  2. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  3. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2468-2469 (1987).
    [CrossRef]
  4. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
    [CrossRef] [PubMed]
  5. J. P. Dowling, "Mirror on the wall: you're omnidirectional after all?" Science 282, 1841-1842 (1998).
    [CrossRef]
  6. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
    [CrossRef]
  7. N. H. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543-3547 (1997).
    [CrossRef]
  8. E. Maciá, "Optical engineering with Fibonacci dielectric multilayers," Appl. Phys. Lett. 73, 3330-3332 (1998).
    [CrossRef]
  9. E. Cojocaru, "Forbidden gaps in finite periodic and quasi-periodic Cantor-like dielectric multilayers at normal incidence," Appl. Opt. 40, 6319-6326 (2001).
    [CrossRef]
  10. D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273-279 (2001).
    [CrossRef]
  11. R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
    [CrossRef]
  12. J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
    [CrossRef]
  13. W. H. Southwell, "Omnidirectional mirror design with quarter-wave dielectric stacks," Appl. Opt. 38, 5464-5467 (1999).
    [CrossRef]
  14. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol. 17, 2018-2024 (1999).
    [CrossRef]
  15. J. Lekner, "Omnidirectional reflection by multilayer dielectric mirrors," J. Opt. A 2, 349-353 (2000).
    [CrossRef]
  16. J. Lekner, "Light in periodically stratified media," J. Opt. Soc. Am. A 11, 2892-2899 (1994).
    [CrossRef]
  17. D. Lusk and F. Placido, "Omnidirectional mirror coating design for infrared applications," Thin Solid Films 492, 226-231 (2005).
    [CrossRef]
  18. M. D. Huang, S. Y. Park, Y. P. Lee, and K. W. Kim, "Simulation of the reflectivity of one-dimensional photonic crystals made of Ti2O3 and Al2O3 films," J. Korean Phys. Soc. 47, 964-969 (2005).
  19. http://www.sspectra.com/designs/omnirefl.html.
  20. T. Yonte, J. J. Monzón, A. Felipe, and L. L. Sánchez-Soto, "Optimizing omnidirectional reflection by multilayer mirrors," J. Opt. A 6, 127-131 (2004).
    [CrossRef]
  21. A. G. Barriuso, J. J. Monzón, L. L. Sánchez-Soto, and A. Felipe, "Comparing omnidirectional reflection from periodic and quasi-periodic one-dimensional photonic crystals," Opt. Express 13, 3913-3920 (2005).
    [CrossRef] [PubMed]
  22. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  23. J. Lekner, Theory of Reflection (Kluwer Academic, 1987).
  24. D. T. F. Marple, "Refractive index of ZnSe, ZnTe, and CdTe," J. Appl. Phys. 35, 539-542 (1964).
    [CrossRef]
  25. 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, 5493-5506 (1996).
    [CrossRef] [PubMed]
  26. J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, "Merit functions for more effective thin film calculations," Appl. Opt. 28, 2824-2831 (1989).
    [CrossRef] [PubMed]
  27. To ensure the reproducibility of our results, we quote here the optimum thicknesses (expressed in nm). For the [LH]20 they are dL = 144 and dH = 59. When all of them are different, we have, for the L medium, 190, 111, 184, 99, 164, 145, 173, 180, 118, 132, 143, 134, 193, 101, 155, 122, 100, 165, 91, and 110. For the H medium they are 58, 141, 92, 140, 54, 122, 88, 71, 79, 46, 47, 72, 125, 143, 87, 112, 106, 59, 120, and 116.
  28. S. J. Orfanidis, Electromagnetic Waves and Antennas (http://www.ece.rutgers.edu/orfanidi/ewa/), Chap. 7.

2005 (3)

D. Lusk and F. Placido, "Omnidirectional mirror coating design for infrared applications," Thin Solid Films 492, 226-231 (2005).
[CrossRef]

M. D. Huang, S. Y. Park, Y. P. Lee, and K. W. Kim, "Simulation of the reflectivity of one-dimensional photonic crystals made of Ti2O3 and Al2O3 films," J. Korean Phys. Soc. 47, 964-969 (2005).

A. G. Barriuso, J. J. Monzón, L. L. Sánchez-Soto, and A. Felipe, "Comparing omnidirectional reflection from periodic and quasi-periodic one-dimensional photonic crystals," Opt. Express 13, 3913-3920 (2005).
[CrossRef] [PubMed]

2004 (1)

T. Yonte, J. J. Monzón, A. Felipe, and L. L. Sánchez-Soto, "Optimizing omnidirectional reflection by multilayer mirrors," J. Opt. A 6, 127-131 (2004).
[CrossRef]

2003 (1)

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

2002 (1)

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

2001 (2)

E. Cojocaru, "Forbidden gaps in finite periodic and quasi-periodic Cantor-like dielectric multilayers at normal incidence," Appl. Opt. 40, 6319-6326 (2001).
[CrossRef]

D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273-279 (2001).
[CrossRef]

2000 (1)

J. Lekner, "Omnidirectional reflection by multilayer dielectric mirrors," J. Opt. A 2, 349-353 (2000).
[CrossRef]

1999 (3)

1998 (3)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

J. P. Dowling, "Mirror on the wall: you're omnidirectional after all?" Science 282, 1841-1842 (1998).
[CrossRef]

E. Maciá, "Optical engineering with Fibonacci dielectric multilayers," Appl. Phys. Lett. 73, 3330-3332 (1998).
[CrossRef]

1997 (1)

N. H. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543-3547 (1997).
[CrossRef]

1996 (1)

1994 (1)

1989 (1)

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2468-2469 (1987).
[CrossRef]

1964 (1)

D. T. F. Marple, "Refractive index of ZnSe, ZnTe, and CdTe," J. Appl. Phys. 35, 539-542 (1964).
[CrossRef]

Abdulhalim, I.

D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273-279 (2001).
[CrossRef]

Barriuso, A. G.

Belkind, A.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol. 17, 2018-2024 (1999).
[CrossRef]

Cojocaru, E.

DeBell, G. W.

Dobrowolski, J. A.

Dong, J. W.

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

Dowling, J. P.

J. P. Dowling, "Mirror on the wall: you're omnidirectional after all?" Science 282, 1841-1842 (1998).
[CrossRef]

J. P. Dowling, "Photonic and sonic band-gap bibliography," http://baton.phys.lsu.edu/ jdowling/pbgbib.html.

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Felipe, A.

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol. 17, 2018-2024 (1999).
[CrossRef]

Han, P.

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

Ho, F. C.

Hu, A.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Huang, M. D.

M. D. Huang, S. Y. Park, Y. P. Lee, and K. W. Kim, "Simulation of the reflectivity of one-dimensional photonic crystals made of Ti2O3 and Al2O3 films," J. Korean Phys. Soc. 47, 964-969 (2005).

Huang, X. Q.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Jiang, S. S.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2468-2469 (1987).
[CrossRef]

Kim, K. W.

M. D. Huang, S. Y. Park, Y. P. Lee, and K. W. Kim, "Simulation of the reflectivity of one-dimensional photonic crystals made of Ti2O3 and Al2O3 films," J. Korean Phys. Soc. 47, 964-969 (2005).

Koss, V. A.

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol. 17, 2018-2024 (1999).
[CrossRef]

Lee, Y. P.

M. D. Huang, S. Y. Park, Y. P. Lee, and K. W. Kim, "Simulation of the reflectivity of one-dimensional photonic crystals made of Ti2O3 and Al2O3 films," J. Korean Phys. Soc. 47, 964-969 (2005).

Lekner, J.

J. Lekner, "Omnidirectional reflection by multilayer dielectric mirrors," J. Opt. A 2, 349-353 (2000).
[CrossRef]

J. Lekner, "Light in periodically stratified media," J. Opt. Soc. Am. A 11, 2892-2899 (1994).
[CrossRef]

J. Lekner, Theory of Reflection (Kluwer Academic, 1987).

Liu, N. H.

N. H. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543-3547 (1997).
[CrossRef]

Lusk, D.

D. Lusk and F. Placido, "Omnidirectional mirror coating design for infrared applications," Thin Solid Films 492, 226-231 (2005).
[CrossRef]

D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273-279 (2001).
[CrossRef]

Maciá, E.

E. Maciá, "Optical engineering with Fibonacci dielectric multilayers," Appl. Phys. Lett. 73, 3330-3332 (1998).
[CrossRef]

Marple, D. T. F.

D. T. F. Marple, "Refractive index of ZnSe, ZnTe, and CdTe," J. Appl. Phys. 35, 539-542 (1964).
[CrossRef]

Mazzer, M.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Monzón, J. J.

Orfanidis, S. J.

S. J. Orfanidis, Electromagnetic Waves and Antennas (http://www.ece.rutgers.edu/orfanidi/ewa/), Chap. 7.

Park, S. Y.

M. D. Huang, S. Y. Park, Y. P. Lee, and K. W. Kim, "Simulation of the reflectivity of one-dimensional photonic crystals made of Ti2O3 and Al2O3 films," J. Korean Phys. Soc. 47, 964-969 (2005).

Peng, R. W.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Placido, F.

D. Lusk and F. Placido, "Omnidirectional mirror coating design for infrared applications," Thin Solid Films 492, 226-231 (2005).
[CrossRef]

D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273-279 (2001).
[CrossRef]

Qiu, F.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Sánchez-Soto, L. L.

Southwell, W. H.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Tikhonravov, A. V.

Trubetskov, M. K.

Wang, H. Z.

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

Wang, M.

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control," J. Lightwave Technol. 17, 2018-2024 (1999).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Yonte, T.

T. Yonte, J. J. Monzón, A. Felipe, and L. L. Sánchez-Soto, "Optimizing omnidirectional reflection by multilayer mirrors," J. Opt. A 6, 127-131 (2004).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. A (1)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

E. Maciá, "Optical engineering with Fibonacci dielectric multilayers," Appl. Phys. Lett. 73, 3330-3332 (1998).
[CrossRef]

R. W. Peng, X. Q. Huang, F. Qiu, M. Wang, A. Hu, S. S. Jiang, and M. Mazzer, "Symmetry-induced perfect transmission of light waves in quasi-periodic dielectric multilayers," Appl. Phys. Lett. 80, 3063-3065 (2002).
[CrossRef]

Chin. Phys. Lett. (1)

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

J. Appl. Phys. (1)

D. T. F. Marple, "Refractive index of ZnSe, ZnTe, and CdTe," J. Appl. Phys. 35, 539-542 (1964).
[CrossRef]

J. Korean Phys. Soc. (1)

M. D. Huang, S. Y. Park, Y. P. Lee, and K. W. Kim, "Simulation of the reflectivity of one-dimensional photonic crystals made of Ti2O3 and Al2O3 films," J. Korean Phys. Soc. 47, 964-969 (2005).

J. Lightwave Technol. (1)

J. Opt. A (2)

J. Lekner, "Omnidirectional reflection by multilayer dielectric mirrors," J. Opt. A 2, 349-353 (2000).
[CrossRef]

T. Yonte, J. J. Monzón, A. Felipe, and L. L. Sánchez-Soto, "Optimizing omnidirectional reflection by multilayer mirrors," J. Opt. A 6, 127-131 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273-279 (2001).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

N. H. Liu, "Propagation of light waves in Thue-Morse dielectric multilayers," Phys. Rev. B 55, 3543-3547 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2468-2469 (1987).
[CrossRef]

Science (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

J. P. Dowling, "Mirror on the wall: you're omnidirectional after all?" Science 282, 1841-1842 (1998).
[CrossRef]

Thin Solid Films (1)

D. Lusk and F. Placido, "Omnidirectional mirror coating design for infrared applications," Thin Solid Films 492, 226-231 (2005).
[CrossRef]

Other (6)

J. P. Dowling, "Photonic and sonic band-gap bibliography," http://baton.phys.lsu.edu/ jdowling/pbgbib.html.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

J. Lekner, Theory of Reflection (Kluwer Academic, 1987).

To ensure the reproducibility of our results, we quote here the optimum thicknesses (expressed in nm). For the [LH]20 they are dL = 144 and dH = 59. When all of them are different, we have, for the L medium, 190, 111, 184, 99, 164, 145, 173, 180, 118, 132, 143, 134, 193, 101, 155, 122, 100, 165, 91, and 110. For the H medium they are 58, 141, 92, 140, 54, 122, 88, 71, 79, 46, 47, 72, 125, 143, 87, 112, 106, 59, 120, and 116.

S. J. Orfanidis, Electromagnetic Waves and Antennas (http://www.ece.rutgers.edu/orfanidi/ewa/), Chap. 7.

http://www.sspectra.com/designs/omnirefl.html.

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Figures (4)

Fig. 1
Fig. 1

(Color online) Averaged reflectance ¯ ( N ) in terms of the number of periods for the optimized [ L H ] N systems (triangles) and for the same system when all the thicknesses can be different (circles). Solid curves represent the fittings to these points.

Fig. 2
Fig. 2

(Color online) Optimum thicknesses d L and d H (in nm) for a [ L H ] N system when the thicknesses can be different, with N = 5 , 10, 15, and 20.

Fig. 3
Fig. 3

(Color online) Plots of the reflectance ( 20 ) as a function of the incidence angle θ (in degrees) and the wavelength λ (in μm). In (a) we have the [ L H ] 20 system, while in (b) the thicknesses are allowed to be different. At the bottom plane, we show the contour plots corresponding to a reflectance 0.99. The white lines delimit the zones in which this reflectance is greater than 0.99 for all the angles of incidence.

Fig. 4
Fig. 4

(Color online) Angle-averaged reflectance in terms of the wavelength λ for the optimized [ L H ] 20 system (blue∕black) and for the analogous system with different thicknesses (red∕gray). The line of reflectance equal to 0.95 is also shown.

Equations (6)

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

| Tr ( M ) | 2.
¯ ( N ) = 1 Δ λ λ min λ max ( 2 π 0 π / 2 ( N ) d θ ) d λ ,
n H 2 ( λ ) = 4 + 1.9 λ 2 λ 2 ( 0.336 ) 2 ,
M F = λ min λ max W ( λ ) D 2 ( λ ) d λ ,
¯ ( N ) = 0.774 + 0.365 × 10 3 N ,
¯ ( N ) = 0.625 + 0.369 [ 1 exp ( 0.132 N ) ] .

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