Abstract

We demonstrate that one-dimensional photonic crystal structures (such as multilayer films) can exhibit complete reflection of radiation in a given frequency range for all incident angles and polarizations. We derive a general criterion for this behavior that does not require materials with very large indices. We perform numerical studies that illustrate this effect.

© 1998 Optical Society of America

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References

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  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (U. Princeton Press, Princeton, N.J., 1995).
  3. J. Pendry, J. Mod. Opt. 41, 209 (1994).
    [CrossRef]
  4. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
    [CrossRef]
  5. P. Baumeister, Opt. Acta 8, 105 (1961).
    [CrossRef]
  6. J. D. Rancourt, Optical Thin Films User Handbook (SPIE Optical Engineering Press, Bellingham, Wash., 1996), pp. 68–71.
  7. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 161–163.
  8. K. V. Popov, J. A. Dobrowolski, A. V. Tikhonravov, and B. T. Sullivan, Appl. Opt. 36, 2139 (1997).
    [CrossRef] [PubMed]
  9. M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
    [CrossRef]
  10. R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. B 77, 8434 (1993).
    [CrossRef]
  11. P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. 67, 423 (1977).
    [CrossRef]
  12. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), pp. 373–378.

1997 (2)

1994 (2)

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
[CrossRef]

J. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

1993 (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. B 77, 8434 (1993).
[CrossRef]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1977 (1)

1961 (1)

P. Baumeister, Opt. Acta 8, 105 (1961).
[CrossRef]

Baumeister, P.

P. Baumeister, Opt. Acta 8, 105 (1961).
[CrossRef]

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. B 77, 8434 (1993).
[CrossRef]

Dapkus, P. D.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
[CrossRef]

Dobrowolski, J. A.

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), pp. 373–378.

Hong, C.-S.

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. B 77, 8434 (1993).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (U. Princeton Press, Princeton, N.J., 1995).

MacDougal, M. H.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
[CrossRef]

Meade, R. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. B 77, 8434 (1993).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (U. Princeton Press, Princeton, N.J., 1995).

Pendry, J.

J. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

Popov, K. V.

Rancourt, J. D.

J. D. Rancourt, Optical Thin Films User Handbook (SPIE Optical Engineering Press, Bellingham, Wash., 1996), pp. 68–71.

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. B 77, 8434 (1993).
[CrossRef]

Steier, W. H.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
[CrossRef]

Sullivan, B. T.

Tikhonravov, A. V.

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (U. Princeton Press, Princeton, N.J., 1995).

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yariv, A.

Yeh, P.

P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. 67, 423 (1977).
[CrossRef]

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 161–163.

Zhao, H.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
[CrossRef]

Ziari, M.

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

M. H. MacDougal, H. Zhao, P. D. Dapkus, M. Ziari, and W. H. Steier, Electron. Lett. 30, 1147 (1994).
[CrossRef]

J. Mod. Opt. (1)

J. Pendry, J. Mod. Opt. 41, 209 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (London) (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

Opt. Acta (1)

P. Baumeister, Opt. Acta 8, 105 (1961).
[CrossRef]

Phys. Rev. B (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. B 77, 8434 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (U. Princeton Press, Princeton, N.J., 1995).

J. D. Rancourt, Optical Thin Films User Handbook (SPIE Optical Engineering Press, Bellingham, Wash., 1996), pp. 68–71.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 161–163.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), pp. 373–378.

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Figures (4)

Fig. 1
Fig. 1

Projected band structure for a quarter-wave stack with n1=1 and n2=2. Electromagnetic modes exist only in the shaded regions. The s-polarized modes are plotted to the right of the origin, and the p-polarized to the left. The dark lines are the light lines ω=ckx. Frequencies are reported in units of 2πc/a.

Fig. 2
Fig. 2

Projected band structure for a quarter-wave stack with n1=1.7 and n2=3.4, with the same conventions as in Fig.  1.

Fig. 3
Fig. 3

Calculated transmission spectra for a quarter-wave stack of ten films n1=1.7,n2=3.4 for three angles of incidence. Solid curves, p-polarized waves; dashed curves, s-polarized waves. The overlapping region of high reflectance >20 dB corresponds to the region between the open and filled circles of Fig.  2.

Fig. 4
Fig. 4

Range–midrange ratio for omnidirectional reflection, plotted as contours. For the solid contours the optimal value of d1/a was chosen. The dashed curve is the 0% contour for the case of a quarter-wave stack. For the general case of an ambient medium with index n01, the abscissa becomes n1/n0.

Equations (3)

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ωp1kx=ωp1c, ky=πa<ωp2kx=0,ky=πa,
Δω2c=a cos-A-2A+2d1n1+d2n2-a cos-B-2B+2d1n12-1+d2n22-1,
An2n1+n1n2,  Bn2n12-1n1n22-1+n1n22-1n2n12-1.

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