Abstract

We demonstrate that a series of one-dimensional photonic crystals made of any dielectric materials, with the periods are distributed in a geometrical progression of a common ratio, r<rc (θ,P), where rc is a structural parameter that depends on the angle of incidence, θ, and polarization, P, is capable of blocking light of any spectral range. If an omni-directional reflection is desired for all polarizations and for all incident angles smaller than θo, then r<rc (θo,p), where p is the polarization with the electric field parallel to the plane of incidence. We present simple and formula like expressions for rc, width of the bandgap, and minimum number of photonic crystals to achieve a perfect light reflection.

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2009

W. C. Tan, S. Kobayashi, T. Aoki, R. E. Johanson, and S. O. Kasap, “Optical properties of amorphous silicon nitride thin-films prepared by VHF-PECVD using silane and nitrogen,” J. Mater. Sci. Mater. Electron. 20(S1), 15–18 (2009).
[CrossRef]

2008

2007

2006

2003

B. Huang, P. Gu, and L. Yang, “Construction of one-dimensional photonic crystals based on the incident angle domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(4 Pt 2), 046601 (2003).
[CrossRef]

2002

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (2002).
[CrossRef]

2000

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).

1998

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23(20), 1573–1575 (1998).
[CrossRef]

1994

1977

Alagappan, G.

Aoki, T.

W. C. Tan, S. Kobayashi, T. Aoki, R. E. Johanson, and S. O. Kasap, “Optical properties of amorphous silicon nitride thin-films prepared by VHF-PECVD using silane and nitrogen,” J. Mater. Sci. Mater. Electron. 20(S1), 15–18 (2009).
[CrossRef]

Barriuso, A. G.

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).

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(5394), 1679–1682 (1998).
[CrossRef]

DeCorby, R. G.

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).

Doan, M. T.

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(5394), 1679–1682 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23(20), 1573–1575 (1998).
[CrossRef]

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(5394), 1679–1682 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23(20), 1573–1575 (1998).
[CrossRef]

Gu, P.

B. Huang, P. Gu, and L. Yang, “Construction of one-dimensional photonic crystals based on the incident angle domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(4 Pt 2), 046601 (2003).
[CrossRef]

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).

Hu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (2002).
[CrossRef]

Huang, B.

B. Huang, P. Gu, and L. Yang, “Construction of one-dimensional photonic crystals based on the incident angle domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(4 Pt 2), 046601 (2003).
[CrossRef]

Jia, W.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (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(5394), 1679–1682 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23(20), 1573–1575 (1998).
[CrossRef]

Johanson, R. E.

W. C. Tan, S. Kobayashi, T. Aoki, R. E. Johanson, and S. O. Kasap, “Optical properties of amorphous silicon nitride thin-films prepared by VHF-PECVD using silane and nitrogen,” J. Mater. Sci. Mater. Electron. 20(S1), 15–18 (2009).
[CrossRef]

Kasap, S. O.

W. C. Tan, S. Kobayashi, T. Aoki, R. E. Johanson, and S. O. Kasap, “Optical properties of amorphous silicon nitride thin-films prepared by VHF-PECVD using silane and nitrogen,” J. Mater. Sci. Mater. Electron. 20(S1), 15–18 (2009).
[CrossRef]

Kobayashi, S.

W. C. Tan, S. Kobayashi, T. Aoki, R. E. Johanson, and S. O. Kasap, “Optical properties of amorphous silicon nitride thin-films prepared by VHF-PECVD using silane and nitrogen,” J. Mater. Sci. Mater. Electron. 20(S1), 15–18 (2009).
[CrossRef]

Lekner, J.

Li, Y.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (2002).
[CrossRef]

Liu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (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(5394), 1679–1682 (1998).
[CrossRef]

Monzón, J. J.

Ponnampalam, N.

Sánchez-Soto, L. L.

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).

Shum, P.

Sun, X. W.

Tan, W. C.

W. C. Tan, S. Kobayashi, T. Aoki, R. E. Johanson, and S. O. Kasap, “Optical properties of amorphous silicon nitride thin-films prepared by VHF-PECVD using silane and nitrogen,” J. Mater. Sci. Mater. Electron. 20(S1), 15–18 (2009).
[CrossRef]

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(5394), 1679–1682 (1998).
[CrossRef]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).

Wang, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (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(5394), 1679–1682 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23(20), 1573–1575 (1998).
[CrossRef]

Xu, C.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (2002).
[CrossRef]

Yang, L.

B. Huang, P. Gu, and L. Yang, “Construction of one-dimensional photonic crystals based on the incident angle domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(4 Pt 2), 046601 (2003).
[CrossRef]

Yariv, A.

Yeh, P.

Yu, M. B.

Zi, J.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one dimensional photonic crystals by using photonic hetero-structures,” Appl. Phys. Lett. 80(23), 4291–4293 (2002).
[CrossRef]

J. Mater. Sci. Mater. Electron.

W. C. Tan, S. Kobayashi, T. Aoki, R. E. Johanson, and S. O. Kasap, “Optical properties of amorphous silicon nitride thin-films prepared by VHF-PECVD using silane and nitrogen,” J. Mater. Sci. Mater. Electron. 20(S1), 15–18 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).

Opt. Lett.

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

B. Huang, P. Gu, and L. Yang, “Construction of one-dimensional photonic crystals based on the incident angle domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(4 Pt 2), 046601 (2003).
[CrossRef]

Science

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998).
[CrossRef]

Other

R. W. Waynant, Electro-Optics Handbook (McGraw-Hill, 2000).

J. D. Joannopoulus, R. D. Meade, and J. N. Winn, Photonic Crystals Molding the Flow of Light (Princeton, 1995).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

V. G. Dmitriev, G. Gurzadayan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997).

M. Born, and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon Press Ltd., 1999).
[PubMed]

J. Asmussen, and D. K. Reinhard, Diamond Films Handbook (Marcel Dekker Inc., 2002).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the hetero-structure with m number of 1D PCs.

Fig. 2.
Fig. 2.

Transmission spectrums of hetero-structures (blue curves) with n 1=1.45, n 2=1.8, θ=0, N=12, p 1=125 nm and (a) m=6 (b) m=8 (c) m=16. The green curve in (a) represents the transmission spectrum of an uniform 1D PC with n 1=1.45, n 2=1.8, N=12 and θ=0.

Fig. 3.
Fig. 3.

Transmission spectrums for θ=0, 30°, 45°, 60°, 75°, and 85° for a hetero-structure with n 1=1.45, n 2=2.4, m=6, p 1=130 nm, and N=12. The blue and red curves represent the transmissions for p- and s-polarizations of light. When θ=0, the transmission curves of both polarizations are identical.

Fig. 4.
Fig. 4.

(a) Refractive index dispersions of silica [8], amorphous silicon nitride (a-Si0.44N0.56) [15] and diamond [14]. (b) Transmission spectrums with the same parameters as in Fig. 3 but with the refractive index dispersions of silica and diamond included [dark green curve] and excluded [red curve].

Fig. 5.
Fig. 5.

Angle averaged reflectance spectrums for a hetero-structure with parameters as in Fig. 3 with the refractive index dispersion [Fig. 4(a)] included [red curves] and excluded [blue curves]. (a) s - polarization. (b) p - polarization.

Tables (2)

Tables Icon

Table 1. - The values of n1, n2, rc (θo, p), p1, pm , and m to achieve omni-directional bandgaps (θo =90°) in the spectral range from 200 nm to 400 nm. In all material systems, the light line is above the point, where the bandgap of p-polarization vanishes.

Tables Icon

Table 2. - The values of n 1, n 2, rc (θo, p), p 1, pm , and m to achieve omni-directional bandgaps (θo =90°) in the spectral range from 380 nm to 780 nm. In all material systems, the light line is above the point, where the bandgap of p-polarization vanishes.

Equations (8)

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

ωc (θ=0) =n1+n24n1n2 ,
gn (θ=0) =Δωωc =4π sin1 n2n1n2+n1 .
1λ,k =ωcpk (1gn2) .
λ+,k1 >λ,k .
rc =pkpk1=1+gn/21gn/2.
g=gp+gn1+gpgn/4 ,
m>ln(pm/p1)ln(rc) +1gpgn +1.
drcθPdgnθP =2[1gnθP/2]2>0.

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