Abstract

We carried out a theoretical investigation on photonic bandgap (PBG) properties of one-dimensional photonic crystals (1D PCs) constructed by our periodically doping metal or semiconductor nanoparticles into polymers with a holographic interference technique. The results reveal not only that both the bandgap width and the midwavelength of the PBG are tunable by the choice of parameters of recording materials and exposure conditions but also that 1D PCs may show an omnidirectional PBG property if the doped nanoparticles are from a higher-refractive-index semiconductor material. Some realistic factors, such as the absorption (in the case of the doped nanoparticles that are from a metallic material) and instability of the holographic recording setup during the exposure process, are also theoretically demonstrated to have no serious bad effect on PBG properties of the 1D PCs fabricated by the method. Our conclusions may open up a robust way for one-step fabrications of three-dimensional PCs, omnidirectional 1D PCs, and other photonic devices by cheap, repeatable, and efficient holography.

© 2004 Optical Society of America

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References

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  3. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
    [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. D. Chigrin, A. Lavrinenko, D. Yarotsky, and S. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
    [CrossRef]
  6. W. H. Southwell, “Omnidirectional mirror design with quarter-wave dielectric stacks,” Appl. Opt. 38, 5464–5467 (1999).
    [CrossRef]
  7. E. Yablonovitch, “Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters,” Opt. Lett. 23, 1648–1649 (1998).
    [CrossRef]
  8. P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
    [CrossRef]
  9. H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
    [CrossRef]
  10. M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
    [CrossRef] [PubMed]
  11. I. Abdulhalim, “Omnidirectional reflection from anisotropic periodic dielectric stack,” Opt. Commun. 174, 43–50 (2000).
    [CrossRef]
  12. I. Abdulhalim, “Analytic propagation matrix method for anisotropic magneto-optic layered media,” J. Opt. A Pure Appl. Opt. 2, 557–564 (2000).
    [CrossRef]
  13. I. Abdulhalim, “Reflective phase-only modulation using one-dimensional photonic crystals,” J. Opt. A Pure Appl. Opt. 2, L9–L11 (2000).
    [CrossRef]
  14. H. M. Smith, Holographic Recording Materials (Springer-Verlag, New York, 1977).
  15. G. P. Wang, C. Tan, Y. Yi, and H. Shan, “Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals by using a single cw laser beam,” J. Mod. Opt. 50, 2155–2161 (2003).
    [CrossRef]
  16. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  17. L. Yuan, G. P. Wang, and X. K. Huang, “Arrangements of four beams for any Bravais lattice,” Opt. Lett. 28, 1769–1771 (2003).
    [CrossRef] [PubMed]
  18. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993), and references therein.
    [CrossRef] [PubMed]
  19. N. Suzuki, Y. Tomita, and T. Kojima, “Holographic recording in TiO2 nanoparticle-dispersed methacrylate photonpolymer films,” Appl. Phys. Lett. 81, 4121–4123 (2002).
    [CrossRef]
  20. Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
    [CrossRef] [PubMed]
  21. G. P. Wang and W. H. Lin, data available from the authors.

2003 (4)

H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
[CrossRef]

G. P. Wang, C. Tan, Y. Yi, and H. Shan, “Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals by using a single cw laser beam,” J. Mod. Opt. 50, 2155–2161 (2003).
[CrossRef]

L. Yuan, G. P. Wang, and X. K. Huang, “Arrangements of four beams for any Bravais lattice,” Opt. Lett. 28, 1769–1771 (2003).
[CrossRef] [PubMed]

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

2002 (1)

N. Suzuki, Y. Tomita, and T. Kojima, “Holographic recording in TiO2 nanoparticle-dispersed methacrylate photonpolymer films,” Appl. Phys. Lett. 81, 4121–4123 (2002).
[CrossRef]

2000 (4)

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[CrossRef] [PubMed]

I. Abdulhalim, “Omnidirectional reflection from anisotropic periodic dielectric stack,” Opt. Commun. 174, 43–50 (2000).
[CrossRef]

I. Abdulhalim, “Analytic propagation matrix method for anisotropic magneto-optic layered media,” J. Opt. A Pure Appl. Opt. 2, 557–564 (2000).
[CrossRef]

I. Abdulhalim, “Reflective phase-only modulation using one-dimensional photonic crystals,” J. Opt. A Pure Appl. Opt. 2, L9–L11 (2000).
[CrossRef]

1999 (3)

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

W. H. Southwell, “Omnidirectional mirror design with quarter-wave dielectric stacks,” Appl. Opt. 38, 5464–5467 (1999).
[CrossRef]

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

1998 (3)

1993 (1)

1987 (1)

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

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Abdulhalim, I.

I. Abdulhalim, “Omnidirectional reflection from anisotropic periodic dielectric stack,” Opt. Commun. 174, 43–50 (2000).
[CrossRef]

I. Abdulhalim, “Analytic propagation matrix method for anisotropic magneto-optic layered media,” J. Opt. A Pure Appl. Opt. 2, 557–564 (2000).
[CrossRef]

I. Abdulhalim, “Reflective phase-only modulation using one-dimensional photonic crystals,” J. Opt. A Pure Appl. Opt. 2, L9–L11 (2000).
[CrossRef]

Bovard, B. G.

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.

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

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Fan, S.

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

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]

Fink, Y.

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

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]

Fujii, T.

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

Fujishima, A.

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

Gaponenko, S.

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

Gilbert, L. R.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[CrossRef] [PubMed]

Huang, X. K.

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]

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

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kojima, T.

N. Suzuki, Y. Tomita, and T. Kojima, “Holographic recording in TiO2 nanoparticle-dispersed methacrylate photonpolymer films,” Appl. Phys. Lett. 81, 4121–4123 (2002).
[CrossRef]

Kubota, Y.

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

Lavrinenko, A.

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

Lee, H.-Y.

H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
[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]

Naoi, K.

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

Nevitt, T. J.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[CrossRef] [PubMed]

Niwa, C.

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

Ohko, Y.

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

Oudekirk, A. J.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[CrossRef] [PubMed]

Roberts, P. J.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Shan, H.

G. P. Wang, C. Tan, Y. Yi, and H. Shan, “Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals by using a single cw laser beam,” J. Mod. Opt. 50, 2155–2161 (2003).
[CrossRef]

Southwell, W. H.

Stover, C. A.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[CrossRef] [PubMed]

Suzuki, N.

N. Suzuki, Y. Tomita, and T. Kojima, “Holographic recording in TiO2 nanoparticle-dispersed methacrylate photonpolymer films,” Appl. Phys. Lett. 81, 4121–4123 (2002).
[CrossRef]

Tan, C.

G. P. Wang, C. Tan, Y. Yi, and H. Shan, “Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals by using a single cw laser beam,” J. Mod. Opt. 50, 2155–2161 (2003).
[CrossRef]

Tatsuma, T.

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

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]

Tomita, Y.

N. Suzuki, Y. Tomita, and T. Kojima, “Holographic recording in TiO2 nanoparticle-dispersed methacrylate photonpolymer films,” Appl. Phys. Lett. 81, 4121–4123 (2002).
[CrossRef]

Tredwell, S.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Wang, G. P.

G. P. Wang, C. Tan, Y. Yi, and H. Shan, “Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals by using a single cw laser beam,” J. Mod. Opt. 50, 2155–2161 (2003).
[CrossRef]

L. Yuan, G. P. Wang, and X. K. Huang, “Arrangements of four beams for any Bravais lattice,” Opt. Lett. 28, 1769–1771 (2003).
[CrossRef] [PubMed]

Weber, M. F.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[CrossRef] [PubMed]

Winn, J. N.

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

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, “Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters,” Opt. Lett. 23, 1648–1649 (1998).
[CrossRef]

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

Yao, T.

H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
[CrossRef]

Yarotsky, D.

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

Yi, Y.

G. P. Wang, C. Tan, Y. Yi, and H. Shan, “Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals by using a single cw laser beam,” J. Mod. Opt. 50, 2155–2161 (2003).
[CrossRef]

Yuan, L.

Appl. Opt. (2)

Appl. Phys. A (1)

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

Appl. Phys. Lett. (1)

N. Suzuki, Y. Tomita, and T. Kojima, “Holographic recording in TiO2 nanoparticle-dispersed methacrylate photonpolymer films,” Appl. Phys. Lett. 81, 4121–4123 (2002).
[CrossRef]

J. Appl. Phys. (1)

H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
[CrossRef]

J. Mod. Opt. (1)

G. P. Wang, C. Tan, Y. Yi, and H. Shan, “Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals by using a single cw laser beam,” J. Mod. Opt. 50, 2155–2161 (2003).
[CrossRef]

J. Opt. A Pure Appl. Opt. (2)

I. Abdulhalim, “Analytic propagation matrix method for anisotropic magneto-optic layered media,” J. Opt. A Pure Appl. Opt. 2, 557–564 (2000).
[CrossRef]

I. Abdulhalim, “Reflective phase-only modulation using one-dimensional photonic crystals,” J. Opt. A Pure Appl. Opt. 2, L9–L11 (2000).
[CrossRef]

Nat. Mater. (1)

Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, “Multicolour photochromism of TiO2 films loaded with silver nanoparticles,” Nat. Mater. 2, 29–31 (2003).
[CrossRef] [PubMed]

Opt. Commun. (2)

I. Abdulhalim, “Omnidirectional reflection from anisotropic periodic dielectric stack,” Opt. Commun. 174, 43–50 (2000).
[CrossRef]

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

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

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]

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Oudekirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[CrossRef] [PubMed]

Other (3)

H. M. Smith, Holographic Recording Materials (Springer-Verlag, New York, 1977).

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

G. P. Wang and W. H. Lin, data available from the authors.

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Figures (11)

Fig. 1
Fig. 1

(a) Relationship between the exposure dose H and the volume-filling fraction of nanoparticles. The curve is divided into three zones: cutoff, linear, and saturated zones. Hc and Hs are the cutoff and saturated thresholds of the exposure dose, respectively. (b) Exposure distribution in the recording medium. Regions P and A are the unexposed emulsion in the cutoff zone and the exposed one in the linear zone, respectively.

Fig. 2
Fig. 2

One-dimensional metallodielectric PC (MDPC) model. The peak volume-filling fraction Vp of Ag nanoparticles corresponds to the peak exposure dose Hp, and Λ is the period of the 1D MDPCs.

Fig. 3
Fig. 3

Calculated dependence of the (a) transmission spectra and (b) bandgap width and midwavelength of 1D MDPCs on Hc. Other parameters are chosen as Hs=1.2, Vmax=0.24, and D=2.4 µm.

Fig. 4
Fig. 4

Calculated absorption spectra of the 1D MDPCs as a function of Hc. Other parameters used for computations are the same as those of Fig. 3.

Fig. 5
Fig. 5

Calculated dependence of the PBG width and midwavelength of 1D MDPCs on saturated threshold Hs. The cutoff threshold is fixed at Hc=0.4.

Fig. 6
Fig. 6

Calculated transmission spectra of the 1D MDPCs with different emulsion thicknesses D. N denotes the period number of the 1D MDPCs. N=4, 6, 8, 10, and 12 correspond to the emulsion thicknesses D=0.84, 1.26, 1.68, 2.10, and 2.52 µm, respectively.

Fig. 7
Fig. 7

Calculated transmission spectra of the 1D MDPCs with incident light at different angles θ. The period number of the 1D MDPCs is N=8, and the other parameters are the same as those of Fig. 6.

Fig. 8
Fig. 8

(a) Vibration model in the recording emulsion. A uniform broadening δ of nanoparticle-embedded emulsion regions due to the instability of the recording setup is introduced in the 1D MDPC model. (b) Calculated transmission spectra of the 1D MDPCs with different broadening values δ=0, 10, 20, 30, and 40 nm. Other parameters used are Hc=0.4, Hs=1.2, Vmax=0.24, and D=2.4 µm.

Fig. 9
Fig. 9

(a) Refractive-index distribution and (b) band structure of an omnidirectional 1D PC formed by holography. The parameters used for the calculations are Hc=0.3 and Vmin=0.1.

Fig. 10
Fig. 10

Calculated transmission spectra of a 1D PC for (a) TM- and (b) TE-polarized illumination light at different incident angles θ. The period number of the 1D PC structure is N=12, and other parameters are the same as those in Fig. 9.

Fig. 11
Fig. 11

Simulated dependence of the ratio of the bandgap to midwavelength η on cutoff exposure Hc as a function of Vmin. Other parameters are the same as those in Figs. 9 and 10.

Equations (2)

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EH=MkEH=cos σk-i sin σk/ρk-iρk sin σkcos σkEH,
eff-2eff+22=1-V1-21+22.

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