Abstract

To minimize the dispersion of defect modes in the Bragg gap of a conventional one-dimensional photonic crystal (1D PC) doped with a defect layer of left-handed material (LHM), a numerical technique is developed for tuning the optimized parameters of the defect. Through a defect couple comprising a pair of adjacent right-handed material and LHM defect layers, omnidirectional defect modes (ODMs), within a determined tolerance limit, are generated and shown to be much less dispersive than some recently reported near-zero dispersion defect modes. A defect couple with a dispersive LHM yields multiple near-zero dispersion channels in the bandgap. We propose the defect-couple 1D PC as a design for generating polarization-independent ODMs.

© 2007 Optical Society of America

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References

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2007 (1)

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

2006 (3)

2005 (3)

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

K.-Y. Xu, X. Zheng, C.-L. Li, and W.-L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

H. Y. Sang, Z. Y. Li, and B. Y. Gu, "Defect modes in multiple-constituent one-dimensional photonic crystals examined by an analytic Bloch-mode approach," Chin. Phys. Lett. 22, 365-368 (2005).
[CrossRef]

2004 (3)

H. Y. Sang, Z. Y. Li, and B. Y. Gu, "Stack-sequence dependent defect modes in one-dimensional photonic crystals," Phys. Lett. A 331, 414-422 (2004).
[CrossRef]

Z. S. Wang, L. Wang, Y. G. Wu, and L. Y. Chen, "Multiple channeled phenomena in heterostructures with defects mode," Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

G. Liang, P. Han, and H. Wang, "Narrow frequency and sharp angular defect mode in one-dimensional photonic crystals from a photonic heterostructure," Opt. Lett. 29, 192-194 (2004).
[CrossRef] [PubMed]

2003 (2)

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

2002 (1)

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 510-513 (2002).
[CrossRef] [PubMed]

2000 (1)

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
[CrossRef] [PubMed]

1998 (2)

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from 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]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

1993 (1)

Appl. Phys. Lett. (2)

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Z. S. Wang, L. Wang, Y. G. Wu, and L. Y. Chen, "Multiple channeled phenomena in heterostructures with defects mode," Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Chin. Phys. Lett. (1)

H. Y. Sang, Z. Y. Li, and B. Y. Gu, "Defect modes in multiple-constituent one-dimensional photonic crystals examined by an analytic Bloch-mode approach," Chin. Phys. Lett. 22, 365-368 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

Laser Phys. Lett. (1)

V. P. Drachev, W. Cai, U. Chettiar, H. K. Yuan, A. K. Sarychev, A. V. Kildishev, G. Klimeck, and V. M. Shalaev, "Experimental verification of an optical negative-index material," Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Nat. Photonics (1)

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, "Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection," Nat. Photonics 1, 176-179 (2007).

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

H. Y. Sang, Z. Y. Li, and B. Y. Gu, "Stack-sequence dependent defect modes in one-dimensional photonic crystals," Phys. Lett. A 331, 414-422 (2004).
[CrossRef]

Phys. Rev. E (1)

K.-Y. Xu, X. Zheng, C.-L. Li, and W.-L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Science (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]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, "External reflection from omnidirectional dielectric mirror fibers," Science 296, 510-513 (2002).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Other (1)

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

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Figures (11)

Fig. 1
Fig. 1

Contour plot of rms ( ω D ω 0 ) ω 0 for the PC { A B A B } { D } { B A B A } , with n A = 1.6 , n B = 4.6 , and d A a = d B a = 0.5 . The triangle symbol shows the location of the minimum rms ( ω D ω 0 ) ω 0 . The dashed curve represents half-wave layers D.

Fig. 2
Fig. 2

Photonic band structure with defect-modes dispersion relation curves for a 1D PC containing a defect cell. The PC parameters are n A = 1.6 , n B = 4.6 , and d A a = d B a = 0.5 . The solid curve corresponds to PC-1/defect-1 with n D = 2.43 and d D a = 0.665 (tuned). Dotted curve: PC-1/defect-2 with n D = 2.34 and n D d D = 0.5 ( n A d A + n B d B ) (from [13]). Dashed curve: PC-1/Dcouple-1 with n D 1 = 1.6206 , d D 1 a = 1.556 , n D 2 = 4.513 , and d D 2 a = 0.504 .

Fig. 3
Fig. 3

Transmittance spectra for the structure { A B } 4 D { B A } 4 , as a finite version of PC-1/defect-1, placed in free space. The solid and dashed curves denote TE and TM polarizations, respectively. θ i is the angle of incidence.

Fig. 4
Fig. 4

Dispersion relation of defect modes in PC-2/defect-3, where n A = 3.909 , n B = 4.6 , n D = 2.546 , layers A and B are quarter-waves, and layer D is half-wave, based on an analytical design for an omnidirectional filter given by Xu et al. [13].

Fig. 5
Fig. 5

Dependence of defect-modes normalized frequency shift on incident angle. The dashed curve corresponds to the curve in Fig. 4. The curves with triangles, circles, and squares correspond to the solid, dashed, and dotted curves, respectively, in Fig. 2.

Fig. 6
Fig. 6

Dispersion relation of defect modes in a PC with n A = 2.2 , n B = 4.6 , and d A a = d B a = 0.5 . Solid curve overlapping channel 2: PC-3/Dcouple-2 with n D 1 = 2.16 , d D 1 a = 2.02 , n D 2 = 4.95 , and d D 2 a = 0.2 . Curves traced by circles: PC-3/Dcouple-3 with ε D 1 = 1 100 ω 2 and μ D 1 = 4.666 100 ω 2 (ω in gigahertz). The other parameters are the same as those for PC-3/Dcouple-2.

Fig. 7
Fig. 7

Dispersion relation of defect modes in the zero- n ¯ gap of PC-4/defect-4, reproduced from [15]. The parameters are: ε A = 1.21 100 ω 2 , μ A = 1.0 100 ω 2 , d A = 51 mm , n B = 3 , μ B = 1 , d B = 25.5 mm , n D = 4.65 , μ D = 1 , and d D = 33 mm , where ω is in gigahertz. Layers A and B are quarter-waves, and layer D is half-wave at ω 0 = 0.985 × 2 π GHz , at which n ¯ = 0 .

Fig. 8
Fig. 8

Dependence of defect-modes normalized frequency shift on incident angle. The curve of triangles corresponds to the curve in Fig. 7. The curves of circles and dashes correspond, respectively, to the solid curve and the curve traced by the circles at channel 2 in Fig. 6.

Fig. 9
Fig. 9

Transmittance spectra of the structure { A B } 5 D 1 D 2 { B A } 5 , a finite version of PC-3/Dcouple-2, placed in vacuum. n A = 2.2 , n B = 4.6 , d A a = d B a = 0.5 , n D 1 = 2.16 , d D 1 a = 2.02 , n D 2 = 4.95 , and d D 2 a = 0.2 . Solid (dashed) curve TE (TM) polarization. θ i = incident angle.

Fig. 10
Fig. 10

Test for omnidirectionality of the defect-couple modes at channel 2 in Fig. 6. The curve with circles (squares) corresponds to the defect modes (channel 2) of PC-3/Dcouple-2 (PC-3/Dcouple-3). Top (bottom) dashed line upper (lower) limit of the tolerance. Since both curves remain fully in between the dashed lines, they satisfy the omnidirectionality condition.

Fig. 11
Fig. 11

Transmittance spectra for the defect-couple PC structure { A B } 7 D 1 D 2 { B A } 7 , as a finite version of PC-3/Dcouple-3, with n 0 = 1.0 and n s = 4.6 . The peaks 1, 2, and 3 correspond to channels 1, 2, and 3, respectively, in Fig. 6. Solid (dashed) curve TE (TM) polarization. θ i = incident angle.

Tables (2)

Tables Icon

Table 1 Summary of the Results for Most Defective PCs Investigated and Compared Here a

Tables Icon

Table 2 Transmittances of the TE and TM Defect Modes for { A B } 5 D 1 D 2 { B A } 5 , as a Finite Version of PC-3/Dcouple-2, at Various Angles of Incidence θ i , n A = 2.2 , n B = 4.6 , d A a = d B a = 0.5 , n D 1 = 2.16 , d D 1 a = 2.02 , n D 2 = 4.95 , and d D 2 a = 0.2 a

Equations (1)

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rms ( ω D ω 0 ω 0 ) = { θ i { [ ω D , TE ( θ i ) ω 0 ] 2 + [ ω D , TM ( θ i ) ω 0 ] 2 } W ( θ i ) 2 ω 0 2 θ i W ( θ i ) } 1 2 ,

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