Abstract

We address the issue of tuning the absolute bandgap in 2D silicon-based photonic crystals by mechanical deformation. The moving least-square (MLS) method, recently proposed by the authors for photonic bandgap materials, is employed for the real-space computation of band structures. The uniaxial tension mode is shown to be more effective for bandgap tuning than both pure and simple shear deformations. We verify that bandgap modifications are strongly influenced by the deformation-induced distortion of interfaces between inclusions and matrix. This result ensures the usefulness of real-space technique for the accurate calculation of strained photonic bandgap materials.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  6. J. Zhou, C.Q. Sun, K. Pita, Y.L. Lam, Y. Zhou, S.L. Ng, C.H. Kam, L.T. Li, and Z.L. Gui, �??Thermally tuning of the photonic band gap of SiO2 colloid-crystal infilled with ferroelectric BaTiO3,�?? Appl. Phys. Lett. 78, 661-663 (2001).
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    [CrossRef]
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Adv. Mater. (1)

Y. Xia, �??Photonic crystals,�?? Adv. Mater. 13, 369 (2001) and papers in this special issue.
[CrossRef]

Appl. Phys. Lett. (5)

Y. Shimoda, M. Ozaki, and K. Yoshino, �??Electric field tuning of a stop band in a reflection spectrum of synthetic opal infiltrated with nematic liquid crystal,�?? Appl. Phys. Lett. 79, 3627-3629 (2001).
[CrossRef]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, �??Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal,�?? Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

J. Zhou, C.Q. Sun, K. Pita, Y.L. Lam, Y. Zhou, S.L. Ng, C.H. Kam, L.T. Li, and Z.L. Gui, �??Thermally tuning of the photonic band gap of SiO2 colloid-crystal infilled with ferroelectric BaTiO3,�?? Appl. Phys. Lett. 78, 661-663 (2001).
[CrossRef]

S. Kim and V. Gopalan, �??Strain-tunable photonic band gap crystals,�?? Appl. Phys. Lett. 78, 3015-3017 (2001).
[CrossRef]

V. Babin, P. Garstecki, and R. Holyst, �??Photonic properties of an inverted face centered cubic opal under stretch and shear,�?? Appl. Phys. Lett. 82, 1553-1555 (2003).
[CrossRef]

Comput. Methods Appl. Mech. Eng. (1)

T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P. Krysl, �??Meshless methods: An overview and recent developments,�?? Comput. Methods Appl. Mech. Eng. 139, 3-47 (1996).
[CrossRef]

Int. J. Solids Struct. (1)

M. Huang, �??Stress effects on the performance of optical waveguides,�?? Int. J. Solids Struct. 40, 1615-1632 (2003).
[CrossRef]

Nature (1)

H. Pier, E. Kapon, and M. Moser, �??Strain effects and phase transitions in photonic resonator crystals,�?? Nature (London) 407, 880-883 (2000).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. B (2)

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, �??Tunable photonic band gap in self-assembled clusters of floating magnetic particles,�?? Phys. Rev. B 66, 195108-195113 (2002).
[CrossRef]

S.W. Leonard, J.P. Mondia, H.M. van Driel, O. Toader, S. John, K. Busch, A. Birner, U. G¨ osele, and V. Lehmann, �??Tunable two-dimensional photonic crystals using liquid-crystal infiltration,�?? Phys. Rev. B 61, R2389-R2392 (2000).
[CrossRef]

Phys. Rev. E (1)

P.A. Bermel and M. Warner, �??Photonic band structure of highly deformable self-assembling systems,�?? Phys. Rev. E 65, 10702-10705 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

K. Busch and S. John, �??Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,�?? Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Science (1)

S. Noda, M. Yokoyama, M. Imada, A. Chutian, and M. Mochizuki, �??Polarization mode controll of twodimensional photonic crystal laser by unit cell structure design,�?? Science 293 1123-1125, (2001)
[CrossRef] [PubMed]

Other (2)

J.M. Gere and S.P. Timoshenko, Mechanics of Materials (PWS Publishing Company, Boston, 1997).

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

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Figures (4)

Fig. 1.
Fig. 1.

Illustrations of fundamental deformation modes: (a) pure shear, (b) simple shear, and (c) uniaxial tension. Dashed square is the undeformed original shape.

Fig. 2.
Fig. 2.

Undeformed (red) and deformed (blue) unit cells of 2D triangular photonic crystal with cylindrical air rods: (a) pure shear, (b) simple shear, and (c) uniaxial tension. In each mode, corresponding shear or tensile strain of 3% is applied.

Fig. 3.
Fig. 3.

Schematic diagrams of symmetry points and zones in the reciprocal lattice of undeformed (left) and deformed (right) photonic crystals.

Fig. 4.
Fig. 4.

Photonic band structures under pure shear (top), simple shear (middle), and uniaxial tension (bottom). TM and TE modes are in blue and red, respectively. Dashed horizontal lines indicate the bandgap of undeformed original photonic crystal. Insets in top low illustrate the quasi-hexagonal symmetry zones of the deformed photonic crystal.

Tables (1)

Tables Icon

Table 1. Correlations between volume fraction and bandgap shift.

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