Abstract

A two-dimensional superlattice photonic crystal structure is investigated in which the holes in adjacent rows of a triangular lattice alternate between two different radii. The superimposition of a superlattice on a triangular lattice is shown to reduce the photonic bandgap, introduce band splitting, and change the dispersion contours so that dramatic effects are seen in the propagation, refraction, and dispersion properties of the structure. For single mode propagation, the superlattice shows regions of both positive and negative refraction as well as refraction at normal incidence. The physical mechanisms responsible for these effects are directly related to Brillouin Zone folding effects on the triangular lattice that lowers the lattice symmetry and introduces anisotropy in the lattice.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering,�?? Appl. Phys. Lett. 74(10), 1370 (1999).
[CrossRef]

T. Baba and T. Matsumoto, �??Resolution of photonic crystal superprism,�?? Appl. Phys. Lett. 81, 2325 (2002).
[CrossRef]

W. Park and C. J. Summers, �??Optical properties of superlattice photonic crystal waveguides,�?? Appl. Phys. Lett. 84(12), 2013 (2004).
[CrossRef]

Comput. Phys. Commun.

A. J. Ward and J. B. Pendry, �??A program for calculating photonic band structures and Green�??s functions using a non-orthogonal FDTD method,�?? Comput. Phys. Commun. 112(1), 23 (1998).
[CrossRef]

IEEE J. Quantum Electron.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, �??Superprism phenomena in planar photonic crystals,�?? IEEE J. Quantum Electron. 38(7), 915 (2002).

T. Baba and M. Nakamura, �??Photonic crystal light deflection devices using the superprism effect,�?? IEEE J. Quantum Electron. 38(7), 909 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

L. Zhao and A. Cangellaris, �??GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids,�?? IEEE Trans. Microwave Theory Tech. 44, 2555�??2563 (1996).
[CrossRef]

J. Comput. Phys.

J. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comput. Phys. 114, 185�??200 (1994).
[CrossRef]

J. Mod. Opt.

J. P. Dowling and C. Bowen, �??Anomalous index of refraction in photonic bandgap materials,�?? J. Mod. Opt. 41, 345 (1994).
[CrossRef]

J. Nonlinear Optical Phys. and Mater.

C. J. Summers, C. W. Neff, and W. Park, �??Active Photonic Crystal Nano-Architectures,�?? J. Nonlinear Optical Phys. and Mater. 12(4), 587 (2003).
[CrossRef]

NATO ASI Series E, Applied Sciences

P. J. Russell and T. A. Birks, �??Bloch wave optics in photonic crystals: physics and applications,�?? in Photonic band gap materials, C. M. Soukoulis, ed., no. 315 in NATO ASI series. Series E, Applied Sciences, p. 71 (Kluwer, 1996).

Opt. Express

S. G. Johnson and J. D. Joannopoulos, �??Block-iterative frequency-domain methods for Maxwell�??s equations in a planewave basis,�?? Opt. Express 8(3), 173 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. B

C. T. Chan, Q. L. Yu, and K. M. Ho, �??Order-N spectral method for electromagnetic waves,�?? Phys. Rev. B 51(23), 16,635 (1995).

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B 60(8), 5751 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, �??Superprism phenomena in photonic crystals,�?? Phys. Rev. B 58, R10,096 (1998).
[CrossRef]

M. Notomi, �??Theory of light propagating in strongly modulated photonic crystal: Refraction like behavior in the vicinity of the photonic band gap,�?? Phys. Rev. B 62(16), 10,696 (2000).

J. Bravo-Abad, T. Ochiai, and J. S`anchez-Dehesa, �??Anomalous refractive properties of a two-dimensional photonic band-gap prism,�?? Phys. Rev. B 67, 115,116 (2003).
[CrossRef]

Phys. Status Solidi B

W. Park, J. S. King, C. W. Neff, C. Liddell, and C. J. Summers, �??ZnS-based photonic crystals,�?? Phys. Status Solidi B 229(2), 949 (2002).
[CrossRef]

Other

N. W. Ashcroft and N. D. Mermin, Solid State Physics (W. B. Saunders, 1976).

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Figures (4)

Fig. 1.
Fig. 1.

Details of the SL structure.(a) An illustration of a SL slab waveguide. (b) A schematic showing the parameters of the structure. (c) Reciprocal lattice representation.

Fig. 2.
Fig. 2.

Photonic band diagrams for SL structures calculated using the PWE method for (a) r 2/r 1=1.0, (b) 0.857, and (c) 0.571.

Fig. 3.
Fig. 3.

Time-averaged magnetic-field energy density of the Hz field component for (a) and (b) the degenerate states at the bottom of the air band at the M point of the triangular lattice and (c) and (d) the 3s and 3p states of the 2D PC-SL with strength 0.571.

Fig. 4.
Fig. 4.

(a) TE polarization equi-frequency contours for the SL structure calculated with the PWE method for a strength of 1.0 (solid line) and 0.857 (dashed line) and with the FDTD method for a radius ratio of 0.857 (scattered dots), gray lines indicate the construction lines for a beam of ωn =0.3185 incident from air onto the PC. (b) Refraction angles with change in incident angle for r 2/r 1=0.857 for a range of ωn with 1% spacing between frequencies (group of lines) and for a 2D slab waveguide structure (scattered plot).

Equations (4)

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S K = j = 1 n f j ( K ) e i K · d j ,
K = n 1 b 1 + n 2 b 2 ,
S K = f 1 ( K ) + ( 1 ) n 1 + n 2 f 2 ( K ) .
ε eff , j = ε b ( 1 ( r 2 r 1 ) 2 ) + ε c , i ( r 2 r 1 ) 2 ,

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