Abstract

In this paper, we propose a device to bend light in non-channel planar photonic crystal (PhC) waveguides using the self-collimation phenomenon. The mode distribution in a non-channel planar PhC waveguide is investigated in detail in order to help understand the proposed bending mechanism. Three-dimensional finite-difference time-domain simulations show an over 80% bending efficiency for a 90° bend. As the first proposal for bending light in a non-channel planar PhC waveguide, the presented device enables the application of routing in non-channel planar PhC waveguides.

© 2003 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional PhC slabs," Phys. Rev. B 62, 4488-4492 (2000).
    [CrossRef]
  6. J. Witzens, M. Loncar, and A. Scherer, "Self-Collimation in Planar PhCs," IEEE J. of Selected Topics in Quantum Electronics 8, 1246 (2002).
    [CrossRef]
  7. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in PhCs," Appl. Phy. Lett. 74, 1212 (1999).
    [CrossRef]
  8. D. N. Chigrin, S. Enoch, C. M. S. Torres, and G. Tayeb, "Self-guiding in two-dimensional PhCs," Optics Express 11, 1203 (2003). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203</a>
    [CrossRef] [PubMed]
  9. J. Witzens and A. Scherer, "Efficient excitation of self-collimated beams and single Bloch modes in planar PhCs," J. Opt. Soc. Am. A 20, 935 (2003).
    [CrossRef]
  10. A. Taflove and S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2000).
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  12. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, Tokyo, 1995).
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APMC 1997 (1)

Z. Ma and E. S. Yamashita, "Performance of the modified Berenger PML absorbing boundary condition for evanescent waves in three-dimensional structures," presented at Asia-Pacific Microwave Conference Proceedings, APMC, 1997.

Appl. Phy. Lett. (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in PhCs," Appl. Phy. Lett. 74, 1212 (1999).
[CrossRef]

IEEE J. Selected Topics in Quantum Elect (1)

J. Witzens, M. Loncar, and A. Scherer, "Self-Collimation in Planar PhCs," IEEE J. of Selected Topics in Quantum Electronics 8, 1246 (2002).
[CrossRef]

IEEE Microwave and Guided Wave Letters (1)

J. P. Berenger, "Effective PML for the absorption of evanescent waves in waveguides," IEEE Microwave and Guided Wave Letters 8, 188-190 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Optics Express (1)

D. N. Chigrin, S. Enoch, C. M. S. Torres, and G. Tayeb, "Self-guiding in two-dimensional PhCs," Optics Express 11, 1203 (2003). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203</a>
[CrossRef] [PubMed]

Phys. Rev. B (2)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in PhCs: Mode Symmetry, Tunability, and Coupling Efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional PhC slabs," Phys. Rev. B 62, 4488-4492 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong Localization of Photons in Certain Disordered Dielectric Superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Other (3)

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

A. Taflove and S. C. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2000).

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, Tokyo, 1995).

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Figures (6)

Fig. 1.
Fig. 1.

Electromagnetic waves incident on a photonic crystal from the free space: (a) the photonic crystal slab, (b) the equifrequency contours (EFCs) for the light cone (the solid circle) and the photonic crystal (the dotted square with round corners) at the wavelength of a/λ=0.3 for explaining the phase and energy propagation of the incident wave, the reflected wave, and the refracted wave, respectively. The structure consists of a rectangular array of air holes in Si slab. The refractive index of Si is 3.5. The radius of air holes is 0.6a and the thickness of the slab is 0.6a, where a is the lattice constant.

Fig. 2.
Fig. 2.

Plot of the incident angle verse the energy propagation angle in the photonic crystal. All angles are relative to the Γ-X1 direction.

Fig. 3.
Fig. 3.

The electromagnetic wave bending structure with a single 90° bend in a non-channel planar photonic crystal waveguide: (a) the entire device, (b) the launched Guassian beam seeing from the propagation direction, (c) the zoom-in display of the bending part of the device. d is defined as the distance from the nearest edge of air holes to the mirror.

Fig. 4.
Fig. 4.

A horizontal cross section of steady state amplitudes of Hz component on the central plane of photonic crystal slab when d=0.107a. The bending efficiency is 82.9%. Bending efficiency is defined as the output energy ratio of a bend waveguide to a straight waveguide with the same length.

Fig. 5.
Fig. 5.

Plot of bending efficiency versus the distance d. The inset explains the two dotted lines which indicate the two mirror positions favored by the symmetry of the photonic crystal and the symmetry of the mirror to the collimated energy. Measured experimental results are depicted by black dots in the figure.

Fig. 6.
Fig. 6.

Experimental routing capability of a material having a square-shaped equi-frequency dispersion contour. (a) A scanning electron micrograph of fabricated dispersion-based PhC waveguide with an open area to act as reflecting mirrors. (b) Image of the scattered light as it propagates through the self-collimating PhC lattice and routed by the etched mirror.

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