Abstract

An optical surface edge Bloch mode is an optical state evanescently bound at an edge on a finite-size three-dimensional photonic crystal; the edge is the intersection of two termination planes on the crystal. Low-loss subwavelength-scale edge modes can appear on an 010 edge of a dielectric woodpile within a complete photonic bandgap. The mode area is as small as 0.066 squared half-in-vacuum-wavelengths. The edge mode has field maxima in vacuum near the termination surface, like surface plasmon modes. This edge mode would provide new opportunities of low-loss light localization in a sub-diffraction-limit space without the use of metal.

© 2012 Optical Society of America

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[CrossRef]

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[CrossRef]

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L. Tang and T. Yoshie, IEEE J. Quantum Electron. 47, 1028 (2011).
[CrossRef]

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[CrossRef]

L. Tang and T. Yoshie, J. Vac. Sci. Technol. B 28, 301 (2010).
[CrossRef]

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Weisbuch, C.

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[CrossRef]

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[CrossRef]

L. Tang and T. Yoshie, IEEE J. Quantum Electron. 47, 1028 (2011).
[CrossRef]

L. Tang and T. Yoshie, J. Vac. Sci. Technol. B 28, 301 (2010).
[CrossRef]

Appl. Phys. Lett

J. K. Yang, S. H. Kim, G. H. Kim, H. G. Park, Y. H. Lee, and S. B. Kim, Appl. Phys. Lett 84, 3016 (2004).
[CrossRef]

Appl. Phys. Lett.

T. Lu, Y. Hsiao, W. Ho, and P. Lee, Appl. Phys. Lett. 94, 141110 (2009).
[CrossRef]

IEEE J. Quantum Electron.

L. Tang and T. Yoshie, IEEE J. Quantum Electron. 47, 1028 (2011).
[CrossRef]

J. Opt. Soc. Am.

J. Vac. Sci. Technol. B

L. Tang and T. Yoshie, J. Vac. Sci. Technol. B 28, 301 (2010).
[CrossRef]

Nat. Photonics

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, Nat. Photonics 5, 91 (2011).
[CrossRef]

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K. Ishizaki and S. Noda, Nature 460, 367 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

A finite-size woodpile 3D photonic crystal (main figure) and two types of surface plane Bloch modes on a semi-infinite-size woodpile (upper and right panels). Main figure: The finite-size structure shows 4×1×4 unit cells; one unit cell corresponds to two primitive cells [9]. An intersection of (100) and (001) planes forms a 010 edge. Panels: The field profiles of (100) and (001) surface plane modes are shown by using the electric field component that is perpendicular to the termination plane. The 100, 010, and 001 crystal directions are parallel to the x, y, and z axes.

Fig. 2.
Fig. 2.

Surface Bloch modes propagating along the 010 (y) direction on a finite-size woodpile and an edge mode: (a) Dispersion relations of surface modes on a woodpile of 4××4 unit cells and (b) dispersion relations of surface modes appearing only on two intersecting right (100) and top (001) surfaces with (tx,ty)=(0,0). The rest of the modes seen in (a) appear on the other two planes, i.e., the left (100) and the bottom (001) surfaces. Solid black, dashed green, and dotted blue curves are dispersion functions for 010 edge modes, (001) plane modes, and (100) plane modes, respectively. (c) The mode profile (Ex component) of the 010 edge mode at βy=π/a, shown by red points in (a) and (b), viewed from different directions. Red arrows show the propagation direction k. The upper panel in (c) shows the field intensity versus Δx, the distance from the right (100) surface along the horizontal dotted blue line; the right panel shows the field intensity versus Δz, the distance from the top (001) surface along the vertical dotted blue line. The edge mode has field maxima in vacuum near the termination surface.

Fig. 3.
Fig. 3.

Dispersion relations of surface Bloch modes versus lattice termination combination (tx, tz). Modes on a 010 edge, on a top (001) surface, on a right (100) surface, and on both top (100) and right (001) surfaces, shown by solid black, dashed green, dotted blue, and dashed-dotted-dotted red curves, respectively. The white regions are mode gap regions within a complete PBG projected along the propagation direction k. We did not show the cases of tz=1/2 and 3/4 as the structures are equivalent for (tx, tz) and (tx+1/2, tz+1/2).

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