Abstract

Coupling characteristics between the single-cell hexapole mode and the triangular-lattice photonic crystal slab waveguide mode is studied by the finite-difference time-domain method. The single-cell hexapole mode has a high quality factor (Q) of 3.3×106 and a small modal volume of 1.18(λ/n)3. Based on the symmetry, three representative types of coupling geometries (shoulder-couple, butt-couple and side-couple structures) are selected and tested. The coupling efficiency shows strong dependence on the transverse overlap of the cavity mode and the waveguide mode over the region of the waveguide. The shoulder-couple structure shows best coupling characteristics among three tested structures. For example, two shoulder-couple waveguides and a hexapole cavity result in a high performance resonant-tunneling-filter with Q of 9.7×105 and transmittance of 0.48. In the side-couple structure, the coupling strength is much weaker than that of the shoulder-couple structure because of the poor spatial overlap between the mode profiles. In the direct-couple structure, the energy transfer from the cavity to the waveguide is prohibited because of the symmetry mismatch and no coupling is observed.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett.

H. Y. Ryu, S. H. Kim, H. G. Park, J. K. Hwang, Y. H. Lee, and J. S. Kim, �??Square-lattice photonic bandgap single-cell laser operating in the lowest-order whispering gallery mode,�?? Appl. Phys. Lett. 80, 3883- 3885 (2002).
[CrossRef]

J. Vu�?kovi�? and Y. Yamamoto, �??Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot,�?? Appl. Phys. Lett. 82, 2374-2376 (2003).
[CrossRef]

H. Y. Ryu, M. Notomi, and Y. H. Lee, �??High-quality-factor and small- mode-volume hexapole modes in photonic-crystal-slab nanocavities,�?? Appl. Phys. Lett. 83, 4294-4296 (2003).
[CrossRef]

H. Takano, Y. Akahane, T. Asano, and S. Noda, �??In-plane-type channel drop filter in a two-dimensional photonic crystal slab,�?? Appl. Phys. Lett. 84, 2226-2228 (2004).
[CrossRef]

M. F. Yanki, S. Fan, and M. Solja�?i�?, �??High-contrast all-optical bistable switching in photonic crystal microcavities,�?? Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, �??Coupled guide and cavity in a two-dimensional photonic crystal,�?? Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Extremely large group velocity dispersio

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,�?? Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," 35, 1322-1331 (1999).
[CrossRef]

C. Seassal, Y. Désières, X. Letartre, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, and T. Benyattou, �??Optical coupling between a two-dimensional photonic crystal-based microcavity and single-line defect waveguide on InP membranes,�?? IEEE J. Quantum Electron. 38, 811-815 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Nature

S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, �??High-Q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

M. F. Yanki, S. Fan, M. Solja�?i�?, and J. D. Joannopoulos, �??All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,�?? Opt. Lett. 28, 2506-2508 (2003).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

(a) Modified single-cell cavity structure. Six nearest-neighbor holes (NNHs) are reduced and pushed away from the cavity center. rn and cn denote the radius of NNH and the distance between the cavity center and NNH center, respectively. (b) Vertical quality factor (QV) and modal volume (V) of isolated hexapole mode when cn =1.18a and rn =0.21~0.25a. Black and red lines represent QV and V, respectively.

Fig. 2.
Fig. 2.

(a) HZ (z-component of magnetic field) distribution of hexapole mode when cn =1.18a and rn =0.23a. (b) Red or blue color is mixed linearly with a white color to represent those regions that have amplitudes smaller than 1/20 of the maximum value. All the other parts that have amplitudes larger than 1/20 of the maximum value have saturated blue or red color.

Fig. 3.
Fig. 3.

(a) Dispersion curve of Γ-K directional PhC waveguide formed by filling in one row of air holes. Blue line represents the hexapole mode frequency. Black line is the light line. (b) Modified Γ-K directional PhC waveguide structure. The first side-hole is enlarged at both sides. rw denotes the radius of the first side-hole. (c) Dispersion curve of modified Γ-K directional PhC waveguide with rw =0.3a. (d) HZ distribution of waveguide mode at cross-point of blue and red lines in (c).

Fig. 4.
Fig. 4.

(a) Shoulder-couple structure of separation=7 with HZ distribution. (b) Modal volume (V) and quality factors (Qs) of hexapole mode. Green line represents modal volume. Black, red and blue lines represent total, horizontal and vertical Qs, respectively.

Fig. 5.
Fig. 5.

(a) Butt-couple structure of separation=7 with HZ distribution. (b) Modal volume (V) and quality factors (Qs) of hexapole mode. Green line represents modal volume. Black line represents the identical total and vertical Qs.

Fig. 6.
Fig. 6.

(a) Side-coupled structure of separation=7 with HZ distribution. (b) Modal volume (V) and quality factors (Qs) of hexapole mode. Green line represents modal volume. Black, red and blue lines represent total, horizontal and vertical Qs, respectively.

Fig. 7.
Fig. 7.

(a) HZ distribution of side-coupled structure showing the odd-like symmetry inside the waveguide. (b) Triangular-lattice photonic crystal and HZ distribution of air-band M-point mode.

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