Abstract

Temporal behaviour of incident pulse in high-quality (Q) factor photonic crystal microcavities are studied by two dimensional finite difference time domain calculations. For high-Q mode excitation, two periods of oscillation are observed in addition to the exponential decay corresponding to the cavity mode photon life time. Long and short period oscillations correspond to beats with low-Q mode (for short pulse widths) and to lattice periodicity for all pulse widths, respectively. For low-Q mode and off-resonant excitations, long period oscillations correspond to coupling to bandedge states.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett. (3)

K. Srinivasan, P. E. Barclay, O.Painter, J. Chen, A. Y. Cho, C. Gmachl, �??Experimental demonstration of a high quality factor photonic crystal microcavity,�?? Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

G.Subramania, S.Y.Lin, J.R.Wendt, and J.M.Rivera, �??Tuning the microcavity resonant wavelength in a two-dimensional photonic crystal by modifying the cavity geometry,�?? Appl. Phys. Lett. 83, 4491-4493, (2003).
[CrossRef]

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

Appl. Phys. Letts. (1)

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

IEE Proc. Optoelectron. (1)

P.R.Villeneuve, S.Fan, S.Johnson, and J.D.Joannopoulos, �??Three-dimensional photon confinement in photonic crystals of low-dimensional periodicity,�?? IEE Proc. Optoelectron. 145, 384-390, (1998).
[CrossRef]

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

J.Opt. Soc. Am B (1)

S.F.Migaleev, and Y.S.Kivshar, �??Nonlinear transmission and light localization in photonic-crystal waveguides,�?? J.Opt. Soc. Am B 19., 2241-2249 (2002).
[CrossRef]

Nature (2)

K.J.Vahala, �??Optical microcavities,�?? Nature 424, 839-846, (2003).
[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]

PECS V (1)

T. Asano, W. Kunishi, K. Kiyota, B-S. Song, A. Noda, �??Dynamic properties of artificial defects in two-dimensional photonic crystal slab,�?? Tech. Digest, Intl. Symposium on Photonic and Electromagnetic Crystal Structures (PECS V), March 2004, Kyoto, Japan, p166

Phys. Rev. A (2)

J. Erland, and I. Balslev, �??Theory of quantum beat and polarization interference in four-wave mixing,�?? Phys. Rev. A 48, R1765-R1768 (1993).
[CrossRef] [PubMed]

D.G.Angelakis, E. Paspalakis, and P.L.Knight, �??Coherent phenomena in photonic crystals,�?? Phys. Rev. A 64 013801, (2001)
[CrossRef]

Phys. Rev. Lett. (1)

V.M.Aplakov, and M.E.Raikh, �??Strongly localized mode at the intersection of the phase slips in a photonic crystal without band gap,�?? Phys. Rev. Lett. 90, 253901, (2003)
[CrossRef]

Science (1)

R.Colombelli etal, �??Quantum cascade surface-emitting photonic crystal laser,�?? Science 302, 1374-1377, (2003).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

A schematic of the 2-D photonic crystal microcavity structure. The typical size of this structure is about 15a2, where a is the lattice periodicity.

Fig. 2.
Fig. 2.

The calculated band structure for TM mode excitation. The hashed region shows the photonic bandgap region with the two defect modes at 1.53 µm and 1.414µm wavelengths. Figure on the right shows the transmission spectrum.

Fig. 3.
Fig. 3.

(a)Temporal evolution of 100 fsec (dashed line) and 16.7 fsec (solid line) incident pulses resonant at 1.53 µm. Inset shows the close up of the exponential decay for the 100fsec pulse (dashed line) along with an exponential fit (solid line). (b) A close up of the long period oscillations observed for short pulse excitation (16.7 fsec pulse width) at 1.53 µm is shown by the dotted line. The oscillation period corresponds to a period of 33.33fsec or a beat energy separation of 63 meV. The solid line is a fit with the energy separation between the two modes to be 65 meV.

Fig. 4.
Fig. 4.

Temporal evolution for 500fsec incident pulse resonant at 1.414 µm. Dashed lines are exponential fits. Inset shows the time evolution of a short (17 fsec) incident pulse resonant at 1.414 µm.

Fig. 5.
Fig. 5.

A close up of the short period oscillations observed for 1.53 µm (solid line) and 1.414 µm (dashed line) excitation.

Fig. 6.
Fig. 6.

Long period oscillations observed for 167 fsec pulse corresponding to non-resonant excitation at 1.57 µm (solid line) and 1.5 µm (dashed line). The observed oscillations correspond to coupling to band edge states though the pulse spectral width covers the high-Q mode at 1.53 µm wavelength.

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