Abstract

A series of microcavities in 2D hexagonal lattice photonic crystal slabs are studied in this paper. The microcavities are small sections of a photonic crystal waveguide. Finite difference time domain simulations show that these cavities preserve high Q modes with similar geometrical parameters and field profile. Effective modal volume is reduced gradually in this series of microcavity modes while maintaining high quality factor. Vertical Q value larger than 106 is obtained for one of these cavity modes with effective modal volume around 5.40 cubic half wavelengths [(λ/2nslab)3]. Another cavity mode provides even smaller modal volume around 2.30 cubic half wavelengths, with vertical Q value exceeding105.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett.

M. Qiu and B. Jaskorzynska, ཿA design of a channel drop filter in a two-dimensional triangular photonic crystalཿ, Appl. Phys. Lett. 83, 1074 (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 (2003)
[CrossRef]

Electron. Lett.

M. Qiu, ཿUltra-compact optical filter in two-dimensional photonic crystal,ཿ Electron. Lett. 40, 539 (2004)
[CrossRef]

IEEE J. of Quantum Electron.

J. Vu¿¡kovi¿ , M. lon¿ar, H. Mabuchi and A. Scherer, ཿOptimization of the Q factor in photonic crystal microcavities,ཿ IEEE J. of Quantum Electron. 38, 850 (2002)
[CrossRef]

IEEE Microwave Wireless Components Lett.

W. H. Guo, W. J. Li, and Y. Z. Huang, ཿComputation of Resonant Frequencies and Quality Factors of Cavities by FDTD Technique and Padé Approximation,ཿ IEEE Microwave Wireless Components Lett. 11, 223 (2001)
[CrossRef]

IEEE Trans. Antennas and Propagation

K. S. Yee, ཿNumerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,ཿ IEEE Trans. Antennas and Propagation, 14, 302 (1966)

J. Appl. Phys.

H. Benisty, ཿModal analysis of optical guides with two-dimensional photonic band-gap boundaries,ཿ J. Appl. Phys. 75, 4753 (1994)

J. Comput. Phys.

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

Nature

Spillane, S. M., Kippenberg, T. J. and Vahala, K. J. ཿUltralow-threshold Raman laser using a spherical dielectric microcavity,ཿ S. M. , Nature 415, 621-623 (2002)
[CrossRef]

C. Santori, D. Fattal, J. Vu¿¡kovi¿ , G. S. Solomon, and Y. Yamamoto, ཿIndistinguishable photons from a single-photon device,ཿ Nature 419, 594 (2002)
[CrossRef] [PubMed]

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

T. F. Krauss, R. M. De La Rue, and S. Brand, ཿTwo-dimensional photonic-bandgap structures operating at near-infrared wavelengthsཿ, Nature 383, 699 (1996)
[CrossRef]

Opt. Express

Phys. Rev. B

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, 5751 (1999)
[CrossRef]

A. Mekis, S. Fan, and J. D. Joannopoulos, ཿBound states in photonic crystal waveguides and waveguide bendsཿ, Phys. Rev. B 58, 4809 (1998)
[CrossRef]

Phys. Rev. E.

J. Vu¿kovi¿, M. lon¿ar, H. Mabuchi and A. Scherer, ཿDesign of photonic crystal microcavities for cavity QED,ཿ Phys. Rev. E. 65, 016608 (2001)
[CrossRef]

Phys. Rev. Lett.

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

S. John, ཿStrong localization of photons in certain disordered dielectric superlattices,ཿ Phys. Rev. Lett. 58, 2486 (1987)
[CrossRef] [PubMed]

S. Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, ཿChannel Drop Tunneling through Localized States,ཿ Phys. Rev. Lett. 80, 960 (1998)
[CrossRef]

E.Yablonovitch and T. J. Gmitter, ཿDonor and acceptor modes in photonic band structure,ཿ Phys. Rev. Lett. 67, 3380 (1991)
[CrossRef] [PubMed]

Proceedings of the SPIE

S. Fan, Proceedings of the SPIE, v 3002, 1997, p 67-73
[CrossRef]

Science

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. OཿBrien, P. D. Dapkus, and I. Kim, ཿTwo-Dimensional Photonic Band-Gap Defect Mode Laser,ཿ Science 284, 1819 (1999)
[CrossRef] [PubMed]

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, ཿQuantum Dot Single-Photon Turnstile Device,ཿ Science 290, 2282 (2000)

Other

M. Qiu, ཿHigh Q cavities in photonic crystal slabs: determining resonant frequency and quality factor accurately,ཿ submitted for publication (2004)

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of 2D PCS microcavities with three central holes missing in a row. The refractive index of the slab is 3.4 and the thickness t is 0.7a. d and R1 are varied to find the largest Q of the M3 mode.

Fig. 2.
Fig. 2.

(a) H �� field distribution of the M3 mode. (b) k space intensity profile I. The region inside the blue dashed circle (the light line) is the leaky region.

Fig. 3.
Fig. 3.

(a) M2 cavity, with d=0.23a and R1 =0.2a . (b) H z field distribution of the M2 mode. (c) k space intensity profile I. Components inside the leaky region are reduced compared to the M3 mode in Fig. 2(b)

Fig. 4.
Fig. 4.

(a) M1 cavity, with d=0.21a, R1 =0.22a and R2 =0.25a (b) H z field distribution of the M1 mode. (c) k space intensity profile I. Components inside the leaky region are greatly reduced compared to the M2 mode in Fig. 3(c)

Fig. 5.
Fig. 5.

(a) M0 cavity, with d=0.14a and R1 =0.27a. (b) H z field distribution of the M0 mode. (c) k space intensity profile I.

Fig. 6.
Fig. 6.

Electric intensity distribution of (a) M3 mode, (b) M2 mode, (c) M1 mode, and (d) M0 mode.

Fig. 7.
Fig. 7.

(a) Q value (the blue line with diamond marker) and modal volume (the green line with circle marker) comparison of the four modes. (b) Q (the blue line with diamond marker) and radiation factor RF (the green line with circle marker) comparison of the four modes. RF is normalized to the M1 mode.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

V = ε ( x , y , z ) · E ( x , y , z ) 2 dxdydz max [ ε ( x , y , z ) · E ( x , y , z ) 2 ] ,
E ( x , y , z ) 2 = E x ( x , y , z ) 2 + E y ( x , y , z ) 2 + E z ( x , y , z ) 2 .
P = η 8 λ 2 k 2 k k I · d k x · d k y ,
I = F T 2 ( H y ) + 1 η F T 2 ( E x ) 2 + F T 2 ( H x ) 1 η F T 2 ( E y ) 2

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