Abstract

We study comprehensively using numerical simulations a new class of resonators, based on a circular photonic crystal reflector. The dependence of the resonator characteristics on the reflector design and parameters is studied in detail. The numerical results are compared to analytic results based on coupled mode theory. High quality factors and small modal volumes are found for a wide variety of design parameters.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett.

C. Y. Chao and L. J. Guo, �??Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,�?? Appl. Phys. Lett. 83, 1527-1529 (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. 21, 4294-4296 (2003).
[CrossRef]

J. Scheuer, W. M. J. Green, G. DeRose and A. Yariv, �??Lasing from a circular Bragg nanocavity with and ultrasmall modal volume,�?? Appl. Phys. Lett. 86, 251101 (2005).
[CrossRef]

IEEE J. Quantum Electron.

J. Scheuer and A. Yariv, "Coupled-waves approach to the design and analysis of Bragg and photonic crystal annular resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

J. Vu�?kovi�? et al., �??Optimization of the Q factor in photonic crystal microcavities,�?? IEEE J. Quantum Electron. 38, 850-856 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Scheuer, W. M. J. Green, G. DeRose and A. Yariv, �??InGaAsP annular Bragg lasers: Theory, applications and modal properties,�?? IEEE J. Sel. Top. Quantum Electron. 11, 476-484 (2005).
[CrossRef]

IEEE Photonics Technol. Lett.

A. Yariv, �??Critical coupling and its control in optical waveguide-ring resonator systems,�?? IEEE Photonics Technol. Lett. 14, 483-485 (2002).
[CrossRef]

IEEE Tansactions on Electromag. Compat.

G. Mur, �??Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,' IEEE Tansactions on Electromagnetic Compatibility EMC-23, 377-382 (1981).
[CrossRef]

J. Mod. Opt.

J. E. Heebner and R. W. Boyd, �??'Slow�?? and 'fast' light in resonator-coupled waveguides,�?? J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

J. Opt. Soc. Am. B.

J. Scheuer and A. Yariv, �??Annular Bragg defect mode resonators,�?? J. Opt. Soc. Am. B. 20, 2285-2291 (2003).
[CrossRef]

Nature

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]

See, for example, K. J. Vahala, �??Optical microcavities,�?? Nature (London) 424, 839-846 (2003), and references therein.
[CrossRef] [PubMed]

Nature Materials

B. S. Song, S. Noda, T. Asano and Y. Akahane, �??Ultra-high-Q photonic double-heterostructure nanocavity,�?? Nature Materials 4, 207-210 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photon. News

J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, �??Coupled resonator optical waveguides: Towards slowing and storing of light,�?? Opt. Photon. News 16, 36-40 (2005).
[CrossRef]

Opt. Quantum Electron.

A. Melloni, F. Morichetti, and M. Mertinelli, �??Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,�?? Opt. Quantum Electron. 35, 365 (2003).
[CrossRef]

Phys. Rev. E

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, �??Design of photonic crystal microcavities for cavity QED,�?? Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Physical Review E

J. Scheuer and A. Yariv, �??Circular photonic crystal resonators,�?? Physical Review E 70, 036603 (2004).
[CrossRef]

Science

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus and I. Kim, �??Two-dimensional photonic band-gap defect mode laser,�?? Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Other

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, (Wiley-Interscience, New York, 1999).

G. N. Watson, Theory of Bessel Functions, 2nd ed. (London, U.K. Cambridge Univ. Press, 1952).

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Figures (6)

Fig. 1.
Fig. 1.

Circular PC reflector structure. (a) rectangular lattice (b) triangular lattice (c) sunflower lattice

Fig. 2.
Fig. 2.

Field Profile of (a) high Q and (b) low Q for a “sunflower” resonator with l=70, αr=0 and αθ=0.1

Fig. 3.
Fig. 3.

Comparison between theoretical (red) and numerical (green) radial field profile

Fig. 4.
Fig. 4.

Quality factor and resonance (angular) frequency vs. Angular Perturbation

Fig. 5.
Fig. 5.

Dependence of the Q and resonant frequency on (a) αθ and (b) on αr

Fig. 6.
Fig. 6.

Impact of neff on the Q and resonant frequency

Equations (6)

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

H z ( x ) = A · H m ( 1 ) ( x ) + B · H m ( 2 ) ( x )
H z ( x ) = A ( x ) · H m ( 1 ) ( x ) + B ( x ) · H m ( 2 ) ( x )
ε x θ = { n 0 2 ( n 0 2 n p 2 ) [ 2 φ ( H m ( 1 ) ( x ) ) , α r ] [ , α θ ] , x > x 0 n 0 2 , x x 0
y α = { 0 , sin ( y ) < α 1 , sin ( y ) α
H z ( x ) = { J m ( x ) x < x 0 J m ( x ) exp [ k ( x x 0 ) ] x x 0
Δ ε 0 = 2 ( n 0 2 n p 2 ) cos [ sin 1 ( α r ) ] cos 1 ( α θ ) π 2

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