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Optimization of circular photonic crystal cavities - beyond coupled mode theory

Derek Chang, Jacob Scheuer, and Amnon Yariv

Open Access Open Access

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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Figures (6)
Fig. 1.
Fig. 1. Circular PC reflector structure. (a) rectangular lattice (b) triangular lattice (c) sunflower lattice

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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

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Fig. 3.
Fig. 3. Comparison between theoretical (red) and numerical (green) radial field profile

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Fig. 4.
Fig. 4. Quality factor and resonance (angular) frequency vs. Angular Perturbation

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Fig. 5.
Fig. 5. Dependence of the Q and resonant frequency on (a) αθ and (b) on αr

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Fig. 6.
Fig. 6. Impact of neff on the Q and resonant frequency

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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 ) ℑ [ 2 φ ( H m ( 1 ) ( x ) ) , α r ] ℑ [ lθ , α θ ] , x > x 0 n 0 2 , x ≤ x 0
ℑ 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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