Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion

Zin Lin; Marko Lončar; Alejandro W. Rodriguez

doi:10.1364/OL.42.002818

Optics Letters
Vol. 42,
Issue 14,
pp. 2818-2821
(2017)
•https://doi.org/10.1364/OL.42.002818

Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion

Zin Lin, Marko Lončar, and Alejandro W. Rodriguez

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Zin Lin, Marko Lončar, and Alejandro W. Rodriguez, "Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion," Opt. Lett. 42, 2818-2821 (2017)

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Table of Contents Category
- Nonlinear Optics
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About this Article
History
- Original Manuscript: April 14, 2017
- Revised Manuscript: June 3, 2017
- Manuscript Accepted: June 23, 2017
- Published: July 13, 2017

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Abstract

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear $χ^{(2)}$ and $χ^{(3)}$ frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and two-dimensional slab microcavities exhibiting long lifetimes $Q ≳ 10^{4}$ , small modal volumes $V ≳ {(λ / 2 n)}^{3}$ , and among the largest nonlinear overlaps (a generalization of phase matching in large-etalon waveguides) possible, paving the way for efficient, compact, and wide-bandwdith integrated nonlinear devices.

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$(m_{1}, m_{2})$	Polarization	$Q_{1}$	$Q_{2}$	$\bar{β} (\frac{χ^{(2)}}{4 \sqrt{(} ε_{0} λ^{3})})$	Thickness $(λ_{1})$
(0, 0)	$(E_{z}, E_{z})$	$10^{5}$	$3 \times 10^{4}$	0.041	0.39
(4, 8)	$(E_{z}, E_{z})$	$3.1 \times 10^{4}$	$3 \times 10^{3}$	0.009	0.30
(5, 10)	$(E_{z}, E_{r})$	$8 \times 10^{3}$	$3.7 \times 10^{4}$	0.008	0.18
(6, 12)	$(E_{z}, E_{z})$	$9.5 \times 10^{4}$	$2.7 \times 10^{4}$	0.008	0.18
(10, 20)	$(E_{z}, E_{z})$	$10^{6}$	$1.2 \times 10^{4}$	0.004	0.22
(10, 21)	$(E_{z}, E_{r})$	$1.6 \times 10^{6}$	$7.4 \times 10^{4}$	0.004	0.24

$ω_{1} : ω_{2} : ω_{3}$	$(m_{1}, m_{2}, m_{3})$	Polarization	$(Q_{1}, Q_{2}, Q_{3})$	$\bar{β} (\frac{χ^{(2)}}{4 \sqrt{(} ε_{0} λ^{3})})$	Thickness $(λ_{1})$
$1 : 1.2 : 2.2$	$(0, 0, 0)$	$(E_{z}, E_{z}, E_{z})$	$(1.8 \times 10^{4}, 1.4 \times 10^{4}, 7800)$	0.031	0.38

$(m_{1}, m_{2})$	Polarization	$Q_{1}$	$Q_{2}$	$\bar{β} (\frac{χ^{(2)}}{4 \sqrt{(} ε_{0} λ^{3})})$	Thickness $(λ_{1})$
(0, 0)	$(E_{z}, E_{z})$	$10^{5}$	$3 \times 10^{4}$	0.041	0.39
(4, 8)	$(E_{z}, E_{z})$	$3.1 \times 10^{4}$	$3 \times 10^{3}$	0.009	0.30
(5, 10)	$(E_{z}, E_{r})$	$8 \times 10^{3}$	$3.7 \times 10^{4}$	0.008	0.18
(6, 12)	$(E_{z}, E_{z})$	$9.5 \times 10^{4}$	$2.7 \times 10^{4}$	0.008	0.18
(10, 20)	$(E_{z}, E_{z})$	$10^{6}$	$1.2 \times 10^{4}$	0.004	0.22
(10, 21)	$(E_{z}, E_{r})$	$1.6 \times 10^{6}$	$7.4 \times 10^{4}$	0.004	0.24

$ω_{1} : ω_{2} : ω_{3}$	$(m_{1}, m_{2}, m_{3})$	Polarization	$(Q_{1}, Q_{2}, Q_{3})$	$\bar{β} (\frac{χ^{(2)}}{4 \sqrt{(} ε_{0} λ^{3})})$	Thickness $(λ_{1})$
$1 : 1.2 : 2.2$	$(0, 0, 0)$	$(E_{z}, E_{z}, E_{z})$	$(1.8 \times 10^{4}, 1.4 \times 10^{4}, 7800)$	0.031	0.38

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Optics Letters