Design of silicon-wire waveguide ultracompact racetrack resonators: geometrical parameters for optimal coupling

Ramón José Pérez Menéndez

doi:10.1364/AO.58.001873

Design of silicon-wire waveguide ultracompact racetrack resonators: geometrical parameters for optimal coupling

Ramón José Pérez Menéndez

Applied Optics
Vol. 58,
Issue 8,
pp. 1873-1885
(2019)
•https://doi.org/10.1364/AO.58.001873

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Ramón José Pérez Menéndez, "Design of silicon-wire waveguide ultracompact racetrack resonators: geometrical parameters for optimal coupling," Appl. Opt. 58, 1873-1885 (2019)

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- Integrated Optics
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About this Article
History
- Original Manuscript: October 10, 2018
- Revised Manuscript: January 28, 2019
- Manuscript Accepted: January 28, 2019
- Published: March 5, 2019

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Abstract

In this paper, it is shown that a suitable choice of the geometrical parameters of a silicon-wire waveguide microracetrack resonator structure can lead to a substantial improvement in the control of coupling coefficients and, hence, the design of ultracompact devices for high-performance channel add-drop filters and all-optical switching applications. On the one hand, some simple theoretical arguments and simulation results indicate that the reduction of the silicon-wire rectangular waveguide cross-section area ( $width \times height$ ) is possible, from standard ( $450 nm \times 220 nm$ ) to ( $380 nm \times 200 nm$ ) on both the bus and the resonator waveguides; this action, apart from still guaranteeing a quasi-TE single-mode operation, would provide an effective improvement into scale-of-integration by a 1.30 factor per device volume. On the other hand, it will be shown by a semianalytical method (analytical calculation + numerical simulation) that achieving the waveguide-racetrack optimal coupling condition for a particular application can be reduced to a prime calculation of the main resonator geometrical parameters (bend radius, straight length, air gap and overall coupling length). In particular, the design of high-performance ultracompact waveguide-racetrack resonator structures, with pre-established $Q$ factor ( $Q \geq 2000$ ), free spectral range ( $FSR \geq 15 nm$ ), full width at half-maximum ( $FWHM \leq 5 nm$ ), finesse ( $F \geq 40$ ) or extinction ratio signals ( $ER \geq 20 dB$ ) can be systematically obtained with this procedure.

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Input parameters: $λ_{0} = 1550 nm$ $n_{core} = n_{Si} = 3.4758$ , $n_{cladding} = n_{SiO 2} = 1.4442$ Waveguide 1: ( $450 nm \times 220 nm$ ), $β_{0} = 8.7183898 {μm}^{- 1}$ Waveguide 2: ( $380 nm \times 200 nm$ ), $β_{0} = 6.4236262 {μm}^{- 1}$
	GVD [ps/nm × km]	Propagation loss [dB/cm]	Scattering loss [dB/cm] ^a	Total-loss [dB/cm]
$450 nm \times 220 nm$	$\sim 2800$ Ref. [16]	0.74 Ref. [8]	2.86	3.60 Ref. [8]
$380 nm \times 200 nm$	$\sim 4400$ Ref. [16]	1.40 Ref. [9]	1.00	2.40 Ref. [9]

Input parameters: $R = 4 μm$ , $g = 100 nm$ , $λ_{0} = 1577.10 nm$ . Fitting parameters: $c_{0} = 0.593875 {μm}^{- 1}$ , $p = 11.522755 {μm}^{- 1}$ , $σ = 0.603016 μm$ , and $b = 6.948406$ . Waveguides: ( $380 nm \times 200 nm$ )
	$Q$ factor	FSR (nm)	FWHM (nm)	Finesse
calculated from this work, Eq. (25)	2408.50	23.11 ^a	0.647	40.22
calculated from 2D FDTD	2445.03	26.00	0.645	40.31

Input parameters: $R = 2 μm$ , $L_{S} = 1 μm$ , $λ_{0} = 1558.8 nm$ (resonance). Fitting parameters: $c_{0} = 0.706393 {μm}^{- 1}$ , $p = 11.241025 {μm}^{- 1}$ , $σ = 0.44139 μm$ , and $b = 4.9616$ . Waveguides: ( $380 nm \times 200 nm$ )
	$Q$ Factor	FSR (nm)	FWHM (nm)	Finesse
calculated from this work, Eq. (24)	4662.88	38.82 ^a	0.334	128.33
calculated from 2D-FDTD	4642.72	42.90	0.336	127.77

Input parameters: $λ_{0} = 1550 nm$ $n_{core} = n_{Si} = 3.4758$ , $n_{cladding} = n_{SiO 2} = 1.4442$ Waveguide 1: ( $450 nm \times 220 nm$ ), $β_{0} = 8.7183898 {μm}^{- 1}$ Waveguide 2: ( $380 nm \times 200 nm$ ), $β_{0} = 6.4236262 {μm}^{- 1}$
	GVD [ps/nm × km]	Propagation loss [dB/cm]	Scattering loss [dB/cm] ^a	Total-loss [dB/cm]
$450 nm \times 220 nm$	$\sim 2800$ Ref. [16]	0.74 Ref. [8]	2.86	3.60 Ref. [8]
$380 nm \times 200 nm$	$\sim 4400$ Ref. [16]	1.40 Ref. [9]	1.00	2.40 Ref. [9]

Input parameters: $R = 4 μm$ , $g = 100 nm$ , $λ_{0} = 1577.10 nm$ . Fitting parameters: $c_{0} = 0.593875 {μm}^{- 1}$ , $p = 11.522755 {μm}^{- 1}$ , $σ = 0.603016 μm$ , and $b = 6.948406$ . Waveguides: ( $380 nm \times 200 nm$ )
	$Q$ factor	FSR (nm)	FWHM (nm)	Finesse
calculated from this work, Eq. (25)	2408.50	23.11 ^a	0.647	40.22
calculated from 2D FDTD	2445.03	26.00	0.645	40.31

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