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Electrically reconfigurable silicon microring resonator-based filter with waveguide-coupled feedback

Linjie Zhou and Andrew W. Poon

Open Access Open Access

Abstract

We demonstrate an electrically reconfigurable silicon microring resonator-based filter with waveguide-coupled feedback. Our experiments and scattering-matrix-based modeling show that the resonance wavelengths, extinction ratios, and line shapes depend on the feedback coupling and can be controllably tuned by means of carrier injection to the feedback-waveguide. We also demonstrate nearly uniform resonance line shapes over multiple free-spectral ranges by nearly phase-matching the feedback and the microring.

©2007 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Schematic of an electrically reconfigurable silicon microring resonator-based filter with waveguide-coupled feedback. Inset: cross-sectional view schematic of the lateral p-i-n diode embedded in the U-bend section. Vd : driving voltage.

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Fig. 2.
Fig. 2. (a). Modeling schematic. (b), (c) Physical interpretations of the terms in Eqs. (3) and (4). The corresponding terms of the electric-field transmissions through various paths are labelled. In (b), M: starting-point in the feedback-waveguide just prior to the input-coupler. N: ending-point in the feedback-waveguide just after the output-coupler. In (c), P: starting- and ending-points in the microring just prior to the input-coupler.

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Fig. 3.
Fig. 3. (a). Illustration of the resonance-dependent line shapes in general cases. Resonances at wavelengths λm +1 and λm see different feedback phase values Δϕm +1 and Δϕm . (b) and (c) Modeled feedback phase Δϕ (λ) and the corresponding transmission spectra with (b) Δϕ(λm +1) - Δϕ(λm )≈1.4π, and (c) Δϕ(λm +1) - Δϕ(λm )≈2π.

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Fig. 4.
Fig. 4. (a).-4(c). Optical micrographs of the three fabricated devices (I), (II), and (III). (d) and (e) Zoom-in view SEMs of (d) the waveguide-circular-microring coupling region, and (e) the waveguide-racetrack-microring coupling region without oxide upper-cladding. (f) Cross-sectional view SEM of the single-mode waveguide without oxide upper-cladding.

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Fig. 5.
Fig. 5. (a)-(c) Measured (solid grey lines) and modeled (dashed red lines) TE-polarized transmission spectra of device (I) upon low injection levels with bias voltages of Vd =(a) 0 V, (b) 0.9 V, and (c) 1.0 V. (d)-(f) Measured (solid grey lines) and modeled (dashed red lines) TE-polarized transmission spectra of device (I) upon high injection levels with bias voltages of Vd =(a) 1.8 V, (b) 2.3 V, and (c) 2.9 V.

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Fig. 6.
Fig. 6. (a).-(d). Measured (solid grey lines) and modeled (dashed red lines) TE-polarized transmission spectra of device (II) under various bias voltages of Vd =(a) 1.2 V, (b) 1.4 V, (c) 2.0 V, and (d) 3.0 V.

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Fig. 7.
Fig. 7. Measured (solid grey lines) and modeled (dashed red lines) TE-polarized transmission spectra of device (III) under various bias voltages of Vd =(a) 0.7 V, (b) 1.5 V, (c) 2.0 V, and (d) 2.9 V.

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Fig. 8.
Fig. 8. (a).-(e). Modeled transmission spectra under various attenuated feedback conditions for a racetrack microring device with strong coupling (κ≈0.94).

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Equations (15)

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[ E o E 2 ] = [ τ e − i φ κ e − i ( φ + π ⁄ 2 ) κ e − i ( φ + π ⁄ 2 ) τ e − i φ ] [ b γ e − i ϕ 0 0 ae − i θ ] [ τ e − i φ κ e − i ( φ + π ⁄ 2 ) κ e − i ( φ + π ⁄ 2 ) τ e − i φ ] [ E i E 1 ] ,
E 1 = ae − i θ E 2 .
I out I in = ∣ E o E i ∣ 2 = ∣ τ 2 b γ e − i ( ϕ + 2 φ ) + κ 2 ae − i ( θ + 2 φ + π ) + a 2 b γ e − i ( 2 θ + 4 φ + ϕ + π ) 1 − [ τ 2 a 2 e − i ( 2 θ + 2 φ ) + κ 2 ab γ e − i ( θ + 2 φ + ϕ + π ) ] ∣ 2 .
A = ∣ A ∣ e − i Φ = τ 2 a 2 e − i ( 2 θ + 2 φ ) + κ 2 ab γ e − i ( θ + 2 φ + ϕ + π ) ,
I out I in = b 2 γ 2 ∣ τ 2 − a 2 e − i ( 2 θ + 2 φ ) 1 − τ 2 a 2 e − i ( 2 θ + 2 φ ) ∣ 2 ,
I out I in = a 2 κ 4 ∣ 1 1 − τ 2 a 2 e − i ( 2 θ + 2 φ ) ∣ 2 ,
I out I in = a 2 ∣ κ 2 − ab γ e − i ( θ + 2 φ + ϕ + π ) 1 − κ 2 ab γ e − i ( θ + 2 φ + ϕ + π ) ∣ 2 ,
Δ ϕ ( λ m ) = 2 n m π + c ,
A = e − i ( 2 θ + 2 φ ) [ τ 2 a 2 − κ 2 ab γ e − ic ] .
Φ = 2 θ + 2 φ − Φ c = 2 m π .
( I out I in ) λ m = ∣ τ 2 b γ e − ic − κ 2 a − a 2 b γ e − i Φ c e − ic 1 − e − i Φ c [ τ 2 a 2 − κ 2 ab γ e − ic ] ∣ 2 .
Δ ϕ ( λ ) = n eff 2 π λ ( L b − L a ) + δ ϕ .
n eff L res = m λ m ,
L b − L a = n L res ( n = 1 , 2 , 3 … ) .
L b ≈ 2 n ( L a + L c ) + L a .
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