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Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling

Ziyang Zhang, Matteo Dainese, Lech Wosinski, and Min Qiu

Open Access Open Access

Abstract

Resonance-splitting and enhanced notch depth are experimentally demonstrated in micro-ring resonators on SOI platform as a result of the mutual mode coupling. This coupling can be generated either by the nanometer-scaled gratings along the ring sidewalls or by evanescent directional coupling between two concentric rings. The transmission spectra are fitted using the time-domain coupled mode analysis. Split-wavelength separation of 0.68 nm for the 5-µm-radius ring, notch depth of 40 dB for the 10-µm-radius ring, and intrinsic Q factor of 2.6×105 for the 20-µm-radius ring are demonstrated. Notch depth improvement larger than 25dB has been reached in the 40-39-µm-radius double-ring structure. The enhanced notch depth and increased modal area for the concentric rings might be promising advantages for bio-sensing applications.

©2008 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Schematic of a ring resonator side coupled to a waveguide. Wave propagating from left to right (S +1 ) in the waveguide only generates the counter-clockwise travelling mode a(t) in the ring. Clockwise travelling mode b(t) are coupled with a(t) by coefficient u due to the grating along the ring. The grating is indicated as the red dashed circle.

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Fig. 2.
Fig. 2. Illustration of the dependence of transmission spectra on the mutual coupling coefficient u. With the presence of mutual coupling, the notch becomes deeper. At optimal coupling um, complete channel drop can be reached. When u further increases, mode splitting occurs.

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Fig. 3.
Fig. 3. The SEM photo of (a) the grating on the side-walls of a 20-µm-radius ring resonator and (b) gold grating couplers at the tapered waveguide end to assist vertical light injection/detection with a single mode fiber.

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Fig. 4.
Fig. 4. (a) SEM photo of a 5-µm-radius ring. (b) broad spectrum transmission. (c) Curve fitting using Eq. (6) for one of the notch groups. The intrinsic Q value obtained is 6×104 and the coupling Q is 2×104. The split notches are deeper than the case without mutual coupling (12dB compared to 6dB).

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Fig. 5.
Fig. 5. (a) SEM photo of a 10-µm-radius ring. (b) broad spectrum transmission. (c) Curve fitting using Eq. (6) for one of the notch groups. The notch depth is much improved, 40dB compared to the case without mutual coupling, where the notch is barely visible.

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Fig. 6.
Fig. 6. (a) SEM photo of a 20-µm-radius ring. (b) broad spectrum transmission. (c) Curve fitting using Eq. (6) for one of the notch groups. The intrinsic Q value obtained is 2.6×105 and the coupling Q is 1.9×104.

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Fig. 7.
Fig. 7. Schematic of two concentric ring resonators side coupled to a waveguide. Wave propagating from left to right (S +1 ) in the waveguide only generates the counter-clockwise travelling mode a(t) in the outer ring. Counter-clockwise travelling mode b(t) in the inner ring can then be generated by evanescent directional coupling from a(t) .

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Fig. 8.
Fig. 8. (a) SEM photo of a single 40-µm-radius ring. (b) SEM photo of a dual 40-39-µm-radius ring structure. (c) broad spectrum transmission for both cases. The double ring structure exhibits much enhanced notch depth. (d)-(e) Curve fitting for two of the deep notches using Eq. (6).

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Equations (14)

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

da dt = ( j ω a − 1 τ a ) a − j κ a S + 1 − jub
db dt = ( j ω b − 1 τ b ) b − j κ b S + 2 − jua
S − 2 = e − j β L ( S + 1 − j κ a * a )
S − 1 = e − j β L ( S + 2 − j κ b * b )
∣ S − 2 ∣ 2 = ∣ S + 1 ∣ 2 ∣ 1 − ∣ κ a 2 ∣ B AB + u 2 ∣ 2
T ( ω ) = ∣ S − 2 ∣ 2 ∣ S + 1 ∣ 2 = ∣ D C ∣ 2
T = ∣ 1 − ∣ κ a 2 ∣ A ∣ 2 = 4 ( ω − ω a ) 2 + ( 1 Q ae − 1 Q ai ) 2 4 ( ω − ω a ) 2 + ( 1 Q ae + 1 Q ai ) 2
Im { D } = 0 ⇒ ω = ω a = ω b .
Re { D } = 0 ⇒ u 2 = u m 2 = ω a ω b 4 Q b ( 1 Q ae − 1 Q ai ) .
da dt = ( j ω a − 1 τ a ) a − j κ a S + 1 − jub
db dt = ( j ω b − 1 τ b ) b − jua
S − 2 = e − j β L ( S + 1 − j κ a * a )
S − 1 = e − j β L S + 2
T ( ω ) = ∣ S − 2 ∣ 2 ∣ S + 1 ∣ 2 = ∣ D C ∣ 2
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