Abstract

We report the design criteria and performance of Si ring resonators for passive athermal applications in wavelength division multiplexing (WDM). The waveguide design rules address i) positive-negative thermo-optic (TO) composite structures, ii) resonant wavelength dependent geometry to achieve constant confinement factor (Γ), and iii) observation of small residual second order effects. We develop exact design requirements for a temperature dependent resonant wavelength shift (TDWS) of 0 pm/K and present prototype TDWS performance of 0.5pm/K. We evaluate the materials selection tradeoffs between high-index contrast (HIC) and low-index contrast (LIC) systems and show, remarkably, that FSR and footprint become comparable under the constraint of athermal design.

© 2010 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010

2009

2008

J.-M. Lee, D.-J. Kim, G.-H. Kim,, O-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguides using slot structure,” Opt. Express 14, 1645–1652 (2008).
[CrossRef]

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20(11), 882–884 (2008).
[CrossRef]

J. T. Robinson, K. Preston, O. Painter, and M. Lipson, “First-principle derivation of gain in high-index-contrast waveguides,” Opt. Express 16(21), 16659–16669 (2008).
[CrossRef] [PubMed]

2007

2002

G. Cocorullo, F. G. Della Corte, L. Moretti, I. Rendina, and A. Rubino, “Measurement of the thermo-optic coefficient of a-Si:H at the wavelength of 1500 nm from room temperature to 200°C,” J. Non-Cryst. Solids 299–302, 310–313 (2002).
[CrossRef]

N.-N. Feng, G.-R. Zhou, C. Xu, and W.-P. Huang, “Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers,” J. Lightwave Technol. 20(11), 1976–1980 (2002).
[CrossRef]

1999

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

1998

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55µm wavelength using a silica-based athermal waveguide,” Electron. Lett. 34(4), 367–369 (1998).
[CrossRef]

1996

Y. Kokubun, S. Yoneda, and H. Tanaka, “Temperature-independent narrowband optical filter at 1.3µm wavelength by an athermal waveguide,” Electron. Lett. 32(21), 1998–2000 (1996).
[CrossRef]

Agarwal, A.

Ahn, H.

Baets, R.

Beals, M. A.

Bogaerts, W.

Carothers, D. N.

Chen, Y. K.

Chu, S. T.

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

Cocorullo, G.

G. Cocorullo, F. G. Della Corte, L. Moretti, I. Rendina, and A. Rubino, “Measurement of the thermo-optic coefficient of a-Si:H at the wavelength of 1500 nm from room temperature to 200°C,” J. Non-Cryst. Solids 299–302, 310–313 (2002).
[CrossRef]

Della Corte, F. G.

G. Cocorullo, F. G. Della Corte, L. Moretti, I. Rendina, and A. Rubino, “Measurement of the thermo-optic coefficient of a-Si:H at the wavelength of 1500 nm from room temperature to 200°C,” J. Non-Cryst. Solids 299–302, 310–313 (2002).
[CrossRef]

Dumon, P.

Feng, N.-N.

Gill, D. M.

Grove, M. J.

Guha, B.

Han, X.

Ho, S.-T.

Hu, J.

Huang, D.

Huang, H.

Huang, W.-P.

Jian, X.

Kim, D.-J.

J.-M. Lee, D.-J. Kim, G.-H. Kim,, O-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguides using slot structure,” Opt. Express 14, 1645–1652 (2008).
[CrossRef]

J.-M. Lee, D.-J. Kim, H. Ahn, S.-H. Park, and G. Kim, “Temperature Dependence of Silicon Nanophotonic Ring Resonator with a Polymeric overlayer,” J. Lightwave Technol. 25(8), 2236–2243 (2007).
[CrossRef]

Kim, G.

J.-M. Lee, D.-J. Kim, G.-H. Kim,, O-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguides using slot structure,” Opt. Express 14, 1645–1652 (2008).
[CrossRef]

J.-M. Lee, D.-J. Kim, H. Ahn, S.-H. Park, and G. Kim, “Temperature Dependence of Silicon Nanophotonic Ring Resonator with a Polymeric overlayer,” J. Lightwave Technol. 25(8), 2236–2243 (2007).
[CrossRef]

Kim, K.-J.

J.-M. Lee, D.-J. Kim, G.-H. Kim,, O-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguides using slot structure,” Opt. Express 14, 1645–1652 (2008).
[CrossRef]

Kim,, G.-H.

J.-M. Lee, D.-J. Kim, G.-H. Kim,, O-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguides using slot structure,” Opt. Express 14, 1645–1652 (2008).
[CrossRef]

Kimerling, L. C.

Kokubun, Y.

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55µm wavelength using a silica-based athermal waveguide,” Electron. Lett. 34(4), 367–369 (1998).
[CrossRef]

Y. Kokubun, S. Yoneda, and H. Tanaka, “Temperature-independent narrowband optical filter at 1.3µm wavelength by an athermal waveguide,” Electron. Lett. 32(21), 1998–2000 (1996).
[CrossRef]

Kwon, O-K.

J.-M. Lee, D.-J. Kim, G.-H. Kim,, O-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguides using slot structure,” Opt. Express 14, 1645–1652 (2008).
[CrossRef]

Kyotoku, B. B.

Lee, J.-M.

J.-M. Lee, D.-J. Kim, G.-H. Kim,, O-K. Kwon, K.-J. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguides using slot structure,” Opt. Express 14, 1645–1652 (2008).
[CrossRef]

J.-M. Lee, D.-J. Kim, H. Ahn, S.-H. Park, and G. Kim, “Temperature Dependence of Silicon Nanophotonic Ring Resonator with a Polymeric overlayer,” J. Lightwave Technol. 25(8), 2236–2243 (2007).
[CrossRef]

Lipson, M.

Little, B. E.

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

Liu, W.

Matsuura, S.

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55µm wavelength using a silica-based athermal waveguide,” Electron. Lett. 34(4), 367–369 (1998).
[CrossRef]

Michel, J.

Moretti, L.

G. Cocorullo, F. G. Della Corte, L. Moretti, I. Rendina, and A. Rubino, “Measurement of the thermo-optic coefficient of a-Si:H at the wavelength of 1500 nm from room temperature to 200°C,” J. Non-Cryst. Solids 299–302, 310–313 (2002).
[CrossRef]

Morthier, G.

Painter, O.

Pan, W.

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

Park, S.-H.

Patel, S. S.

Pomerene, A. T. S.

Preston, K.

Rasras, M. S.

Rendina, I.

G. Cocorullo, F. G. Della Corte, L. Moretti, I. Rendina, and A. Rubino, “Measurement of the thermo-optic coefficient of a-Si:H at the wavelength of 1500 nm from room temperature to 200°C,” J. Non-Cryst. Solids 299–302, 310–313 (2002).
[CrossRef]

Robinson, J. T.

Rubino, A.

G. Cocorullo, F. G. Della Corte, L. Moretti, I. Rendina, and A. Rubino, “Measurement of the thermo-optic coefficient of a-Si:H at the wavelength of 1500 nm from room temperature to 200°C,” J. Non-Cryst. Solids 299–302, 310–313 (2002).
[CrossRef]

Sato, S.

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

Sparacin, D. K.

Sun, X.

Suzuki, S.

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

Tanaka, H.

Y. Kokubun, S. Yoneda, and H. Tanaka, “Temperature-independent narrowband optical filter at 1.3µm wavelength by an athermal waveguide,” Electron. Lett. 32(21), 1998–2000 (1996).
[CrossRef]

Teng, J.

Tu, K. Y.

Tu, Y.

White, A. E.

Xu, C.

Ye, W. N.

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20(11), 882–884 (2008).
[CrossRef]

Yoneda, S.

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55µm wavelength using a silica-based athermal waveguide,” Electron. Lett. 34(4), 367–369 (1998).
[CrossRef]

Y. Kokubun, S. Yoneda, and H. Tanaka, “Temperature-independent narrowband optical filter at 1.3µm wavelength by an athermal waveguide,” Electron. Lett. 32(21), 1998–2000 (1996).
[CrossRef]

Zhang, H.

Zhao, M.

Zhou, G.-R.

Appl. Opt.

Electron. Lett.

Y. Kokubun, S. Yoneda, and S. Matsuura, “Temperature-independent optical filter at 1.55µm wavelength using a silica-based athermal waveguide,” Electron. Lett. 34(4), 367–369 (1998).
[CrossRef]

Y. Kokubun, S. Yoneda, and H. Tanaka, “Temperature-independent narrowband optical filter at 1.3µm wavelength by an athermal waveguide,” Electron. Lett. 32(21), 1998–2000 (1996).
[CrossRef]

IEEE Photon. Technol. Lett.

S. T. Chu, W. Pan, S. Suzuki, B. E. Little, S. Sato, and Y. Kokubun, “Temperature Insensitive Vertically Coupled Microring Resonator Add/Drop Filters by Means of a Polymer Overlay,” IEEE Photon. Technol. Lett. 11(9), 1138–1140 (1999).
[CrossRef]

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20(11), 882–884 (2008).
[CrossRef]

J. Lightwave Technol.

J. Non-Cryst. Solids

G. Cocorullo, F. G. Della Corte, L. Moretti, I. Rendina, and A. Rubino, “Measurement of the thermo-optic coefficient of a-Si:H at the wavelength of 1500 nm from room temperature to 200°C,” J. Non-Cryst. Solids 299–302, 310–313 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Other

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, 1998).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic view of an a-Si racetrack resonator and (b) the transmission spectra showing the resonance peak shift with temperature for both oxide clad and polymer clad devices. We compare a-Si rings of the same cross-section (700nm × 216nm) and different top claddings (oxide and polymer). In the case of an oxide clad ring, the positive TO coefficient of both core and cladding result in a positive peak shift of 63pm/K. There is significant TO compensation for the polymer clad ring and the peak shift is reduced to 7pm/K for this waveguide design.

Fig. 2
Fig. 2

Experimental results showing d λ r / d T variation with λ r for TM mode propagation. The slope of the d λ r / d T variation with λ r reflects the role of Γ (see Eq. (1), (2)) on TO and d λ r / d T . Hence the wavelength at the dashed-line crossover point is an unique condition for d λ r / d T = 0. The hexagonal bold data points correspond to the spectral data shown in Fig. (1)

Fig. 3
Fig. 3

Variation of athermal waveguide width with wavelength for TE and TM modes. These simulation results are for an a-Si waveguide of 206nm height with an SiO2 underclad and the EP polymer over-cladding. The desired waveguide width for athermal operation increases with wavelength to keep the confinement factor constant, consistent with the theory presented in section 2.2.

Fig. 4
Fig. 4

Measured second order variations of resonant wavelength with fit to a quadratic dependence. The residual second order effects become important when the first order terms vanish at low peak shifts (<2pm/K). The quadratic term has contributions from the temperature dependence of the confinement factor and from the second order material coefficients.

Tables (2)

Tables Icon

Table 1 Refractive index and TO coefficient of materials in this study

Tables Icon

Table 2 Performance comparison of two athermal waveguide designs, for an a-Si core and a Si3N4 core, with the same EP polymer overclad

Equations (3)

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

d n e f f d T ( λ ) = Γ c ( λ ) d n c d T ( λ ) + Γ t c l ( λ ) d n t c l d T ( λ ) + Γ b c l ( λ ) d n b c l d T ( λ )
1 λ r d λ r d T ( λ ) = 1 n g d n e f f d T ( λ )
d n e f f ( n c , n c l ) = ( Γ c n c T + Γ c l n c l T ) d T + 1 2 [ Γ c 2 n c T 2 + Γ c l 2 n c l T 2 + Γ c n c ( n c T ) 2 + Γ c l n c l ( n c l T ) 2 + Γ c n c l n c T n c l T + Γ c l n c n c T n c l T ] d T 2

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