Abstract

We present a method for determining the core and cladding refractive indices of a microring resonator from its measured quasi-transverse electric and magnetic resonant modes. We use single wavelength reflective microrings to resolve the azimuthal order ambiguity of the measured resonances. We perform accurate electromagnetic simulations to model the dependence of the resonances on geometrical and material parameters. We linearize the model and use the singular value decomposition method to find the best fit parameters for the measured data. At 1550 nm, we determine nSi3N4=1.977±0.003 for stoichiometric silicon nitride deposited using low-pressure chemical vapor deposition (LPCVD) technique and nSiOx=1.428±0.011 for plasma-enhanced chemical vapor deposition (PECVD) oxide. By measuring the temperature sensitivities of microring resonant modes with different polarizations, we find the thermo-optic coefficient of the stoichiometric silicon nitride to be dnSi3N4/dT=(2.45±0.09)×105(RIU/°C) and the PECVD oxide to be dnSiOx/dT=(0.95±0.10)×105(RIU/°C).

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. A. Arbabi, Y. M. Kang, and L. L. Goddard, in Proceedings of 2010 Frontiers in Optics (FiO) Conf. (2010), paper FThQ3.
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  13. A. C. Hryciw, S. Y. R. D. Kekatpure, L. D. Negro, and M. L. Brongersma, Appl. Phys. Lett. 98, 041102 (2011).
    [CrossRef]
  14. D. B. Leviton and B. J. Frey, Proc. SPIE 6273, 62732K (2006).
    [CrossRef]

2012 (2)

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 574 (2012).
[CrossRef]

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 1702 (2012).
[CrossRef]

2011 (3)

A. Arbabi, Y. M. Kang, C. Lu, E. Chow, and L. L. Goddard, Appl. Phys. Lett. 99, 091105 (2011).
[CrossRef]

A. C. Hryciw, S. Y. R. D. Kekatpure, L. D. Negro, and M. L. Brongersma, Appl. Phys. Lett. 98, 041102 (2011).
[CrossRef]

Y. Ding, M. Pu, L. Liu, J. Xu, C. Peucheret, X. Zhang, D. Huang, and H. Ou, Opt. Express 19, 6462 (2011).
[CrossRef]

2010 (2)

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Express 18, 16813 (2010).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, IEEE J. Quantum Electron. 46, 1769 (2010).
[CrossRef]

2009 (1)

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Quantum Electron. 41, 689 (2009).
[CrossRef]

2007 (1)

2006 (1)

D. B. Leviton and B. J. Frey, Proc. SPIE 6273, 62732K (2006).
[CrossRef]

1975 (1)

R. T. Kersten, Opt. Acta 22, 503 (1975).
[CrossRef]

1973 (1)

Arbabi, A.

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 574 (2012).
[CrossRef]

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 1702 (2012).
[CrossRef]

A. Arbabi, Y. M. Kang, C. Lu, E. Chow, and L. L. Goddard, Appl. Phys. Lett. 99, 091105 (2011).
[CrossRef]

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Express 18, 16813 (2010).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, IEEE J. Quantum Electron. 46, 1769 (2010).
[CrossRef]

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Quantum Electron. 41, 689 (2009).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, in Proceedings of 2010 Frontiers in Optics (FiO) Conf. (2010), paper FThQ3.

Baets, R.

Bartolozzi, I.

Bienstman, P.

Brongersma, M. L.

A. C. Hryciw, S. Y. R. D. Kekatpure, L. D. Negro, and M. L. Brongersma, Appl. Phys. Lett. 98, 041102 (2011).
[CrossRef]

Chow, E.

A. Arbabi, Y. M. Kang, C. Lu, E. Chow, and L. L. Goddard, Appl. Phys. Lett. 99, 091105 (2011).
[CrossRef]

De Vos, K.

Ding, Y.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 2002).

Frey, B. J.

D. B. Leviton and B. J. Frey, Proc. SPIE 6273, 62732K (2006).
[CrossRef]

Goddard, L. L.

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 574 (2012).
[CrossRef]

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 1702 (2012).
[CrossRef]

A. Arbabi, Y. M. Kang, C. Lu, E. Chow, and L. L. Goddard, Appl. Phys. Lett. 99, 091105 (2011).
[CrossRef]

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Express 18, 16813 (2010).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, IEEE J. Quantum Electron. 46, 1769 (2010).
[CrossRef]

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Quantum Electron. 41, 689 (2009).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, in Proceedings of 2010 Frontiers in Optics (FiO) Conf. (2010), paper FThQ3.

Hryciw, A. C.

A. C. Hryciw, S. Y. R. D. Kekatpure, L. D. Negro, and M. L. Brongersma, Appl. Phys. Lett. 98, 041102 (2011).
[CrossRef]

Huang, D.

Kang, Y. M.

A. Arbabi, Y. M. Kang, C. Lu, E. Chow, and L. L. Goddard, Appl. Phys. Lett. 99, 091105 (2011).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, IEEE J. Quantum Electron. 46, 1769 (2010).
[CrossRef]

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Express 18, 16813 (2010).
[CrossRef]

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Quantum Electron. 41, 689 (2009).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, in Proceedings of 2010 Frontiers in Optics (FiO) Conf. (2010), paper FThQ3.

Kekatpure, S. Y. R. D.

A. C. Hryciw, S. Y. R. D. Kekatpure, L. D. Negro, and M. L. Brongersma, Appl. Phys. Lett. 98, 041102 (2011).
[CrossRef]

Kersten, R. T.

R. T. Kersten, Opt. Acta 22, 503 (1975).
[CrossRef]

Leviton, D. B.

D. B. Leviton and B. J. Frey, Proc. SPIE 6273, 62732K (2006).
[CrossRef]

Liu, L.

Lu, C.

A. Arbabi, Y. M. Kang, C. Lu, E. Chow, and L. L. Goddard, Appl. Phys. Lett. 99, 091105 (2011).
[CrossRef]

Negro, L. D.

A. C. Hryciw, S. Y. R. D. Kekatpure, L. D. Negro, and M. L. Brongersma, Appl. Phys. Lett. 98, 041102 (2011).
[CrossRef]

Ou, H.

Peucheret, C.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 2002).

Pu, M.

Schacht, E.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 2002).

Torge, R.

Ulrich, R.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 2002).

Xu, J.

Zhang, X.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Arbabi, Y. M. Kang, C. Lu, E. Chow, and L. L. Goddard, Appl. Phys. Lett. 99, 091105 (2011).
[CrossRef]

A. C. Hryciw, S. Y. R. D. Kekatpure, L. D. Negro, and M. L. Brongersma, Appl. Phys. Lett. 98, 041102 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Arbabi, Y. M. Kang, and L. L. Goddard, IEEE J. Quantum Electron. 46, 1769 (2010).
[CrossRef]

IEEE Photon. J. (2)

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 574 (2012).
[CrossRef]

A. Arbabi and L. L. Goddard, IEEE Photon. J. 4, 1702 (2012).
[CrossRef]

Opt. Acta (1)

R. T. Kersten, Opt. Acta 22, 503 (1975).
[CrossRef]

Opt. Express (3)

Opt. Quantum Electron. (1)

Y. M. Kang, A. Arbabi, and L. L. Goddard, Opt. Quantum Electron. 41, 689 (2009).
[CrossRef]

Proc. SPIE (1)

D. B. Leviton and B. J. Frey, Proc. SPIE 6273, 62732K (2006).
[CrossRef]

Other (2)

A. Arbabi, Y. M. Kang, and L. L. Goddard, in Proceedings of 2010 Frontiers in Optics (FiO) Conf. (2010), paper FThQ3.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 2002).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Illustration of the cross section of the microring waveguide. (b) Schematic diagram of a single wavelength reflective microring, which is realized by patterning a DBR on the top part of the ring waveguide.

Fig. 2.
Fig. 2.

Schematic of the setup for measuring the transmission and reflection spectra of microring devices. OI, optical isolator; PC, polarization controller; OP, optical polarizer; PD, photodetector; and DUT, device under test. The DUT’s input fiber is physically rotated to select TE or TM polarization.

Fig. 3.
Fig. 3.

Typical transmission spectra of a microring resonator for (a) TE and (b) TM input polarizations.

Fig. 4.
Fig. 4.

Measured reflection and transmission spectra of a single wavelength reflective microring for TE polarization for (a) the first and (b) the second set of devices.

Fig. 5.
Fig. 5.

Resonant wavelength shift of TE and TM modes of two microring resonators as a function of temperature. (a) Microring one with 1 μm wide waveguide and 30 μm inner ring radius. (b) Microring two with 1.25 μm wide waveguide and 46.7 μm ring radius.

Tables (2)

Tables Icon

Table 1. Calculated Device Parameters and Their Standard Deviations

Tables Icon

Table 2. Sensitivities of Resonant Wavelengths and Refractive Indices

Equations (6)

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

ΔP=VWUTb,
σPi2=j=14(VijWjj)2,
dλTEdT=λTEncoredncoredT+λTEncladdncladdT,
dλTMdT=λTMncoredncoredT+λTMncladdncladdT.
dnSi3N4dT=(2.45±0.09)×105(RIU/°C),
dnSiO2dT=(0.95±0.10)×105(RIU/°C).

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