Abstract

A class of whispering-gallery-mode resonators, herein referred to as adiabatic microring resonators, is proposed and numerically demonstrated. Adiabatic microrings enable electrical and mechanical contact to be made to the resonator without inducing radiation, while supporting only a single radial mode and therein achieving an uncorrupted free spectral range (FSR). Rigorous finite-difference time-domain simulations indicate that adiabatic microrings with outer diameters as small as 4μm can achieve resonator quality factors (Qs) as high as Q = 88,000 and an FSR of 8.2THz, despite large internal contacts.

© 2010 Optical Society of America

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  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
    [CrossRef]
  2. T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
    [CrossRef]
  3. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
    [CrossRef] [PubMed]
  4. M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, in 2008 5th IEEE International Conference on Group IV Photonics (IEEE, 2008).
  5. M. R. Watts, M. J. Shaw, and G. N. Nielson, Nat. Photon. 1, 632 (2007).
    [CrossRef]
  6. A. M. Armani and K. J. Vahala, Opt. Lett. 31, 1896 (2006).
    [CrossRef] [PubMed]
  7. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
    [CrossRef] [PubMed]
  8. Q. Xu, D. Fattal, and R. G. Beausoleil, Opt. Express 16, 4309 (2008).
    [CrossRef] [PubMed]
  9. M. R. Watts, H. A. Haus, and E. P. Ippen, Opt. Lett. 30, 967 (2005).
    [CrossRef] [PubMed]
  10. M. R. Watts and H. A. Haus, Opt. Lett. 30, 138 (2005).
    [CrossRef] [PubMed]
  11. A. W. Snyder, Optical Waveguide Theory (Chapman & Hall, 1983).

2008 (1)

2007 (2)

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

M. R. Watts, M. J. Shaw, and G. N. Nielson, Nat. Photon. 1, 632 (2007).
[CrossRef]

2006 (1)

2005 (3)

2003 (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Armani, A. M.

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Barwicz, T.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

Beausoleil, R. G.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Fattal, D.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Haus, H. A.

Ippen, E. P.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

M. R. Watts, H. A. Haus, and E. P. Ippen, Opt. Lett. 30, 967 (2005).
[CrossRef] [PubMed]

Kaertner, F. X.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Lentine, A. L.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, in 2008 5th IEEE International Conference on Group IV Photonics (IEEE, 2008).

Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Nielson, G. N.

M. R. Watts, M. J. Shaw, and G. N. Nielson, Nat. Photon. 1, 632 (2007).
[CrossRef]

Popovic, M. A.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

Rakich, P. T.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

Shaw, M. J.

M. R. Watts, M. J. Shaw, and G. N. Nielson, Nat. Photon. 1, 632 (2007).
[CrossRef]

Smith, H. I.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

Snyder, A. W.

A. W. Snyder, Optical Waveguide Theory (Chapman & Hall, 1983).

Socci, L.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Trotter, D. C.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, in 2008 5th IEEE International Conference on Group IV Photonics (IEEE, 2008).

Vahala, K. J.

A. M. Armani and K. J. Vahala, Opt. Lett. 31, 1896 (2006).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Watts, M. R.

M. R. Watts, M. J. Shaw, and G. N. Nielson, Nat. Photon. 1, 632 (2007).
[CrossRef]

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

M. R. Watts and H. A. Haus, Opt. Lett. 30, 138 (2005).
[CrossRef] [PubMed]

M. R. Watts, H. A. Haus, and E. P. Ippen, Opt. Lett. 30, 967 (2005).
[CrossRef] [PubMed]

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, in 2008 5th IEEE International Conference on Group IV Photonics (IEEE, 2008).

Xu, Q.

Young, R. W.

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, in 2008 5th IEEE International Conference on Group IV Photonics (IEEE, 2008).

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Nat. Photon. (2)

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kaertner, E. P. Ippen, and H. I. Smith, Nat. Photon. 1, 57 (2007).
[CrossRef]

M. R. Watts, M. J. Shaw, and G. N. Nielson, Nat. Photon. 1, 632 (2007).
[CrossRef]

Nature (2)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Other (2)

A. W. Snyder, Optical Waveguide Theory (Chapman & Hall, 1983).

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, in 2008 5th IEEE International Conference on Group IV Photonics (IEEE, 2008).

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Figures (2)

Fig. 1
Fig. 1

(a) 2D FDTD simulation of a microdisk resonator with w g = 0.3 μm , R = 2 μm , n c = 3 , n c l = 1 , and s = 0.1 μm . Microdisks provide natural contacts from the interior of the resonator but support high-order radial modes. (b) 2D FDTD simulation of a directly contacted microring resonator ( w r = 0.4 μm and a = 0.8 μm ). The microring supports only a single radial mode, but the contact induces scattering and radiation thereby degrading the Q [see Fig. 2b]. (c) DFT outputs for the through and drop ports of the microdisk. Higher-order modes corrupt the available FSR.

Fig. 2
Fig. 2

(a) 2D FDTD simulation of an AMR with w g = 0.3 μm , w min = 0.4 μm , R = 2 μm , a = 0.8 μm , n c = 3 , and n c l = 1 . (b) Results of a cavity ringdown simulations, Q versus maximum guide width, w max , showing an internal Q of 88,000 for the resonator ( w max = 0.8 μm ). (c) Spectrum of the adiabatic microring obtained from DFTs of the output ports ( s = 0.1 μm and w max = 0.8 μm ), revealing an 8.2 THz FSR.

Equations (4)

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d b m d θ + j β m ( θ ) b m ( θ ) = n κ m n ( θ ) b n ( θ ) ,
κ m n ( θ ) = ω 4 δ β ( θ ) e m * ( r , θ , z ) · e n ( r , θ , z ) d d θ ϵ ( θ ) d A .
b m ( θ ) = b k ( 0 ) exp [ j 0 θ β m ( θ ) d θ ] × 0 θ κ m k ( θ ) exp [ j δ β ¯ ( θ ) θ ] d θ ,
P m ( θ ) = 2 | κ ¯ δ β ¯ | 2 [ 1 cos ( δ β ¯ θ ) ] ,

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