Abstract

Electromagnetic resonators are important not only as realizable models of fundamental concepts in classical and quantum physics, based on the existence and properties of eigenmodes, but also in the practical design of lasers, amplifiers, sensors, filters, and delay lines. Coupled-eigenmode systems may be realized via the multiple eigenmodes of a single resonator or by the coupling of a mode across multiple resonators. Mode cycling is demonstrated as a distinct concept of sequential population transfer in coupled multiple-eigenvalue resonators. Based on this principle, a coupled polymeric microring resonator interferometer is fabricated and characterized; the device achieves greater than 30dB extinction and (loaded) Q5.5×103.

© 2005 Optical Society of America

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2005 (1)

T. J. Wang, Y. H. Huang, and H. L. Chen, IEEE Photon. Technol. Lett. 17, 582 (2005).
[CrossRef]

2004 (1)

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

2003 (3)

2002 (4)

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D. Rabus, M. Hamacher, H. Heidrich, and U. Troppenz, IEEE Photon. Technol. Lett. 14, 1442 (2002).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Opt. Lett. 27, 1669 (2002).
[CrossRef]

S. Suzuki, Y. Hatakeyama, Y. Kokubun, and S. T. Chu, J. Lightwave Technol. 20, 745 (2002).
[CrossRef]

2000 (1)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

1996 (1)

P. Katila, P. Heimala, and J. Aarnio, Electron. Lett. 32, 1005 (1996).
[CrossRef]

1995 (1)

1973 (1)

1969 (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).
[CrossRef]

Aarnio, J.

P. Katila, P. Heimala, and J. Aarnio, Electron. Lett. 32, 1005 (1996).
[CrossRef]

Absil, P. P.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Campbell, K.

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

Chao, C.-Y.

C.-Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Chen, H. L.

T. J. Wang, Y. H. Huang, and H. L. Chen, IEEE Photon. Technol. Lett. 17, 582 (2005).
[CrossRef]

Chu, S. T.

Costa, R.

Dalton, L.

P. Rabiei, W. H. Steier, C. Zhang, and L. Dalton, IEEE Photon. Technol. Lett. 20, 1968 (2002).

Fainman, Y.

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

Groisman, A.

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

Guo, L. J.

C.-Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Hale, G. M.

Hamacher, M.

D. Rabus, M. Hamacher, H. Heidrich, and U. Troppenz, IEEE Photon. Technol. Lett. 14, 1442 (2002).
[CrossRef]

Hare, J.

Haroche, S.

Hatakeyama, Y.

Haus, H. A.

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer-Verlag, 2000).
[CrossRef]

Heidrich, H.

D. Rabus, M. Hamacher, H. Heidrich, and U. Troppenz, IEEE Photon. Technol. Lett. 14, 1442 (2002).
[CrossRef]

Heimala, P.

P. Katila, P. Heimala, and J. Aarnio, Electron. Lett. 32, 1005 (1996).
[CrossRef]

Ho, P.-T.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Hryniewicz, J. V.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Huang, Y.

Huang, Y. H.

T. J. Wang, Y. H. Huang, and H. L. Chen, IEEE Photon. Technol. Lett. 17, 582 (2005).
[CrossRef]

Katila, P.

P. Katila, P. Heimala, and J. Aarnio, Electron. Lett. 32, 1005 (1996).
[CrossRef]

Kippenberg, T. J.

Kokubun, Y.

Lefevre-Seguin, V.

Levy, U.

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

Little, B. E.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, 1999).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).
[CrossRef]

Martinelli, M.

Melloni, A.

Monguzzi, P.

Mookerjea, S.

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

Mookherjea, S.

Paloczi, G. T.

Pang, L.

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

Psaltis, D.

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

Querry, M. R.

Rabiei, P.

P. Rabiei, W. H. Steier, C. Zhang, and L. Dalton, IEEE Photon. Technol. Lett. 20, 1968 (2002).

Rabus, D.

D. Rabus, M. Hamacher, H. Heidrich, and U. Troppenz, IEEE Photon. Technol. Lett. 14, 1442 (2002).
[CrossRef]

Raimond, J.-M.

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).
[CrossRef]

Sandoghdar, V.

Spillane, S. M.

Steier, W. H.

P. Rabiei, W. H. Steier, C. Zhang, and L. Dalton, IEEE Photon. Technol. Lett. 20, 1968 (2002).

Suzuki, S.

Troppenz, U.

D. Rabus, M. Hamacher, H. Heidrich, and U. Troppenz, IEEE Photon. Technol. Lett. 14, 1442 (2002).
[CrossRef]

Vahala, K. J.

Wang, T. J.

T. J. Wang, Y. H. Huang, and H. L. Chen, IEEE Photon. Technol. Lett. 17, 582 (2005).
[CrossRef]

Weiss, D. S.

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Yariv, A.

Zhang, C.

P. Rabiei, W. H. Steier, C. Zhang, and L. Dalton, IEEE Photon. Technol. Lett. 20, 1968 (2002).

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, 1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. Campbell, A. Groisman, U. Levy, L. Pang, S. Mookerjea, D. Psaltis, and Y. Fainman, Appl. Phys. Lett. 85, 6119 (2004).
[CrossRef]

C.-Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).
[CrossRef]

Electron. Lett. (1)

P. Katila, P. Heimala, and J. Aarnio, Electron. Lett. 32, 1005 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

T. J. Wang, Y. H. Huang, and H. L. Chen, IEEE Photon. Technol. Lett. 17, 582 (2005).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

D. Rabus, M. Hamacher, H. Heidrich, and U. Troppenz, IEEE Photon. Technol. Lett. 14, 1442 (2002).
[CrossRef]

P. Rabiei, W. H. Steier, C. Zhang, and L. Dalton, IEEE Photon. Technol. Lett. 20, 1968 (2002).

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (3)

Other (3)

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, 1999).
[CrossRef]

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer-Verlag, 2000).
[CrossRef]

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

a, Optical micrograph of the coupled-microring interferometer. The racetrack microring resonators support clockwise and counterclockwise traveling-wave eigenmodes (Kramers degeneracy), corresponding to states a and b in part b. Cross coupling of the two-state resonators ( a 1 b 2 , etc.) is implemented by multimode interference waveguide couplers with coupling coefficient κ. The bridge waveguide is shown at the top, connecting the outer edges of the rings with coupling coefficient γ.

Fig. 2
Fig. 2

a, Scanning electron microscope image of the SU-8 waveguide ( n = 1.56 ) cross section; the undercut profile was helpful in compensating for the modal asymmetry that arises from the difference in the refractive indices of the aqueous cladding surrounding the waveguide on the top, left, and right sides ( n = 1.32 ) and of the substrate ( n = 1.45 ) . b, Microscope image of light from a helium–neon laser coupled into the waveguide from a fiber taper. c, Fundamental mode of the waveguide at λ = 1560 nm as measured by an IR-sensitive CCD camera and beam analyzer.

Fig. 3
Fig. 3

Transmission spectra for TE polarized light (a) of the air-clad device (detuned from critical coupling, weak extinction) and (b) near a resonance with a fluidic overlay layer to tune the absorption and coupling coefficients to critical coupling ( 30 dB extinction). From the measured 3 dB linewidth, Q loaded = 5.45 × 10 3 .

Equations (4)

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

d d t [ a 1 b 1 a 2 b 2 ] = [ i ω 1 0 0 κ 12 0 i ω 2 κ 21 γ 22 γ 11 κ 12 i ω 1 0 κ 21 0 0 i ω 2 ] [ a 1 b 1 a 2 b 2 ] .
ω = ω 1 + ω 2 2 ± [ ( ω 1 ω 2 2 ) 2 + κ 12 κ 21 ] 1 2 ,
H ( λ ) b ̂ 3 a 0 = [ ( C A D B ) 2 A D B 2 ] α ¯ exp ( i β L wg ) ,
[ A B C D ] = 1 κ 3 [ t 3 1 κ 3 2 t 3 2 t 3 * ] [ 0 α 2 exp ( i β d 2 ) α 2 1 exp ( i β d 2 ) 0 ] 1 κ 2 [ t 2 1 κ 2 2 t 2 2 t 2 * ] ( 0 α 1 exp ( i β d 1 ) α 1 1 exp ( i β d 1 ) 0 ) 1 κ 1 [ t 1 1 κ 1 2 t 1 2 t 1 * ] ,

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