Abstract

We report tunable two-stage self-coupled optical waveguide (SCOW) resonators composed of a pair of mirror-imaged single SCOW resonators connected by a phase shifter in between. Experimental results show that the coupled-resonator-induced-transparency and high-order bandstop filtering characteristics can be obtained in the transmission spectra of the devices with two different configurations. The resonance spectrum can be tuned by using either a p-i-p microheater or a p-i-n diode in the phase shifter. Our theoretical modeling based on the transfer matrix method has a good agreement with the experimental results.

© 2013 Optical Society of America

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  1. W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
    [CrossRef]
  2. S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
    [CrossRef]
  3. K. J. Vahala, Nature 424, 839 (2003).
    [CrossRef]
  4. J. Heebner, R. Grover, and T. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer, 2008).
  5. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
    [CrossRef]
  6. L. Zhou, T. Ye, and J. Chen, Opt. Lett. 36, 13 (2011).
    [CrossRef]
  7. A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phy. Rev. A 71, 043804 (2005).
    [CrossRef]
  8. M. Mancinelli, P. Bettotti, J. M. Fedeli, and L. Pavesi, Opt. Express 20, 23856 (2012).
    [CrossRef]
  9. M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, M. Beals, J. Michel, and L. C. Kimerling, J. Lightwave Technol. 27, 2105 (2009).
    [CrossRef]
  10. L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

2012 (3)

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

M. Mancinelli, P. Bettotti, J. M. Fedeli, and L. Pavesi, Opt. Express 20, 23856 (2012).
[CrossRef]

2011 (1)

2009 (1)

2006 (1)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

2005 (1)

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phy. Rev. A 71, 043804 (2005).
[CrossRef]

2003 (1)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

Baets, R.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Beals, M.

Beattie, J.

Bettotti, P.

Bienstman, P.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Cai, H.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

Carothers, D.

Chen, H.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

Chen, J.

L. Zhou, T. Ye, and J. Chen, Opt. Lett. 36, 13 (2011).
[CrossRef]

L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

Chen, Y.

Claes, T.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

De Heyn, P.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

De Vos, K.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Dumon, P.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Fan, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Farca, G.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phy. Rev. A 71, 043804 (2005).
[CrossRef]

Fedeli, J. M.

Feng, S.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

Gill, D. M.

Grover, R.

J. Heebner, R. Grover, and T. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer, 2008).

Heebner, J.

J. Heebner, R. Grover, and T. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer, 2008).

Ibrahim, T.

J. Heebner, R. Grover, and T. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer, 2008).

Kimerling, L. C.

Kumar Selvaraja, S.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Lei, T.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

Lipson, M.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Lu, L.

L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

Luo, X.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

Mancinelli, M.

Michel, J.

Naweed, A.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phy. Rev. A 71, 043804 (2005).
[CrossRef]

Patel, S. S.

Pavesi, L.

Pomerene, A.

Poon, A. W.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Rasras, M. S.

Rosenberger, A. T.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phy. Rev. A 71, 043804 (2005).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Shakya, J.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Shopova, S. I.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phy. Rev. A 71, 043804 (2005).
[CrossRef]

Sun, X.

L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

Tu, K.

Vahala, K. J.

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

van Thourhout, D.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

White, A. E.

Xie, J.

L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

Xu, Q.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Ye, T.

Zhou, L.

L. Zhou, T. Ye, and J. Chen, Opt. Lett. 36, 13 (2011).
[CrossRef]

L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

Zou, Z.

L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

J. Lightwave Technol. (1)

Laser Photon. Rev. (2)

W. Bogaerts, P. De Heyn, T. van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, Laser Photon. Rev. 6, 145 (2012).
[CrossRef]

Nature (1)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phy. Rev. A (1)

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phy. Rev. A 71, 043804 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Other (2)

J. Heebner, R. Grover, and T. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer, 2008).

L. Zhou, J. Xie, L. Lu, Z. Zou, X. Sun, and J. Chen, in Proceedings of the Conference on Asia Communication and Photonics (ACP2012) (Optical Society of America, 2012), paper ATh4B.

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Figures (3)

Fig. 1.
Fig. 1.

(a) SEM image of the two-stage SCOW resonators before upper-cladding. (b) Microscope image of the final active device. (c) and (d) Cross-sectional view schematics of the two phase shifters used in our devices: (c) p-i-p junction and (d) p-i-n diode.

Fig. 2.
Fig. 2.

(a) and (b) Experimental transmission spectra of the two-stage SCOW resonators without tuning. (c) CRIT resonance spectra under various thermal powers. (d) High-order bandstop filtering spectra under various electrical powers. The coupling lengths in the individual resonator are (a) and (c) Lc1=6μm, Lc2=10μm, and (b) and (d) Lc1=8μm, Lc2=12μm. Curves in (c) and (d) are vertically shifted for clarity.

Fig. 3.
Fig. 3.

(a) and (b) Intensity transmission |tS1,2|2 and reflection |rS1,2|2 spectra of the two individual SCOW resonators. (c) and (d) Intensity transmission spectrum of the two-stage coupled SCOW resonators. The coupling coefficients in (a) and (c) are κ12=0.650, κ22=0.890 and in (b) and (d) κ12=0.725, κ22=0.951. (e) CRIT spectra and (f) high-order bandstop filtering spectra under various phase shifts. FSR is the free spectral range of the SCOW resonator.

Equations (5)

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

ts1=ts2=eiθb[(κ1κ2aeiϕ)(κ2κ1aeiϕ)(1κ1κ2aeiϕ)2+(t1t2a1/2eiϕ/21κ1κ2aeiϕ)2],
rs1=2eiθbt1t2a1/2eiϕ/21κ1κ2aeiϕκ1κ2aeiϕ1κ1κ2aeiϕ,
rs2=2eiθbt1t2a1/2eiϕ/21κ1κ2aeiϕκ2κ1aeiϕ1κ1κ2aeiϕ,
[E3E4]=1ts1ts2tc[ts1ts2rs1rs2rs1rs21][tc2001][ts1ts2rs1rs2rs2rs11][E1E2],
E3E1=ts1ts2tc1rs22tc2.

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