Abstract

We experimentally examined the propagation of temporally square modulated optical pulses through a coupled ring resonator. Sharp transient spikes appeared as the square pulses entered the system. The main signal gradually grew up through coupled-resonator-induced transparency (CRIT), with the time constant determined by a second resonator. Transient spikes were attributed to the higher and lower spectral components of the incident pulse, to which the resonators cannot respond; hence, they were interpreted as optical precursors. The experiments, therefore, demonstrated that precursors and the main signal can be observed separately, with amplitudes comparable to that of the incident step in CRIT.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. K. Totsuka and M. Tomita, J. Opt. Soc. Am. B 23, 2194 (2006).
    [CrossRef]

2011 (2)

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, Phys. Rev. A 84, 043843 (2011).
[CrossRef]

K. Di, C. Xie, and J. Zhang, Phys. Rev. Lett. 106, 1536021 (2011).
[CrossRef]

2010 (1)

2009 (3)

H. Jeong and S. Du, Phys. Rev. A 79, 011802 (2009).
[CrossRef]

B. Macke and B. Ségard, Phys. Rev. A 80, 011803 (2009).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

2007 (1)

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

2006 (2)

K. Totsuka and M. Tomita, J. Opt. Soc. Am. B 23, 2194 (2006).
[CrossRef]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

2005 (2)

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Phys. Rev. Lett. 94, 053902 (2005).
[CrossRef]

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

2003 (1)

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[CrossRef]

1991 (1)

J. Aaviksoo, J. Kuhl, and K. Ploog, Phys. Rev. A 44, R5353 (1991).
[CrossRef]

Aaviksoo, J.

J. Aaviksoo, J. Kuhl, and K. Ploog, Phys. Rev. A 44, R5353 (1991).
[CrossRef]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity(Academic, 1960).

Chen, J. F.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao and A. M. Steinberg, in Progress in Optics XXXVII, E. Wolf, ed. (Elsevier, 1997), p. 345.

Dawes, A. M. C.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

Di, K.

K. Di, C. Xie, and J. Zhang, Phys. Rev. Lett. 106, 1536021 (2011).
[CrossRef]

Du, S.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

H. Jeong and S. Du, Phys. Rev. A 79, 011802 (2009).
[CrossRef]

Farca, G.

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

Gauthier, D. J.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Phys. Rev. Lett. 94, 053902 (2005).
[CrossRef]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[CrossRef]

Jeong, H.

H. Jeong and S. Du, Phys. Rev. A 79, 011802 (2009).
[CrossRef]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Kuhl, J.

J. Aaviksoo, J. Kuhl, and K. Ploog, Phys. Rev. A 44, R5353 (1991).
[CrossRef]

Loy, M. M. T.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Macke, B.

B. Macke and B. Ségard, Phys. Rev. A 80, 011803 (2009).
[CrossRef]

Matsumoto, T.

Naweed, A.

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

Neifeld, M. A.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Phys. Rev. Lett. 94, 053902 (2005).
[CrossRef]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[CrossRef]

Oishi, T.

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, Phys. Rev. A 84, 043843 (2011).
[CrossRef]

Oughstun, K. E.

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

Ploog, K.

J. Aaviksoo, J. Kuhl, and K. Ploog, Phys. Rev. A 44, R5353 (1991).
[CrossRef]

Rosenberger, A. T.

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

Ségard, B.

B. Macke and B. Ségard, Phys. Rev. A 80, 011803 (2009).
[CrossRef]

Sherman, G. C.

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

Shopova, S. I.

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

Steinberg, A. M.

R. Y. Chiao and A. M. Steinberg, in Progress in Optics XXXVII, E. Wolf, ed. (Elsevier, 1997), p. 345.

Stenner, M. D.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Phys. Rev. Lett. 94, 053902 (2005).
[CrossRef]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[CrossRef]

Sultana, P.

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, Phys. Rev. A 84, 043843 (2011).
[CrossRef]

P. Sultana, A. Takami, T. Matsumoto, and M. Tomita, Opt. Lett. 35, 3414 (2010).
[CrossRef]

Takami, A.

Tomita, M.

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, Phys. Rev. A 84, 043843 (2011).
[CrossRef]

P. Sultana, A. Takami, T. Matsumoto, and M. Tomita, Opt. Lett. 35, 3414 (2010).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

K. Totsuka and M. Tomita, J. Opt. Soc. Am. B 23, 2194 (2006).
[CrossRef]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

K. Totsuka and M. Tomita, J. Opt. Soc. Am. B 23, 2194 (2006).
[CrossRef]

Uesugi, H.

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, Phys. Rev. A 84, 043843 (2011).
[CrossRef]

Wei, D.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Wong, G. K. L.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Xie, C.

K. Di, C. Xie, and J. Zhang, Phys. Rev. Lett. 106, 1536021 (2011).
[CrossRef]

Zhang, J.

K. Di, C. Xie, and J. Zhang, Phys. Rev. Lett. 106, 1536021 (2011).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (5)

M. Tomita, H. Uesugi, P. Sultana, and T. Oishi, Phys. Rev. A 84, 043843 (2011).
[CrossRef]

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

J. Aaviksoo, J. Kuhl, and K. Ploog, Phys. Rev. A 44, R5353 (1991).
[CrossRef]

H. Jeong and S. Du, Phys. Rev. A 79, 011802 (2009).
[CrossRef]

B. Macke and B. Ségard, Phys. Rev. A 80, 011803 (2009).
[CrossRef]

Phys. Rev. Lett. (5)

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Phys. Rev. Lett. 94, 053902 (2005).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

K. Di, C. Xie, and J. Zhang, Phys. Rev. Lett. 106, 1536021 (2011).
[CrossRef]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

Other (3)

L. Brillouin, Wave Propagation and Group Velocity(Academic, 1960).

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

R. Y. Chiao and A. M. Steinberg, in Progress in Optics XXXVII, E. Wolf, ed. (Elsevier, 1997), p. 345.

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Figures (3)

Fig. 1.
Fig. 1.

Transmission spectra as a function of the laser detuning frequency from resonance (a) through a single ring resonator under the critical coupling condition, and (b) through a coupled resonator. Lines A through D indicate the frequencies at which the pulse propagation was examined in Fig. 2. The signal was normalized by the off-resonance transmission intensity.

Fig. 2.
Fig. 2.

Transmitted temporal pulse profiles through the single and coupled resonators. The left column shows experimental observations; the right column is calculated curves. (a) and (b) show input square modulated pulses; (c) and (d) are transmitted pulses through the single ring resonator under the critical coupling condition at the on-resonance condition, indicated by A in Fig. 1(a). (e), (g), and (i) are transmitted pulses through the coupled ring resonator observed at the frequencies indicated by B to D in Fig. 1(b). B, at the induced transparency window; C, at the high-frequency side of the transmission curve; and D, at the off-resonance frequency. In the right column, the black lines represent the total transmitted profile. The blue dashed lines in (d), (f), (h), and (j) are intensities in the first ring. The red dashed lines in (f), (h), and (j) are intensities in the second ring as a function of time. Parameters: y1=0.775, y2=0.975, x1=0.85, and x2=0.9.

Fig. 3.
Fig. 3.

Expanded plots for the transmitted temporal pulse profiles through coupled resonators for the on-resonance condition. (a) and (b) are in the rising edge region, and (c) and (d) are in the trailing edge region. Left and right columns are experimental observations and calculated curves, respectively. The couplers between the first and second ring resonators were 9010 for the black curves and 955 for the blue curves.

Equations (2)

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E¯(ν)=(1γ1)1/2[y1x1S2(ν)exp(iϕ1)1x1y1S2(ν)exp(iϕ1)],
S2(ν)=(1γ2)1/2[y2x2exp(i(ϕ2)1x2y2exp(iϕ2)].

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