Abstract

Four-wave mixing (FWM) can be either stimulated or occur spontaneously. The first process is intrinsically much stronger and well understood through classical nonlinear optics. The latter, also known as parametric fluorescence, can be explained only in the framework of a quantum theory of light. We experimentally demonstrated that, in a microring resonator, there is a simple relation between the efficiencies of these two processes that is independent of the nonlinearity and ring size. In particular, we have shown the average power generated by parametric fluorescence can be immediately estimated from a classical FWM experiment. These results suggest that classical nonlinear characterization of a photonic integrated structure can provide accurate information on its nonlinear quantum properties.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Little, S. Chu, and H. Haus, Opt. Lett. 23, 1570 (1998).
    [CrossRef]
  2. J. Robinson, L. Chen, and M. Lipson, Opt. Express 16, 4296 (2008).
    [CrossRef]
  3. V. R. Almeida and M. Lipson, Opt. Lett. 29, 2387 (2004).
    [CrossRef]
  4. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
    [CrossRef]
  5. M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
    [CrossRef]
  6. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
    [CrossRef]
  7. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, Opt. Lett. 25, 554 (2000).
    [CrossRef]
  8. A. Turner, M. Foster, A. Gaeta, and M. Lipson, Opt. Express 16, 4881 (2008).
    [CrossRef]
  9. S. Clemmen, K. Phan Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, Opt. Express 17, 16558 (2009).
    [CrossRef]
  10. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  11. L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, Opt. Lett. 35, 3006 (2010).
    [CrossRef]
  12. L. G. Helt, M. Liscidini, and J. E. Sipe, J. Opt. Soc. Am. B 29, 2199 (2012).
    [CrossRef]
  13. Unlike in Ref. [12], here we assume losses in the ring resonator. At the critical coupling, the on-resonance field enhancement in the ring resonator is FE≃2Qvgω0L, with ω0 the resonant frequency (see also Ref. [7]).
  14. M. Liscidini, L. G. Helt, and J. E. Sipe, Phys. Rev. A 85, 013833 (2012).
    [CrossRef]
  15. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H.-Y. Ryu, Opt. Express 12, 1551 (2004).
    [CrossRef]
  16. The variation of the quality factor between the signal, pump, and idler resonances is below 2% for all four rings. The value we have taken for the quality factor in the equations is an average between the Qs of the three resonances.
  17. We verified that the quadratic trend is maintained up to the maximum available pump power if the pump wavelength is retuned to compensate for the thermo-optic redshift of the resonances for Pp>2  mW. This implies that Q degradation due to free carrier absorption can be neglected for all the investigated Pp. The data of Fig. 2 are taken with a fixed value of the pump energy.

2012 (2)

L. G. Helt, M. Liscidini, and J. E. Sipe, J. Opt. Soc. Am. B 29, 2199 (2012).
[CrossRef]

M. Liscidini, L. G. Helt, and J. E. Sipe, Phys. Rev. A 85, 013833 (2012).
[CrossRef]

2010 (3)

L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, Opt. Lett. 35, 3006 (2010).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

2009 (1)

2008 (3)

A. Turner, M. Foster, A. Gaeta, and M. Lipson, Opt. Express 16, 4881 (2008).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

J. Robinson, L. Chen, and M. Lipson, Opt. Express 16, 4296 (2008).
[CrossRef]

2004 (2)

2000 (1)

1998 (1)

Absil, P. P.

Almeida, V. R.

Baets, R. G.

Bogaerts, W.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Chen, L.

Cho, P. S.

Chu, S.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

B. Little, S. Chu, and H. Haus, Opt. Lett. 23, 1570 (1998).
[CrossRef]

Clemmen, S.

Duchesne, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

Emplit, Ph.

Ferrera, M.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

Foster, M.

Foster, M. A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
[CrossRef]

Gaeta, A.

Gaeta, A. L.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
[CrossRef]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
[CrossRef]

Haus, H.

Helt, L. G.

Ho, P.-T.

Hryniewicz, J. V.

Huy, K. Phan

Joneckis, L. G.

Kuramochi, E.

Levy, J. S.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
[CrossRef]

Lipson, M.

Liscidini, M.

L. G. Helt, M. Liscidini, and J. E. Sipe, J. Opt. Soc. Am. B 29, 2199 (2012).
[CrossRef]

M. Liscidini, L. G. Helt, and J. E. Sipe, Phys. Rev. A 85, 013833 (2012).
[CrossRef]

L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, Opt. Lett. 35, 3006 (2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

Little, B.

Little, B. E.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, Opt. Lett. 25, 554 (2000).
[CrossRef]

Massar, S.

Mitsugi, S.

Morandotti, R.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

Moss, D. J.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

Notomi, M.

Razzari, L.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

Robinson, J.

Ryu, H.-Y.

Shinya, A.

Sipe, J. E.

M. Liscidini, L. G. Helt, and J. E. Sipe, Phys. Rev. A 85, 013833 (2012).
[CrossRef]

L. G. Helt, M. Liscidini, and J. E. Sipe, J. Opt. Soc. Am. B 29, 2199 (2012).
[CrossRef]

L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, Opt. Lett. 35, 3006 (2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

Turner, A.

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
[CrossRef]

Wilson, R. A.

Yang, Z.

L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, Opt. Lett. 35, 3006 (2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

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

Nature Photon. (3)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, Nature Photon. 4, 37 (2010).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 2, 737 (2008).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, Nature Photon. 4, 41(2010).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. A (1)

M. Liscidini, L. G. Helt, and J. E. Sipe, Phys. Rev. A 85, 013833 (2012).
[CrossRef]

Other (4)

The variation of the quality factor between the signal, pump, and idler resonances is below 2% for all four rings. The value we have taken for the quality factor in the equations is an average between the Qs of the three resonances.

We verified that the quadratic trend is maintained up to the maximum available pump power if the pump wavelength is retuned to compensate for the thermo-optic redshift of the resonances for Pp>2  mW. This implies that Q degradation due to free carrier absorption can be neglected for all the investigated Pp. The data of Fig. 2 are taken with a fixed value of the pump energy.

Unlike in Ref. [12], here we assume losses in the ring resonator. At the critical coupling, the on-resonance field enhancement in the ring resonator is FE≃2Qvgω0L, with ω0 the resonant frequency (see also Ref. [7]).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Transmission spectrum of the R=5μm ring. The inset shows a high-resolution spectrum of the resonance at 1558.5.

Fig. 2.
Fig. 2.

(a) Example of a spontaneous FWM spectrum for a R=5μm ring resonator. (b) Scaling of the estimated number of generated signal (blue circles) and idler (red triangles) photons inside the ring for spontaneous FWM with varying PP. It is the same for idler photons in classical FWM (black squares), with 47 μW injected at the signal resonance. The black dashed line is the best fit to the stimulated data from Eq. (1) and the blue short dashed line is the theoretical prediction from Eq. (2).

Fig. 3.
Fig. 3.

(a) Scaling of the generated idler intensities with the ring radius, for stimulated and spontaneous processes. The dashed lines are guides to the eye proportional to R2. (b) Ratio between the generated idler photons in spontaneous and classical processes [see Eq. (3)] for all the four rings investigated. The dashed line is given by Eq. (3).

Equations (3)

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

Pi,ST=(γ2πR)2(QvgωpπR)4PsPp2,
Pi,SP=(γ2πR)2(QvgωpπR)3ωpvg4πRPp2,
Pi,SPPi,ST=14Qωp2Ps,

Metrics