Abstract

In optical parametric oscillators, the line shape of the pump resonance becomes strongly distorted above the oscillation threshold. We model this behavior and find good agreement with the literature data and our original experimental data. A fit of the model to the data provides valuable information about the loss mechanisms in the parametric process. In particular, the modal properties of the parametric waves can be gained, which is important for both classical and quantum aspects of optical parametric oscillation.

© 2013 Optical Society of America

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References

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  1. M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999).
    [CrossRef]
  2. A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
    [CrossRef]
  3. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
    [CrossRef]
  4. M. Martinelli, C. L. Garrido Alzar, P. H. Souto Ribeiro, and P. Nussenzveig, Braz. J. Phys. 31, 597 (2001).
    [CrossRef]
  5. C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (Paris) 50, 1209 (1989).
    [CrossRef]
  6. M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
    [CrossRef]
  7. K. J. Vahala, Nature 424, 839 (2003).
    [CrossRef]
  8. L. Maleki, V. S. Ilchenko, A. A. Savchenkov, and A. B. Matsko, in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsto, ed. (CRC Press, 2009), pp. 133–209.
  9. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
    [CrossRef]
  10. T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
    [CrossRef]
  11. V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 1304 (2003).
    [CrossRef]
  12. B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011).
    [CrossRef]
  13. B. Sturman, T. Beckmann, and I. Breunig, J. Opt. Soc. Am. B 29, 3087 (2012).
    [CrossRef]
  14. A. Yariv, Electron. Lett. 36, 321 (2000).
    [CrossRef]
  15. J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
    [CrossRef]
  16. N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
    [CrossRef]

2013 (1)

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

2012 (1)

2011 (3)

B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011).
[CrossRef]

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

2010 (2)

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

2003 (2)

2001 (1)

M. Martinelli, C. L. Garrido Alzar, P. H. Souto Ribeiro, and P. Nussenzveig, Braz. J. Phys. 31, 597 (2001).
[CrossRef]

2000 (1)

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

1999 (1)

M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999).
[CrossRef]

1989 (1)

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (Paris) 50, 1209 (1989).
[CrossRef]

1988 (1)

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef]

1987 (1)

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef]

Aiello, A.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

Andersen, U. L.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

Beckmann, T.

B. Sturman, T. Beckmann, and I. Breunig, J. Opt. Soc. Am. B 29, 3087 (2012).
[CrossRef]

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

Breunig, I.

B. Sturman, T. Beckmann, and I. Breunig, J. Opt. Soc. Am. B 29, 3087 (2012).
[CrossRef]

B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011).
[CrossRef]

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

Buse, K.

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

Drummond, P. D.

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef]

Dunn, M. H.

M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999).
[CrossRef]

Ebrahimzadeh, M.

M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999).
[CrossRef]

Elser, D.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

Fabre, C.

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (Paris) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef]

Falk, M.

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

Fejer, M. M.

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

Fieberg, S.

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

Fürst, J. U.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

Garrido Alzar, C. L.

M. Martinelli, C. L. Garrido Alzar, P. H. Souto Ribeiro, and P. Nussenzveig, Braz. J. Phys. 31, 597 (2001).
[CrossRef]

Giacobino, E.

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (Paris) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef]

Gomes, G.

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

Haertle, D.

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

Hauser, J.

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

Heidmann, A.

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (Paris) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef]

Horowicz, R. J.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef]

Ilchenko, V. S.

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

L. Maleki, V. S. Ilchenko, A. A. Savchenkov, and A. B. Matsko, in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsto, ed. (CRC Press, 2009), pp. 133–209.

Jundt, D. H.

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

Kajiyama, M. C. C.

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

Kühnemann, F.

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

Leuchs, G.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

Linnenbank, H.

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

Maleki, L.

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

L. Maleki, V. S. Ilchenko, A. A. Savchenkov, and A. B. Matsko, in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsto, ed. (CRC Press, 2009), pp. 133–209.

Marquardt, C.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

Marquardt, Ch.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

Martinelli, M.

M. Martinelli, C. L. Garrido Alzar, P. H. Souto Ribeiro, and P. Nussenzveig, Braz. J. Phys. 31, 597 (2001).
[CrossRef]

Matsko, A. B.

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

L. Maleki, V. S. Ilchenko, A. A. Savchenkov, and A. B. Matsko, in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsto, ed. (CRC Press, 2009), pp. 133–209.

Nussenzveig, P.

M. Martinelli, C. L. Garrido Alzar, P. H. Souto Ribeiro, and P. Nussenzveig, Braz. J. Phys. 31, 597 (2001).
[CrossRef]

Reid, M. D.

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef]

Reynaud, S.

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (Paris) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef]

Savchenkov, A. A.

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 1304 (2003).
[CrossRef]

L. Maleki, V. S. Ilchenko, A. A. Savchenkov, and A. B. Matsko, in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsto, ed. (CRC Press, 2009), pp. 133–209.

Schwesyg, J. R.

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

Souto Ribeiro, P. H.

M. Martinelli, C. L. Garrido Alzar, P. H. Souto Ribeiro, and P. Nussenzveig, Braz. J. Phys. 31, 597 (2001).
[CrossRef]

Steigerwald, H.

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

Strekalov, D. V.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

Sturman, B.

Vahala, K. J.

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

Waasem, N.

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

Yariv, A.

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

Appl. Phys. B (1)

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010).
[CrossRef]

Braz. J. Phys. (1)

M. Martinelli, C. L. Garrido Alzar, P. H. Souto Ribeiro, and P. Nussenzveig, Braz. J. Phys. 31, 597 (2001).
[CrossRef]

Electron. Lett. (1)

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. (Paris) (1)

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (Paris) 50, 1209 (1989).
[CrossRef]

Nature (1)

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

Phys. Rev. Lett. (5)

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[CrossRef]

T. Beckmann, H. Linnenbank, H. Steigerwald, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[CrossRef]

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011).
[CrossRef]

Rev. Sci. Instrum. (1)

N. Waasem, S. Fieberg, J. Hauser, G. Gomes, D. Haertle, F. Kühnemann, and K. Buse, Rev. Sci. Instrum. 84, 023109 (2013).
[CrossRef]

Science (1)

M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999).
[CrossRef]

Other (1)

L. Maleki, V. S. Ilchenko, A. A. Savchenkov, and A. B. Matsko, in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsto, ed. (CRC Press, 2009), pp. 133–209.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of a WGR OPO experiment; the WGR circumference is L=2πR. A pump beam of power Pp at frequency ωp is coupled to the WGR via a prism and coupled out with power Pp*. The signal and idler waves leave the prism with the powers Ps,i*, and the frequencies ωs,i. (b) Initial line shape (solid line) and its distortion during OPO (in the gray region). The data points correspond to [9].

Fig. 2.
Fig. 2.

Resonant frequencies ωjp,js,ji, the linewidths γp,s,i, the actual frequencies ωp,s,i, and the frequency detunings δωp,s,i used in the text.

Fig. 3.
Fig. 3.

Pump line shape ηp(δ^p) according to Eq. (1) for different values of rp and m at ξ=3 and δ^0=0. For δ^00, the deviation from the Lorentzian shape (the dashed lines) moves according to the arrows.

Fig. 4.
Fig. 4.

Experimental data (circles) for the dependences ηp,s(δωp) at different temperatures. The solid lines are plotted according to Eqs. (1) for the relevant normalized detunings δ^0. The other model parameters are given in the text.

Equations (2)

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

ηs,i=4qs,i(1+rs,i1)(1+rp1)Φξηp=|12(1+rp1)(1iδ^p)(1+DΦ)|2.
δ^p=m(δ^δ^0)withm=(γs+γi)/γp.

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