Abstract

We analyze the process of cascaded four-wave mixing in a high-Q microcavity and show that under conditions of suitable cavity-mode dispersion, broadband frequency combs can be generated. We experimentally demonstrate broadband, cascaded four-wave mixing parametric oscillation in the anomalous group-velocity dispersion regime of a high-Q silica microsphere with an overall bandwidth greater than 200 nm.

© 2009 OSA

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References

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  1. M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38(10), 5193–5196 (1988).
    [CrossRef] [PubMed]
  2. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
    [CrossRef]
  3. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
    [CrossRef] [PubMed]
  4. A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
    [CrossRef]
  5. A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
    [CrossRef]
  6. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
    [CrossRef] [PubMed]
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).
  8. R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
    [CrossRef]
  9. T. T. Ng, J. L. Blows, J. T. Mok, R. W. McKerracher, and B. J. Eggleton, “Cascaded four-wave mixing in fiber optical parametric amplifiers: Application to residual dispersion monitoring,” J. Lightwave Technol. 23(2), 818–826 (2005).
    [CrossRef]
  10. I. H. Agha, J. E. Sharping, M. A. Foster, and A. L. Gaeta, “Optimal sizes of silica microspheres for linear and nonlinear optical interactions,” Appl. Phys. B 83(2), 303–309 (2006).
    [CrossRef]
  11. R. A. Fisher and W. Bischel, “The role of linear dispersion in plane-wave self-phase modulation,” Appl. Phys. Lett. 23(12), 661–663 (1973).
    [CrossRef]
  12. A. Korpel, K. E. Lonngren, P. P. Banerjee, H. K. Sim, and M. R. Chatterjee, “Split-step-type angular plane-wave spectrum method for the study of self-refractive effects in nonlinear wave propagation,” J. Opt. Soc. Am. B 3(6), 885–890 (1986).
    [CrossRef]
  13. P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
    [CrossRef] [PubMed]
  14. A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” J. Opt. Soc. Am. B 22(2), 459–465 (2005).
    [CrossRef]
  15. T. Carmon, L. Yang, and K. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
    [CrossRef] [PubMed]

2008

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
[CrossRef] [PubMed]

2007

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

2006

I. H. Agha, J. E. Sharping, M. A. Foster, and A. L. Gaeta, “Optimal sizes of silica microspheres for linear and nonlinear optical interactions,” Appl. Phys. B 83(2), 303–309 (2006).
[CrossRef]

2005

2004

T. Carmon, L. Yang, and K. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

1988

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38(10), 5193–5196 (1988).
[CrossRef] [PubMed]

1986

1982

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[CrossRef]

1973

R. A. Fisher and W. Bischel, “The role of linear dispersion in plane-wave self-phase modulation,” Appl. Phys. Lett. 23(12), 661–663 (1973).
[CrossRef]

Agha, I. H.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
[CrossRef]

I. H. Agha, J. E. Sharping, M. A. Foster, and A. L. Gaeta, “Optimal sizes of silica microspheres for linear and nonlinear optical interactions,” Appl. Phys. B 83(2), 303–309 (2006).
[CrossRef]

Arcizet, O.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Banerjee, P. P.

Bischel, W.

R. A. Fisher and W. Bischel, “The role of linear dispersion in plane-wave self-phase modulation,” Appl. Phys. Lett. 23(12), 661–663 (1973).
[CrossRef]

Bjorkholm, J.

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[CrossRef]

Blows, J. L.

Carmon, T.

Chatterjee, M. R.

Del’Haye, P.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Eggleton, B. J.

Fisher, R. A.

R. A. Fisher and W. Bischel, “The role of linear dispersion in plane-wave self-phase modulation,” Appl. Phys. Lett. 23(12), 661–663 (1973).
[CrossRef]

Fomin, A. E.

Foster, M. A.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
[CrossRef]

I. H. Agha, J. E. Sharping, M. A. Foster, and A. L. Gaeta, “Optimal sizes of silica microspheres for linear and nonlinear optical interactions,” Appl. Phys. B 83(2), 303–309 (2006).
[CrossRef]

Gaeta, A. L.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
[CrossRef]

I. H. Agha, J. E. Sharping, M. A. Foster, and A. L. Gaeta, “Optimal sizes of silica microspheres for linear and nonlinear optical interactions,” Appl. Phys. B 83(2), 303–309 (2006).
[CrossRef]

Gorodetsky, M. L.

Grudinin, I. S.

Haus, H. A.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38(10), 5193–5196 (1988).
[CrossRef] [PubMed]

Holzwarth, R.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Ilchenko, V. S.

A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” J. Opt. Soc. Am. B 22(2), 459–465 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

Kippenberg, T. J.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

Korpel, A.

Lonngren, K. E.

Maleki, L.

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

McKerracher, R. W.

Mohageg, M.

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

Mok, J. T.

Nakazawa, M.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38(10), 5193–5196 (1988).
[CrossRef] [PubMed]

Ng, T. T.

Okawachi, Y.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
[CrossRef]

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

Schliesser, A.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
[CrossRef]

I. H. Agha, J. E. Sharping, M. A. Foster, and A. L. Gaeta, “Optimal sizes of silica microspheres for linear and nonlinear optical interactions,” Appl. Phys. B 83(2), 303–309 (2006).
[CrossRef]

Sim, H. K.

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

Stolen, R.

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[CrossRef]

Strekalov, D.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

Strekalov, D. V.

Suzuki, K.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38(10), 5193–5196 (1988).
[CrossRef] [PubMed]

Vahala, K.

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Yang, L.

Appl. Phys. B

I. H. Agha, J. E. Sharping, M. A. Foster, and A. L. Gaeta, “Optimal sizes of silica microspheres for linear and nonlinear optical interactions,” Appl. Phys. B 83(2), 303–309 (2006).
[CrossRef]

Appl. Phys. Lett.

R. A. Fisher and W. Bischel, “The role of linear dispersion in plane-wave self-phase modulation,” Appl. Phys. Lett. 23(12), 661–663 (1973).
[CrossRef]

IEEE J. Quantum Electron.

R. Stolen and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nature

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38(10), 5193–5196 (1988).
[CrossRef] [PubMed]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q optical microspheres,” Phys. Rev. A 76(4), 043837 (2007).
[CrossRef]

Phys. Rev. Lett.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF(2) resonator,” Phys. Rev. Lett. 93(24), 243905 (2004).
[CrossRef]

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101(5), 053903 (2008).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

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Figures (4)

Fig. 1
Fig. 1

Simulation results for a 150-μm microsphere showing the cascaded FWM peaks in steady state. Inset shows the shape of the FWM peaks, which is asymmetric due to the detuning of the gain from the cavity mode.

Fig. 2
Fig. 2

Experimental demonstration of the thermal frequency shift as a function of coupled pump power. As the laser pump power is increased, the PID controller constantly re-locks the laser near the peak of the microsphere resonance.

Fig. 3
Fig. 3

Setup for cascaded FWM. The switch allows for toggling the laser between frequency locked mode and scanning mode. An external cavity diode laser sent to the silica microsphere via a fiber taper with the output split between an optical spectrum analyzer and a photodiode. The signal on the photodiode allows for frequency locking via a lock-in amplifier.

Fig. 4
Fig. 4

Experimental optical spectrum analyzer traces of cascaded FWM in a 250-μm silica microsphere. (a) At 10 mW input, phase-matching occurs near the pump and oscillation occurs. (b) At 30 mW, the peaks cascade to produce 60 nm of bandwidth. (c) For 80 mW of input power, 150 nm of bandwidth is observed, and (d) with a 100-mW input, Raman oscillation occurs, yielding an overall bandwidth 250 nm.

Equations (3)

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

ΔkNL=ks+ki2kp+2γPp,
g=(γPp)2(ΔkNL/2)2,
Ec(z=0,t)= R Ein+ιT Ec(z=L,t1),  

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