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Optics Letters

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  • Editor: Alan E. Willner
  • Vol. 37, Iss. 20 — Oct. 15, 2012
  • pp: 4224–4226
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Blue-pumped whispering gallery optical parametric oscillator

Christoph Sebastian Werner, Tobias Beckmann, Karsten Buse, and Ingo Breunig  »View Author Affiliations


Optics Letters, Vol. 37, Issue 20, pp. 4224-4226 (2012)
http://dx.doi.org/10.1364/OL.37.004224


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Abstract

We demonstrate a whispering gallery optical parametric oscillator pumped at 488 nm wavelength. This millimeter-sized device has a pump threshold of 160 μW. The signal field is tunable between 707 and 865 nm wavelength and the idler field between 1120 and 1575 nm through temperature variation. Although the conversion efficiency is fundamentally limited to several percent because of absorption loss for the pump wave, the results provide evidence that such oscillators will be able to cover finally the entire visible range.

© 2012 Optical Society of America

Fig. 1. Illustration of the experimental setup: Pp, Pp*, and Ps represent powers of the pump wave at 488 nm, of its transmitted portion, and of the signal light, respectively. The inset shows a microscope picture of the resonator, whereas the arrow indicates the direction of the crystallographic z-axis.

In order to determine the quality factor of the optical whispering gallery, we scan the pump laser frequency ν across a cavity mode and measure the transmitted power Pp* versus the frequency shift. This is shown in Fig. 2. The linewidth Δν in absence of parametric oscillation ranges from 80 (prism far from the resonator) to 140 MHz (prism touching the resonator). The first value yields the intrinsic quality factor Qpν/Δν=7.7×106 for the pump wave. From here, we can deduce the absorption coefficient αp=2πnp/λpQp3.8m1 with the refractive index np=2.25 [6

6. D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

], assuming that the intrinsic cavity loss is dominated by absorption. This value agrees quite well with the previously measured coefficient (23)m1 for congruent lithium niobate [7

7. 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]

]. The ratio between the highest and lowest linewidth is smaller than two. From this, we can conclude that we are not able to achieve critical coupling or overcoupling; i.e., the internal loss is always larger than the coupling loss. The coupling efficiency κ was limited to 40% for a vanishing gap between the prism and the resonator.

Fig. 2. Transmitted pump power Pp* and signal power Ps as a function of the frequency shift of the pump laser at 40 °C resonator temperature.

If the input power exceeds the pump threshold Pth for the optical parametric oscillation, we can measure the signal power Ps while scanning the pump frequency across a cavity mode. Figure 2 shows that at Pp=200μW, we generate Ps0.9μW of signal light at 40 °C resonator temperature. Using a spectrometer, we have confirmed the parametric oscillation at λs=800nm and λi=1250nm. The signal power grows with increasing pump power as shown in Fig. 3. Theoretically, this input–output curve should have a shape according to [8

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

]
Ps=4(Pp˜/Pth1)Pth×λpλs(rp1+1)(rs1+1),
(3)
with the pump threshold
Pth=πε0c0np2ns2ni216d2λpVeff1QpQsQi×(rp+1)2(rs+1)(ri+1)rp.
(4)
Here, the coefficients rs,i are the ratios between the coupling losses and the intrinsic losses of the signal and idler waves, respectively. The second factor of Eq. (4), Veff, is the effective mode volume, and Qj are the intrinsic quality factors of the three interacting waves. The latter factor of Eq. (3) gives the maximum achievable conversion efficiency ηmax at Pp˜=4Pth. Only in the case of strong overcoupling for both waves it reaches λp/λs corresponding to the Manley–Rowe limit. We determine ηmax=2.6% and Pth=66μW (160 μW total pump threshold) by a fit of Eq. (3) to our experimental data. Reducing the gap between the resonator and the prism, hence increasing rp,s, enhances the conversion efficiency to 7%. However, as indicated before, even for a vanishing gap we stay in the undercoupled regime for the pump wave. This limits the conversion efficiency.

Fig. 3. Signal power Ps versus total pump power Pp and versus the fraction Pp˜ available for the parametric process at 40 °C resonator temperature. The dots are the experimental data, and the solid line corresponds to a fit according to Eq. (3).

The gap reduction also increases the pump threshold of the parametric oscillation up to 330 μW. According to Eq. (4), this is expected. In order to compare the measured pump thresholds with the prediction of this equation, we chose the following realistic parameters: nj=2.2 [6

6. D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

], d=5pm/V [9

9. J. Seres, Appl. Phys. B 73, 705 (2001). [CrossRef]

], Veff=1012m3, Qp=7.7×106, Qs=5×107 [10

10. A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]

], and Qi=108 [10

10. A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]

]. From the linewidth measurements, we know that the pump field is undercoupled; we set rp=0.5. The signal and idler fields have larger wavelengths and might be critically coupled or overcoupled rs=1, ri=2. This yields Pth=10μW, which is a factor of 6 smaller than the measured value. One reason might be a significantly larger effective mode volume due to different transversal mode structures of the three interacting waves.

By changing the resonator temperature from 30 to 170 °C in steps of 10 °C, we can tune the signal and idler wavelengths. Figure 4 shows this behavior for 4 mW total pump power and a vanishing gap between the coupling prism and the resonator. At every investigated temperature value, we scan the pump frequency over 6 GHz, enabling us to couple to different transversal pump modes. The signal wavelength λs ranges from 707 to 865 nm, and the idler wavelength λi from 1120 to 1575 nm. In order to compare the measured tuning behavior to the theoretically expected one, we calculate the wavelengths λs,i fulfilling the phase matching condition np/λp=ns/λs+ni/λi. Here, the effective refractive index depends on the bulk refractive index [6

6. D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

], on the temperature, on the resonator shape, and on the transversal mode structure of the interacting waves [11

11. M. L. Gorodetsky and A. E. Fomin, IEEE J. Sel. Top. Quantum Electron. 12, 33 (2006). [CrossRef]

]. Figure 4 shows a good agreement between experiment and simulation.

Fig. 4. Signal and idler wavelengths versus the resonator temperature. The solid and dashed curves correspond to theoretically expected values under the assumption of different transversal mode combinations sketched in the inset for pump (p), signal (s), and idler (i) waves. The curved line in the inset indicates the resonator rim.

We gratefully acknowledge the financial support from the Deutsche Forschungsgemeinschaft.

References

1.

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

2.

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

3.

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

4.

M. Förtsch, J. U. Fürst, C. Wittmann, D. V. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and Ch. Marquardt, “Accurate group delay measurement for radial velocity instruments using the dispersed fixed delay interferometer method,” arXiv 1204.3056 (2012).

5.

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]

6.

D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

7.

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]

8.

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

9.

J. Seres, Appl. Phys. B 73, 705 (2001). [CrossRef]

10.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]

11.

M. L. Gorodetsky and A. E. Fomin, IEEE J. Sel. Top. Quantum Electron. 12, 33 (2006). [CrossRef]

12.

A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999). [CrossRef]

13.

J.-P. Meyn and M. M. Fejer, Opt. Lett. 22, 1214 (1997). [CrossRef]

14.

C. Chen, Y. Wang, B. Wu, K. Wu, W. Zeng, and L. Yu, Nature 373, 322 (1995). [CrossRef]

OCIS Codes
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(230.5750) Optical devices : Resonators

ToC Category:
Nonlinear Optics

History
Original Manuscript: August 7, 2012
Manuscript Accepted: August 21, 2012
Published: October 5, 2012

Virtual Issues
October 17, 2012 Spotlight on Optics

Citation
Christoph Sebastian Werner, Tobias Beckmann, Karsten Buse, and Ingo Breunig, "Blue-pumped whispering gallery optical parametric oscillator," Opt. Lett. 37, 4224-4226 (2012)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-37-20-4224


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References

  1. M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999). [CrossRef]
  2. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]
  3. T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011). [CrossRef]
  4. M. Förtsch, J. U. Fürst, C. Wittmann, D. V. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and Ch. Marquardt, “Accurate group delay measurement for radial velocity instruments using the dispersed fixed delay interferometer method,” arXiv 1204.3056 (2012).
  5. 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]
  6. D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]
  7. 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]
  8. B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011). [CrossRef]
  9. J. Seres, Appl. Phys. B 73, 705 (2001). [CrossRef]
  10. A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]
  11. M. L. Gorodetsky and A. E. Fomin, IEEE J. Sel. Top. Quantum Electron. 12, 33 (2006). [CrossRef]
  12. A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999). [CrossRef]
  13. J.-P. Meyn and M. M. Fejer, Opt. Lett. 22, 1214 (1997). [CrossRef]
  14. C. Chen, Y. Wang, B. Wu, K. Wu, W. Zeng, and L. Yu, Nature 373, 322 (1995). [CrossRef]

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