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

Optical parametric oscillators (OPOs) can be employed to generate coherent light at almost arbitrary frequency [1]. The only fundamental limitation is that the optical pump field has a shorter wavelength λp compared to the wavelengths λs and λi of the two generated fields, called signal and idler waves. Here, the relation 1/λp=1/λs+1/λi holds. Conventional OPOs comprise a nonlinear-optical crystal inside of a mirror cavity. The mirrors have to be specially coated for the spectral range in which the device is aimed to operate. Recently, a new class of OPOs has been demonstrated—whispering gallery OPOs [2,3]. They do not require any external mirrors. In these exceptional devices, light is guided by total internal reflection inside the nonlinear-optical crystal. Thus, whispering gallery OPOs provide a low-loss cavity over the whole transparency range of the crystal. This has enabled pump thresholds below 10 μW [2]. The green-pumped devices demonstrated so far have a tuning range between 1010 and 1120 nm [2,4] while the near-infrared-pumped devices are tunable between 1800 and 2500 nm [3]. Pump lasers operating in the blue can extend the tunability into the visible spectral range. This is of interest, e.g., for coupling of nonclassical light from a whispering gallery OPO [5] to rubidium atoms or diamond vacancies. Such experiments require signal wavelengths around 795 or 639 nm, respectively.

In this Letter, we present a whispering gallery OPO pumped in the blue at 488 nm wavelength. The experimental setup sketched in Fig. 1 comprises a spheroidally shaped monolithic cavity (1.8 mm major diameter, 0.7 mm minor diameter, 1 mm thickness) made of a z-cut stoichiometric lithium niobate crystal doped with 1.2% magnesium oxide. The resonator is mounted in an oven whose temperature can be varied between 30 and 170 °C. We use a rutile prism to couple the pump light with the power Pp into the resonator. The gap between the resonator and the coupling prism can be adjusted using a piezo translator. Inside the cavity, the pump wave is converted to signal and idler waves, while all interacting waves oscillate in the cavity. The pump field is extraordinarily polarized, whereas the signal and the idler fields are ordinarily polarized. This ensures type I phase matching. Two detectors are used to measure the power Pp* of the transmitted portion of the pump light and the power Ps of the signal wave. The silicon-based detector for the signal wave is not influenced by the idler light (wavelength larger than 1200 nm). Furthermore, we investigate the spectrum of the light generated by the parametric process in the wavelength range between 300 and 2500 nm.

 figure: Fig. 1.

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.

Download Full Size | PPT Slide | PDF

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], 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]. 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.

 figure: Fig. 2.

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.

Download Full Size | PPT Slide | PDF

Later, we want to compare the pump threshold as well as the conversion efficiency of the OPO to the theoretically expected values. For this purpose, we take here a closer look on the measured linewidths and coupling efficiencies. With the coefficient rp being the ratio between the coupling loss and the internal loss for the pump wave, we get [8]

Δν=ν(1Qp+1Qc)=Δν0(rp+1),
κ=4QpQc(Qp+Qc)2=4rp(rp+1)2,
with Qc as the coupling quality factor and Δν0=ν/Qp as the linewidth determined by the intrinsic loss. At rp<1, the resonator is undercoupled, and at rp>1 the resonator is overcoupled. From Eq. (1) we deduce rp=0.75 for the prism touching the resonator. For this value, Eq. (2) shows that 98% of the pump light could be coupled into the resonator for perfect mode matching. Since we achieve 40% coupling efficiency instead, only the power Pp˜=0.41Pp is available for the parametric process. This reduction mainly originates from an imperfect spatial overlap between the pump beam and the whispering gallery mode.

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]

Ps=4(Pp˜/Pth1)Pth×λpλs(rp1+1)(rs1+1),
with the pump threshold
Pth=πε0c0np2ns2ni216d2λpVeff1QpQsQi×(rp+1)2(rs+1)(ri+1)rp.
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.

 figure: Fig. 3.

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).

Download Full Size | PPT Slide | PDF

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], d=5pm/V [9], Veff=1012m3, Qp=7.7×106, Qs=5×107 [10], and Qi=108 [10]. 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], on the temperature, on the resonator shape, and on the transversal mode structure of the interacting waves [11]. Figure 4 shows a good agreement between experiment and simulation.

 figure: Fig. 4.

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.

Download Full Size | PPT Slide | PDF

If the whispering gallery OPO is aimed to generate tunable signal light in the green or yellow spectral range, the system should be pumped at wavelengths around 400 nm. Based on our experimental results, we can predict that in this case the pump threshold will increase to hundreds of microwatts. This is mainly due to decreasing values for the intrinsic quality factor Qp and for the ratio rp. Furthermore, the decreasing rp will limit the maximum achievable conversion efficiency to several percent, which can be seen from Eq. (3). Thus, for a practical device with some 10% conversion efficiency, a material with significantly lower absorption in the ultraviolet region compared to that of lithium niobate is required. Possible candidates are lithium tantalate and borates. Lithium tantalate is transparent down to 300 nm wavelengths [12] and can be periodically poled to achieve quasi phase matching [13]. Borates are transparent even below 200 nm wavelengths [14]. However, here birefringent phase matching is the only current option since no method to grow orientation-patterned borates is known so far.

In conclusion, we demonstrated and characterized a blue-pumped whispering gallery OPO. This monolithic device with about 2 mm diameter has a submilliwatt pump threshold and is tunable over hundreds of nanometers between the red and near infrared. Furthermore, our experiments show that the conversion efficiency is limited to several percent because of absorption loss for the pump wave. We consider this special OPO as a step to a compact system that covers the whole visible spectral range with tunable nonclassical light.

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]  

References

  • View by:

  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]

2011 (3)

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, 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]

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

2010 (2)

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]

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]

2006 (1)

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

2004 (1)

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

2001 (1)

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

1999 (2)

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

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

1997 (1)

1995 (1)

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

1990 (1)

D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990).
[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, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

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).

Alexandrovski, A. L.

A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999).
[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, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

Beckmann, T.

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

Breunig, I.

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

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

Buse, K.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, 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]

Byer, R. L.

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

Chekhova, M. V.

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).

Chen, C.

C. Chen, Y. Wang, B. Wu, K. Wu, W. Zeng, and L. Yu, Nature 373, 322 (1995).
[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, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[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]

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

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

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

Fomin, A. E.

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

Förtsch, M.

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).

Foulon, G.

A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999).
[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, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

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).

Gorodetsky, M. L.

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

Haertle, D.

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

Ilchenko, V.

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

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]

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

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, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

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).

Linnenbank, H.

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

Maleki, L.

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

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]

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).

Matsko, A.

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

Meyn, J.-P.

Myers, L. E.

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

Route, R. K.

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

Savchenkov, A.

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

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]

Seres, J.

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

Silberhorn, C.

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).

Steigerwald, H.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, 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, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

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).

Sturman, B.

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

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

Wang, Y.

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

Wittmann, C.

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).

Wu, B.

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

Wu, K.

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

Yu, L.

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

Zeng, W.

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

Appl. Phys. B (2)

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]

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

IEEE J. Quantum Electron. (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

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

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

Nature (1)

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

Opt. Lett. (1)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (3)

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]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, 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]

Proc. SPIE (1)

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

Science (1)

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

Other (1)

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).

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
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.
Fig. 2.
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.
Fig. 3.
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).
Fig. 4.
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.

Equations (4)

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

Δν=ν(1Qp+1Qc)=Δν0(rp+1),
κ=4QpQc(Qp+Qc)2=4rp(rp+1)2,
Ps=4(Pp˜/Pth1)Pth×λpλs(rp1+1)(rs1+1),
Pth=πε0c0np2ns2ni216d2λpVeff1QpQsQi×(rp+1)2(rs+1)(ri+1)rp.

Metrics