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 ${\lambda }_p$ compared to the wavelengths ${\lambda }_s$ and ${\lambda }_i$ of the two generated fields, called signal and idler waves. Here, the relation $1/{\lambda }_p=1/{\lambda }_s+1/{\lambda }_i$ 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 $P_p$ 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 $P_p^{*}$ of the transmitted portion of the pump light and the power $P_s$ 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.

 

Fig. 1. Illustration of the experimental setup: $P_p$, $P_p^{*}$, and $P_s$ 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.

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In order to determine the quality factor of the optical whispering gallery, we scan the pump laser frequency $\nu$ across a cavity mode and measure the transmitted power $P_p^{*}$ versus the frequency shift. This is shown in Fig. 2. The linewidth $\mathrm{\Delta }\nu$ 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 $Q_p\equiv \nu /\mathrm{\Delta }\nu =7.7\times {10}^6$ for the pump wave. From here, we can deduce the absorption coefficient ${\alpha }_p=2\pi n_p/{\lambda }_p{Q}_p\approx 3.8{\mathrm{m}}^{-1}$ with the refractive index $n_p=2.25$ [6], assuming that the intrinsic cavity loss is dominated by absorption. This value agrees quite well with the previously measured coefficient $(2\dots 3){\mathrm{m}}^{-1}$ 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 $\kappa$ was limited to 40% for a vanishing gap between the prism and the resonator.

 

Fig. 2. Transmitted pump power $P_p^{*}$ and signal power $P_s$ as a function of the frequency shift of the pump laser at 40 °C resonator temperature.

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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 $r_p$ being the ratio between the coupling loss and the internal loss for the pump wave, we get [8]

If the input power exceeds the pump threshold $P_{\text{th}}$ for the optical parametric oscillation, we can measure the signal power $P_s$ while scanning the pump frequency across a cavity mode. Figure 2 shows that at $P_p=200\mathrm{\mu W}$, we generate $P_s\approx 0.9\mathrm{\mu W}$ of signal light at 40 °C resonator temperature. Using a spectrometer, we have confirmed the parametric oscillation at ${\lambda }_s=800\mathrm{nm}$ and ${\lambda }_i=1250\mathrm{nm}$. 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]

 

Fig. 3. Signal power $P_s$ versus total pump power $P_p$ and versus the fraction $\widetilde{P_p}$ 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).

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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: $n_j=2.2$ [6], $d=5\mathrm{pm}/\mathrm{V}$ [9], $V_{\text{eff}}={10}^{-12}{\mathrm{m}}^3$, $Q_p=7.7\times {10}^6$, $Q_s=5\times {10}^7$ [10], and $Q_i={10}^8$ [10]. From the linewidth measurements, we know that the pump field is undercoupled; we set $r_p=0.5$. The signal and idler fields have larger wavelengths and might be critically coupled or overcoupled $r_s=1$, $r_i=2$. This yields $P_{\text{th}}=10\mathrm{\mu W}$, 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 ${\lambda }_s$ ranges from 707 to 865 nm, and the idler wavelength ${\lambda }_i$ from 1120 to 1575 nm. In order to compare the measured tuning behavior to the theoretically expected one, we calculate the wavelengths ${\lambda }_{s,i}$ fulfilling the phase matching condition $n_p/{\lambda }_p=n_s/{\lambda }_s+n_i/{\lambda }_i$. 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.

 

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.

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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 $Q_p$ and for the ratio $r_p$. Furthermore, the decreasing $r_p$ 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.