1. Introduction

Mid-infrared continuous-wave singly-resonant optical parametric oscillators (SROs) are used in various spectroscopic applications such as trace gas analysis, as well as in different industrial and security applications, for instance countermeasures against heat-seeking missiles [1–3]. With the emergence of reliable fiber-laser pump sources with versatile tuning capabilities, the prospect of cost-efficient SROs addressing various wavelength ranges has attracted increased interest [4–6]. In particular, the improved access to considerable pump power has enabled high-power SROs with output powers in excess of 20 W [7]. However, operating SROs at these power levels requires accurate control of the circulating intra-cavity power in order to reach both optimum conversion efficiency to the idler wave [8] and suppress detrimental effects, such as thermal loading, cascaded nonlinear conversion processes, and Raman scattering, all of which can diminish spatial and spectral quality of the output signals [9, 10].

It has been shown theoretically that an optimal ratio of pump to threshold power of (π/2)² (roughly 2.5) ensures maximal power extraction from SROs described with plane waves [11]. Other studies showed that this value remains unaffected even when collimated Gaussian beams are used to describe the interacting fields [12]. However, it has also been suggested that SROs would be susceptible to modulation instabilities at high pump intensities, which could even require pumping with less than the optimal ratio [13].

These difficulties have been recognized and the introduction of sufficient output coupling by using a set of different mirrors as output couplers [14] or variable output coupling through an anti-resonant ring interferometer [15] have been used to operate SROs with optimal extraction efficiency. However, these approaches either require a time consuming search for the optimal mirror, or some extra optical elements that increase the internal losses and space requirements.

In this work, we propose and demonstrate the utilization of a volume Bragg grating (VBG) with variable reflectivity along the transverse direction as an output coupler, which allows continuous variation of the SROs threshold by means of a straightforward one-dimensional translation of the grating. Moreover, using a VBG as a cavity delimiter also obviates the need for any additional intra-cavity elements i.e. etalons for frequency stabilization. Although, the tuning capabilities of such a cavity configuration is reduced at first glance, it was demonstrated earlier that the implementation of a transversal chirp of the VBGs design wavelength is an efficient opportunity to reintroduce wavelength tuning of OPO cavities [16,17]. This would require a VBG reflectivity profile where along one direction of the grating the reflectivity is varied, while in the other direction the spectral position of the reflectivity peak changes gradually. Additionally, in previous work on VBG-locked SROs [18, 19] it was demonstrated, that by employing the VBG in a tilted configuration within a ring cavity single-longitudinal mode output signals are easily achieved.

2. Experimental setup

The schematic of the experimental SRO configuration is given in Fig. 1. The SRO was pumped with an in-house built continuous wave Yb-doped fiber laser [20]. The pump laser provided low-noise (<0.2% RMS), single-transversal-mode, tunable, linearly polarized output, with a good beam quality (M²<1.2) and a multi-longitudinal mode as well as a relatively narrowband output spectrum (<15 GHz) as measured at output powers of up to 100 W. The pump laser spectrum was locked using a transversally-chirped volume Bragg grating. After passing the pump beam through a waveplate-polarizer arrangement, in order to control the pump power, the beam was focused to a spot size of 75 µm 1/e²-radius within a 50 mm long MgO-doped periodically poled lithium niobate crystal (MgO:PPLN) (HC Photonics Inc.). The Λ = 30.5 µm grating period of the crystal phase matched the nonlinear conversion of 1.064 µm pump light to 1.55 µm signal and 3.4 µm idler radiation, while fine tuning of the phase matching condition was facilitated by placing the crystal in a temperature stabilized copper holder maintained at ~25°C. The crystal was antireflection coated (R<0.5%) for the pump, signal and idler waves.

 

Fig. 1 Schematic of the SRO bow-tie cavity with a variable-reflectivity VBG as output coupler.

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The actual cavity for the nonlinear gain medium was a bow-tie ring cavity consisting of four reflective elements. The two mirrors enclosing the crystal, M1 and M2, had a radius of curvature of 100 mm and coatings providing high transmission for the pump and idler waves, while being highly reflective (>99.9%) for the resonating signal. The third cavity element M3 was a flat mirror with the same coating as mirrors M1 and M2. With the fourth reflector being the varying-reflectivity VBG, the cavity formed a singly-resonant ring cavity with a mode radius of 85 µm inside the crystal leading to a good overlap with the pump mode. The overall geometric cavity length was 420 mm. Since the VBG reflectivity of finite beams is gradually reduced for increasing incidence angle to the grating [21], we chose a rather small folding angle of β = 4.5° for the bow-tie cavity. The VBG (Optigrate Inc.) was written in a 3.5 mm thick glass block whose clear aperture was 18x4 mm². Using white light transmission spectroscopy we characterized the VBG under normal incidence. From this data and the calculations described in [21], we deduced the actual reflectivity data of the grating, when used in an angled configuration as in the present bow-tie cavity. Since, the measured peak reflectivity for normal incidence varied between 91.9 and 99.2% along the transversal direction of the VBG, which corresponds to a refractive index modulation between (2.72-4.39) × 10⁻⁴, we calculated that the peak reflectivities under oblique incidence reduce to values between 88.8 and 99.0%, see Fig. 2. The calculations assumed a Gaussian signal beam waist of w₀ = 200 µm at the grating position as well as an internal angle of incidence of 3.2°.

 

Fig. 2 Measured VBG peak reflectivity at normal incidence (black squares) and calculated peak reflectivities under oblique incidence at 3° assuming a Gaussian beam waist of 200 µm at the grating position (red circles).

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3. Results

For alignment and evaluation purposes, the VBG was initially replaced by a highly reflecting mirror M4 (>99.9% for the signal). As the threshold power of a SRO, given confocally focused Gaussian beams, can be calculated according to [22]

The threshold power when replacing the VBG with M4 was 0.9 W, corresponding to a cavity round trip loss for the signal wave of ~0.5%, which is caused by the crystal and mirror coatings as well as scattering losses in the crystal.

Subsequently, the SRO was operated with the VBG at different transversal positions, leading to the desired continuous variation in threshold power, due to the transversally varying reflectivity of the VBG. Results of that measurement are depicted in Fig. 3(a), at this stage of the experiments threshold powers above 20 W were not evaluated in order to avoid any risk of catastrophic damage to the crystal. Moreover, we confirmed the linear dependence of threshold power on the VBG transmission, see Fig. 3(b). By fitting this data with the theoretical prediction from Eq. (1), we determined an overall parasitic loss of 1.2% in the SRO cavity containing the VBG. The 0.7% increase of the parasitic losses in comparison to the previous case, when using mirror M4, can be readily attributed to the anti-reflection coating on the VBG surface which is transversed twice by the reflected signal. Additionally, the theoretical fit shows that it should be possible to further increase the SRO threshold to roughly 25 W using the VBG in the investigated configuration, which would correspond to a variation of threshold power by a factor of almost 6, although experimentally only a variation by a factor of 4.5 was demonstrated.

 

Fig. 3 (a) Measured threshold power for different positions of the VBG and (b) measured (black squares) and calculated (dashed red line) correlation between SRO threshold and VBG transmission.

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To evaluate the concept of operating the described high-power SRO at optimal output coupling using the variable transmission output coupler, we increased the pump power to 2.5 times above the threshold power for several distinct threshold powers P_th, namely 4.4 W, 8 W, 12 W and 16 W, corresponding to maximum pump powers of 11 W, 20 W, 30 W and 40 W, respectively. The results are shown in Fig. 4. Evidently, a significant deviation between the extraction efficiency η_e = (P_s + P_i)/P_p (Fig. 4(b)) and the depletion η_d (Fig. 4(a)) occurs, which is especially striking for the lowest investigated output coupling (black squares). Considering the dependence of the extraction efficiency η_e on the ratio between the signal output coupling and the overall cavity round trip loss including parasitic losses [22]

 

Fig. 4 (a) Depletion and (b) extraction efficiencies for different maximum pump thresholds (VBG transmissions) as indicated in the legend of the graphs. Dashed lines correspond to the calculated extraction efficiencies using the measured depletion values and previously determined parasitic loss of 1.2% according to Eq. (2).

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Interestingly, in the case with the highest threshold of 16 W, the extraction efficiency reaches its peak value already at power levels of roughly two times the threshold power and remains fairly constant for higher powers, a behavior which could be caused by the onset of a thermally induced optical guiding effect as described in [24].

Although, an additional measurement with a threshold power of 20 W was performed in order to study the SRO at even higher powers, further power scaling could not be investigated properly since the MgO:PPLN crystal suffered catastrophic damage after several minutes of operation at the maximum pump power of 50 W. At this point, even though the pump power did not exceed the threshold power by more than 2.5 times, power fluctuations and multimode behavior where observed. Anyhow, the SRO operated for some minutes generating 23 W of signal and 12 W of idler before the damage – probably assisted by photorefraction – occurred.

Nevertheless, for a pump power of 40 W we demonstrated 19 W of signal and 11 W of idler, where we characterized both long term frequency and power stability. A temperature-stabilized scanning Fabry-Pérot interferometer (FPI, (Toptica FPI 100)) allowed us, not only to confirm single longitudinal mode operation, but also to determine the long-term frequency stability of the SRO signal. The results of the bandwidth measurement are presented in Fig. 5.

 

Fig. 5 Measurement on signal bandwidth using a scanning Fabry-Pérot interferometer with 1 GHz free spectral range; the FWHM bandwidth of the signal was 1.65 MHz.

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The linewidth of the single peak was measured to be 1.65 MHz, and since the free spectral range of the SRO cavity was 310 MHz it shows that the SRO clearly operated on a single longitudinal mode. During the long-term frequency stability measurements the central wavelength was monitored using a wavemeter (HP86120B) and the FPI. The frequency drift is shown in Fig. 6, together with a recording of the room temperature, the signal power and the idler power. The wavemeter had a resolution of 1 pm and the two results show excellent agreement. The jumps seen in the data from the wavemeter correspond to the minimum step size possible i.e. are identical to the resolution of 1 pm (125 MHz). Observe that over a period of 1.5 h the frequency drift is as small as 200 MHz, and the short term variation is on the order of 30 MHz. The long term drift is attributed to the increase in room temperature, however, as the VBG was not temperature stabilized it might have had a minor contribution to the frequency drift as well. The signal and idler powers are essentially unaffected by this small frequency deviation, as both signal and idler show a point-to-point stability of better than 5% over 1.5 hours.

 

Fig. 6 Long-term measurements over 1.5 hours of (a) the frequency deviation of the signal from the initial central frequency measured with a wavemeter (circles) and a Fabry-Pérot interferometer (line), (b) the output power of the signal, (c) the output power of the idler, and (d) the room temperature

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4. Discussion and conclusion

We have demonstrated a functional method for continuously varying the output coupling of cw singly-resonant OPO, thus enabling operation with optimal extraction efficiency independent of the employed pump level. Fine tuning of the signal output coupling was achieved by a simple one-dimensional translation of a VBG with gradually chirped reflectivity without adding any additional intra-cavity elements which would increase the internal losses. Since we used the VBG under oblique incidence within a ring cavity wavelength locking was ensured, enabling a single-longitudinal-mode signal output with a bandwidth of <2 MHz.

Moreover, by deploying a carefully characterized VBG we could determine parasitic cavity losses within the SRO cavity and were thus able to match experimental results on the power scaling behavior of the SRO with existing theoretical models.

The best long term stable performance we could demonstrate for the described output optimized SRO achieved a 75% conversion efficiency of 40 W incident pump power, generating 19 W signal power at 1.55 µm and 11 W of idler power at 3.4 µm.