Power Scaling of a Narrowband-Seeded, Non-Resonant Optical Parametric Oscillator Based on Periodically Poled LiNbO₃

Abstract

A periodically poled LiNbO₃ (PPLN) non-resonant optical parametric oscillator injectionseeded by narrowband sub-50-mW CW radiation at the signal wavelength produces a >3 W average idler power at 2376 nm for a 20 kHz repetition rate, with a ~2 nm spectral linewidth. Seed levels as low as 5 mW are sufficient to produce the desired spectral narrowing effect, and spectral tuning is possible by changing the seed wavelength and simultaneously adjusting the crystal temperature. The spectral features are in good agreement with numerical simulations based on the plane wave approximation.

1. Introduction

Optical parametric oscillators (OPOs) are widely used to convert the emission of powerful laser sources to longer wavelengths based on a three-wave nonlinear process (χ⁽²⁾ interaction). Using a cavity that can be resonant for one or both (signal and idler) of the waves, which are generated by frequency down-conversion of the pump radiation, they can operate in continuous-wave (CW) or pulsed (mostly nanosecond) regimes, where the latter is capable of providing much higher conversion efficiencies due to the higher pump intensity of the Q-switched pump laser. Away from degeneracy, normally the shorter (signal) wavelength is resonated in the so-called singly-resonant OPO or SRO, whereas the longer (idler) wavelength produced by intracavity difference-frequency generation (DFG) is totally outcoupled. There are multiple reasons for this, including instabilities that occur when both waves are resonated; the requirement to simultaneously satisfy energy, momentum, and phase constraints; and the desire to extract higher energies and average powers at longer wavelengths, where the tunability range is wider. Technical limitations related to manufacturing damage-resistant dielectric mirrors are another reason. Intuitively, one would expect the shorter wavelength of an SRO (signal) not to be outcoupled at all. In other words, both cavity mirrors should be 100% reflective to reach maximum conversion efficiency. However, in practice, it must also be outcoupled to some extent, to suppress the optical damage effects to the nonlinear crystal, which are mainly due to the pump radiation but which are enhanced by the presence of the resonant signal wave.

The limiting case when the signal wave is also 100% outcoupled is reached in the so-called non-resonant OPO, abbreviated as NRO, in which none of the waves are resonant, with the signal and idler leaving the cavity after just one round trip in opposite directions. One of the NRO cavity mirrors is highly reflective (HR) at the signal and highly transmissive (HT) at the idler wavelength, while the other cavity mirror exhibits the opposite properties (HT signal/HR idler). In an NRO, the feedback is realized by the nonlinear process, propagating the pump wave in both directions via a retro-reflection through the cavity. The pump threshold of an NRO will be obviously higher compared to that of a conventional SRO, but on the positive side, apart from the fact that it provides simultaneous output at two wavelengths, degradation of beam quality and conversion efficiency caused by back conversion will be intrinsically suppressed in an NRO. While the idea of such a resonatorless parametric oscillator, along with its first realization, date back to 1971 [1,2], it was only recently that we demonstrated that high gain quasi-phase-matching (QPM) materials, such as periodically poled LiNbO₃ (PPLN), are highly suitable for use in NROs pumped near 1 µm by commercially available Nd lasers [3].

Most applications will benefit from a narrowband output of the OPO due to its superior spectral resolution and/or selectivity. That is also true for our main interest in using such 1 µm pumped OPOs in a cascade scheme, i.e., to pump a second stage based on a non-oxide nonlinear crystal for further parametric down-conversion into the mid-IR part of the spectrum beyond 3 µm, ideally between 5 and 15 µm. In this case, the linewidth of the first stage output will affect not only the spectral linewidth achievable in the mid-IR from the second stage but also the conversion efficiency to the mid-IR due to limited spectral acceptance for the pump wave in the second stage.

Without wavelength selective elements, the output spectrum of such an OPO is usually much broader than the pump spectrum near 1 µm due to the large parametric gain spectral bandwidth of the nonlinear crystal. The main contributing factor is the spectral acceptance for the three-wave interaction process, assuming narrowband pump radiation near 1 µm, which is inversely proportional to the crystal length and the difference between the group velocities of the signal and idler. This is also true for an SRO, but the problem is more severe in an NRO based on QPM, where the polarizations of all waves are the same. In an SRO, the bandwidth of the idler, which is produced by DFG, can be controlled by the bandwidth of the signal, provided that the pump radiation has a relatively narrow bandwidth. Volume Bragg gratings (VBGs), based on photorefractive glass acting on the signal wave, are a simple and robust solution which we recently implemented in a nanosecond PPLN NRO [3,4,5], showing that the spectral narrowing is transferred to the idler, notwithstanding the non-resonant character of the cavity. The use of both thick (3 mm) and long (50 mm) PPLN, which recently became commercially available, ensured a simultaneously low NRO threshold and the highest output and efficiency for this configuration in the narrowband regime, with minimum risk for optical damage [5].

CW injection seeding is another well-known method for spectral narrowing, and NROs seem well suited for this approach, given that their cavity is open from one side for each of the output waves. This is clear, considering that such a modeless cavity can be equally regarded and employed as a multipass parametric amplifier [6]. Injection-seeded NROs offer some potential advantages over VBG NRO operation, including the broader tuning capability (compared to that of a single chirped VBG) and the straightforward reconfiguration to single frequency operation using low-power seed laser diodes if the pump laser is also a single-frequency type. However, our initial studies of this approach with a 1 mm thick PPLN revealed that at high parametric gain, the spectral narrowing effect is overwhelmed by parametric generation in the nanosecond NRO [7]. Thus, at a repetition rate of 20 kHz, the maximum average pump powers that could be applied at 1064 nm were in the 3–4 W range, independent of the CW seed power level at the signal wavelength [7]. Subsequently, we investigated the power scaling capabilities of the injection-seeded narrowband NRO utilizing the full power available from the pump laser by employing a larger aperture PPLN crystal (3 × 3 mm² in Ref. [8] versus 1 × 1 mm² in Ref. [7]).

PPLN is currently the most widely used nonlinear crystal in OPOs pumped by commercially available laser sources emitting near 1 µm (Nd- or Yb-lasers). PPLN samples exhibit a limited thickness in the electric field poling direction, but their length can reach a few centimeters. Hence, PPLN is most suitable for operation at high average powers with kilohertz repetition rates because of surface optical damage limitations related to the pump fluence. As mentioned above, recently, both relatively thick (3 mm) and long (5 cm) PPLN became commercially available [5]. Here, we study CW injection seeding of an NRO based on such a PPLN sample to establish the seed threshold for highly efficient, narrowband operation. Seed levels as low as 5 mW, ~8 times lower compared to those reached in our previous work with a 25 mm long crystal [8], were sufficient to produce the desired spectral narrowing effect, with >3 W of idler output average powers at 20 kHz. The results are supported by numerical simulations performed in the plane wave approximation.

2. Experimental Setup

The PPLN NRO is pumped by a multi-longitudinal mode (spectral linewidth ~0.66 nm) Nd:YVO₄ master oscillator power amplifier (MOPA) laser system (Canlas GmbH, Berlin, Germany), delivering a maximum average power of 20 W for a pulse duration of ~8 ns at a repetition rate of 20 kHz. The laser beam quality factor is M² ~1.15.

A combination of a half waveplate (HWP) and a polarizing beam splitter (PBS) is used to attenuate the pump power while keeping the pump laser parameters (spatial, spectral and temporal) constant at the maximum output level. A subsequent Faraday isolator (FI-1, Pavos Ultra Series, EOT, Coherent, Palo Alto, CA, USA) prevents the optical feedback to the pump laser. A second HWP is integrated at the isolator output as a compensator, rotating the polarization to vertical for type-0 (eee) phase-matching in the PPLN crystal. The pump beam is down-collimated by an achromatic beam expander (GBE02-C, Thorlabs, Newton, NJ, USA) to a 1/e² beam diameter of ~2.2 mm. The 50 mm long, antireflection (AR)-coated 5 mol% MgO-doped PPLN (PPMgLN, OPMIR-SD-50, HC Photonics, Hsinchu City, Taiwan) has an aperture of 3 × 3 mm². Its QPM period of 32.25 μm corresponds to a signal wavelength of 1927 nm and an idler wavelength of 2376 nm for a pump wavelength of 1064 nm at an oven temperature of 33 °C. The measured residual reflectivity per surface is 0.2% at the pump wavelength, 1.5% at the signal wavelength, and 3.5% at the idler wavelength. The parallelism of the AR-coated faces is specified by the supplier as 3′.

The narrowband NRO cavity consists of signal and idler output couplers (OC-1 and OC-2) separated by a physical length of 13.5 cm, as shown in Figure 1. OC-1 is 95% reflective for the idler and 95% transmissive for the signal. OC-2 is 99% reflective for the signal and 90% transmissive for the idler. The dichroic mirrors DM-1/DM-2 couple the pump in and out of the NRO—they are highly transmissive for the signal (95%) and idler (91%) and highly reflective at the pump and its second harmonic. The dichroic mirror DM-3 is highly reflective at the pump and transmissive at 532 nm, enabling the obligatory double pass pumping of the NRO and the outcoupling of parasitic green second harmonic light. The CW seed source is a tunable (1908–1937 nm), narrow linewidth (<0.5 nm) 1 W Tm fiber laser (TLT-1-1930, IPG Photonics, Marlborough, MA, USA), collimated with a 5.95 mm aspheric lens (CO228TME-D, Thorlabs, Newton, NJ, USA) to a diameter of 1.75 mm to match the pump. A second FI (FI-2, IO-6-1950-HP, Thorlabs, Newton, NJ, USA) is used to prevent back reflections to the seed laser, and another HWP-PBS combination is used to adjust the seed level and match the pump polarization in the PPMgLN. The maximum applied CW seed level measured behind the PBS was 45 mW.

Being primarily interested in the longer wavelength idler output, we did not attempt to separate the signal seed input and amplified output as we did in Ref. [7], but characterized only the idler behind OC-2, using a long pass filter to eliminate residual pump and signal light. Narrowband idler output can be achieved by DFG only if the amplified signal is also narrowband. Comparing the results with those from unseeded broadband NRO operation, we characterized both the idler (behind OC-2) and the signal (behind OC-1) outputs in this case.

3. Results and Discussion

All pump powers quoted below were measured at the input of the NRO cavity (in front of DM-1). The passive losses at 1064 nm of all optical elements from the laser output until this point were about 12%. All presented idler powers are already corrected for the transmission (96%) of the cut-on filter used in front of the power meter. The same is true for the signal power measured behind a different cut-on filer (99%) in the unseeded case. The CW seed powers are those measured in front of OC-1. Figure 2 shows the average idler output power at 2376 nm and the calculated quantum conversion efficiency versus the average pump power for the unseeded case (a) and at a seed level of 20 mW at 1927 nm (b). At a pump level of 18 W at 20 kHz, the maximum idler average power in the unseeded case reaches 2.97 W with a conversion efficiency of 38.4%. Both the idler average power, 3.19 W, and the quantum conversion efficiency or pump depletion, 39.5%, are slightly higher when the NRO is seeded. It is also evident that the NRO threshold is somewhat lower for the seeded case. The long term rms instability for the seeded regime measured for the idler output over 10 min at maximum level was 1.2%, or roughly three times worse than that of the pump laser at 20 kHz.

The dependence of the average idler output power on the seed level is not very pronounced. This is shown in Figure 3a up to a CW seed level of 45 mW at 1927 nm, for which the average idler output power reached 3.23 W. Some saturation is observed starting from about 20 mW; however, much lower seed levels were sufficient to achieve narrowband operation of the NRO.

The pulse durations were measured with a <200 ps InGaAs photodetector (UPD-5N-IR2-P, Alphalas, Göttingen, Germany) connected to a 1 GHz oscilloscope. The pump and idler pulse profiles are compared in Figure 3b for a CW seed level of 20 mW. The idler pulse duration at maximum power (full width at half maximum, FWHM = 7 ns) was slightly shorter compared to the pump pulse (8 ns). It was unchanged compared to the unseeded case when the measured signal pulse duration was 6 ns. There was a more pronounced dependence on the pump level, with the pulse durations getting shorter at lower pump levels. Thus the idler pulse duration at an average pump power of 13 W was ~6 ns, independent of the seed level, while the signal pulse duration in the unseeded case was ~5 ns. The pulse broadening at maximum pump level can be explained by gain saturation.

The influence of the injection seed level on the idler spectrum is illustrated in Figure 4a, at the maximum pump level of 18 W average power at 1064 nm. While the main effect of the seed level is on the pedestal, it can be seen that linewidths (FWHM) of the order of 2 nm (1.8 nm for the seed levels shown in the figure) for the idler spectrum at 2376 nm can be achieved at a seed level as low as 5 mW. For comparison, the idler spectrum for the unseeded case at the same maximum pump level shows an FWHM of 16 nm, while the signal spectrum displays an FWHM of ~11 nm, in good agreement with the expected wavelength dependence for the same spectral extent in terms of frequency (cm⁻¹). In comparison with our previous experiments using an analogous but 25 mm long PPLN crystal, the CW seed power necessary to achieve the same effect of idler spectral narrowing has been reduced by a factor of roughly eight, from 40 to 5 mW. This constitutes the main result of the present research because such power levels are readily available from widely used distributed feedback (DFB) laser diodes operating in the single-frequency regime.

As expected, at lower pump levels, the unseeded NRO output spectra were narrower (e.g., FWHM = 11 nm for the idler and FWHM = 8 nm for the signal at a 10 W average pump power at 1064 nm). As can be seen from Figure 4b, at the same CW seed level of 10 mW, the main difference in the narrowed idler spectra is the level of the pedestal. Thus we attribute the occurrence of this pedestal to operation far above threshold, where back conversion starts to play an essential role at the seed wavelength.

Tuning of the present NRO idler wavelength was possible by tuning the Tm fiber laser seed wavelength. By simultaneously optimizing the PPMgLN oven temperature (see Figure 5), it was possible to maintain the same output power level within 2%. In Figure 5, the seed wavelength was tuned between 1920 and 1935 nm at a constant CW seed level of 20 mW under the maximum pump level of 18 W average power at 20 kHz. The oven temperature was adjusted between 31.2 and 35.1 °C to match the maximum parametric gain to the seed wavelength. The achieved idler tuning range in narrowband operation extended from 2365 to 2387 nm.

4. Numerical Modeling

We developed a code, OPO_SPECTRUM, for the simulation of the spectral distribution of the NRO output beams, widely following the split-step method #1 presented in Ref. [9] for plane waves. In the time domain, the mixing equations are integrated in the propagation direction to account for the nonlinear parametric amplification and ignoring dispersion, followed by a step in the frequency domain, taking linear effects into account, particularly the temporal walk-off as a result of the group velocity mismatch (GVM) and the effect of group velocity dispersion (GVD). The code allows for the effect of the actual spectral transmission and reflection of the cavity mirrors or residual reflections from the crystal surfaces. Back conversion and pump depletion are inherent features of the model, but diffraction is ignored. Spatial walk-off is absent for QPM. The quantum noise the code starts with in the case of unseeded NRO operation is generated in the standard manner, i.e., by one half photon (signal, idler) energy per frequency interval, on average (electric field with random phase and Gaussian amplitude distribution with zero mean and variance 1).

For the 5 mol% PPMgLN, the simulation code uses the temperature-dependent Sellmeier relations from Ref. [10]. The effective nonlinearity of PPLN was directly evaluated in Ref. [10] as d_eff = 14 pm/V, which takes into account the imperfect poling quality, a figure largely quoted by manufacturers, including the present provider. In Ref. [11], this was considered to be 78% of the ideal value for a first order grating, which leads to d₃₃ = 28.2 pm/V. This value for the diagonal tensor element is close to the results more recently reported for 5 mol% MgO-doped congruent LiNbO₃ by non-phase-matched methods, d₃₃ = 25 pm/V [12]. Thus, we only converted the value of 14 pm/V for frequency doubling of 1064 nm radiation to our three-wave parametric process using Miller’s rule and the corresponding refractive indices, and adopted d_eff = 11.8 pm/V in the code.

The temporal walk-off between the signal and idler is the underlying crucial mechanism in the code. The walk-off time for signal and idler is defined as

$${\tau }_{s,i}=L_{c }\left|{\displaystyle \frac{1}{v_s}}-{\displaystyle \frac{1}{v_i}}\right|,$$

(1)

where the group velocities $v_s$ and $v_i$ are given by $v={\displaystyle \frac{c}{n_g}}$, with the group refractive indices ${ n}_g=n+\omega {\displaystyle \frac{dn}{d\omega }}$, and $L_{c }$ denoting the crystal length. Temporal features with time scales shorter than ${\tau }_{s,i}$ are smoothed out by the GVM, and the spectra are limited to widths of ${\tau }_{s, i}^{-1}$ or smaller in this approximation [9]. For larger spectral widths, the GVD terms in the coupled wave equations must be retained.

For our experimental wavelengths, ${\tau }_{s,i}$ = 0.67 ps in the 50 mm long PPLN. The walk-off time is directly related to the spectral acceptance for the low parametric gain case (DFG) in the limit of a narrowband pump wave, $∆\nu = {0.886/\tau }_{s,i}$ [13], which yields about 44 cm⁻¹, equivalent to 16 nm for the signal and 25 nm for the idler spectral bandwidths. This simple estimate ignores pump depletion and is obviously valid only in the low signal case. Although often used, it in fact presents an oversimplification, since the derivation is based on analytical parametric gain expressions obtained by ignoring GVM and GVD. Strictly speaking, it is applicable for tunable monochromatic waves but not for broadband radiation. Usually, broadband oscillators will display narrower bandwidths due to multiple passes, as also evidenced by the present experiment; however, saturation effects at higher conversion efficiency lead to the opposite trend, again seen in Figure 4b above. Thus, realistic estimations for an OPO or an NRO, particularly in regard to depletion and back conversion, can be achieved only through numerical simulations.

The simulations were performed for a pump pulse energy of 0.90 mJ or a plane wave peak intensity equal to the spatially averaged value of ~2.8 MW/cm², corresponding to the maximum pump power level applied in the experiment at 20 kHz and 8 ns pulse duration (FWHM), assuming Gaussian spatial and temporal shapes for the pump, and the specified (see Section 2) pump and seed spectral bandwidths. For a signal wavelength of 1927 nm, a crystal temperature of 30.2 °C is computed to yield perfect matching. This is in good agreement with the results of the experiment in which we measured and specified the oven temperature. We also applied random phase shifts to the incoming pulsed pump wave with respect to the signal and idler, taking into account that the pump is retro-reflected by a separate mirror, but we established that this has no effect on the simulation results.

The spectra obtained by such a numerical modeling within the plane-wave approximation in the broadband and narrowband regimes, after smoothing over 20 simulation runs (20 pump pulses), are presented in Figure 6. The assumed seed intensity for the signal plane wave was about 0.5 W/cm², which will be close to the experimental case with a 10 mW CW seed power at 1927 nm. The high-resolution spectral data (computed with a frequency step corresponding to ~0.01 nm for the signal and ~0.015 nm for the idler) were additionally smoothed to account for the spectral resolution in the experiment (about 0.5 nm). This was realized by convolution with a Gaussian apparatus function with the corresponding FWHM in the frequency domain prior to conversion to wavelength units. We established that such a smoothing procedure in fact makes multiple simulations (averaging over many pulses) redundant.

The simulation results demonstrate that injection seeding at the signal wavelength dramatically narrows the signal and idler spectra (see Figure 6), which strongly supports the experimental observations in terms of spectral behavior. After smoothing the spectra with the spectrometer apparatus function, the FWHM estimated for the idler (see Figure 6) was 1 nm, which is in good agreement with the experimentally measured spectra in Figure 4 for the NRO. The spectral narrowing effect obtained from the simulations in fact depended only weakly on the seed level, and this is also the case in the experimentally measured data for the idler in Figure 4a. Some deviation from the experimental observations is also noted for the unseeded case, with a FWHM of 9.5 nm for the idler and 6 nm for the signal output. These deviations can be attributed to transversal spatial effects not taken into account in the plane wave model. However, the plane wave model predicts the pedestal observed in the experimental spectra, which confirms that it is not related to spatial effects but rather to the high parametric gain in the pulsed regime.

For modeling the pump power dependence of the signal and idler output, we employed a different code, called OPODESIGN, to account for spatial intensity distributions and diffraction. It is based on a standard single-frequency approach, e.g., presented in Refs. [14,15] and the references therein. In the crystal, the coupled wave equations are integrated in the propagation direction via the split-step method using a fast Fourier transform for the diffraction terms and a 4th order Runge–Kutta integration scheme for the nonlinear terms in the spatial domain. The temporal evolution is realized by sampling the pump pulse using slices of the round-trip time duration. The pump power dependence of the NRO output powers in Figure 7a and the temporal output pulse shapes in Figure 7b were obtained after integration over the transversal beam distributions. To compare them with the experimental results, the temporal output pulse shapes were smoothed with an instrumental function of 1 ns FWHM.

It can be seen that the single-frequency 3D model well predicts the idler output power and NRO threshold in the narrowband seeded case. On the other hand, the OPODESIGN code inherently implies the propagation of “time-slices” of the cavity round-trip time duration. With the rather short pump pulse duration of 8 ns, this yields a comparatively coarse temporal sampling of the pulses (about 5 points across their FWHM). The numerical model predicts a strong deformation of the pump pulse shape and output pulse durations of similar length (8 ns) as that of the undepleted pump (see Figure 7b).

5. Conclusions

We demonstrate a nanosecond non-resonant optical parametric oscillator based on periodically poled LiNbO₃ injection seeded by narrowband CW radiation at the signal wavelength, which produces a >3 W of average idler power in the narrowband regime for a 20 kHz repetition rate. Spectral linewidths of ~2 nm are achievable at seed levels as low as 5 mW, available from single-frequency DFB laser diodes. The present results can, in principle, be extended to single frequency operation employing such a pump source. Wavelength tuning is possible by varying the seed wavelength and simultaneous adjustment of the crystal temperature. The spectral features are in good agreement with numerical simulations based on the plane wave approximation. The on-axis pump fluence at 1064 nm, taking into account the double pump pass, is of the order of only 10 MW/cm², which ensures long-term damage-free operation. The high parametric gain in the nanosecond regime results in some pedestal growth in the output spectra far above the OPO threshold, which is also confirmed by the simulations. Thus, injection seeding seems to be less efficient as a parametric generation suppression mechanism when compared to the VBG, which acts at each cavity round trip [5]. This can be attributed to the specific action of these two spectral narrowing methods. Seeding at the signal wavelength occurs at zero signal wave power but for an already amplified broadband idler wave, which on its way back, generates a broadband signal via DFG. In contrast, the VBG as a spectral narrowing element for the signal wave acts halfway through the signal round trip, when the signal has reached a significant power level, while the idler starts to grow from zero.

The present setup can be considered optimized for the given pump laser parameters. Different average pump powers, repetition rates, or pulse durations will affect the actual parametric gain and will require additional optimization of the focusing in the nonlinear crystal.

While PPLN is preferable for kilohertz repetition rate OPOs because of its limited aperture, for the same reason, it is also perfect for pairing with orientation patterned GaAs (OP-GaAs) in a second stage, which is the best QPM material for the mid-IR, with transparency extending up to 18 µm [13]. However, the pump spectral acceptance of OP-GaAs is rather small, and therefore, such a cascade scheme will greatly profit from the spectrally narrowed output of the PPLN NRO achieved in the present work. More precisely, the obtained spectral bandwidths will permit the pumping of OP-GaAs as long as 20 mm, without affecting the conversion efficiency [16]. The demonstrated tuning range of the seeded PPLN NRO will permit DFG using both outputs, covering the 9.8–10.6 µm wavelength range in the mid-IR.