2.1

Background

The BWOPO, initially proposed by Harris¹⁹ in 1966, relies on the interaction of counter-propagating parametric waves in a χ⁽²⁾ nonlinear crystal where the feedback required for oscillation build-up is distributed along the crystal itself as opposed to usual OPOs with co-propagating parametric waves where a resonant cavity provides an external feedback. The concept comes with the attractive prospect of avoiding the drawbacks generally associated with conventional OPOs such as the necessity of multi-wavelengths mirrors coatings subject to optical damage when intracavity power increases, resonant cavity(ies) alignments, or a limited miniaturization potential²⁰. The key condition to realizing BWOPO is to compensate for the very large phase mismatch of counter-propagating signal and idler waves Δk = k_p - k_f + k_b, where k_p, k_f, and k_b stand for the pump, forward, and backward wave vectors. The first proposal considered birefringence phase matching, applicable in principle for an idler wavelength deep in the far infrared. With the advent of quasi-phase matching (QPM) nonlinear crystals in the 90’s, BWOPO closer to degeneracy was considered again, and oscillation threshold intensity estimations showed typical values in the 100 MW/cm² range accessible with available pump lasers technologies²¹. However, in BWOPO the required QPM orientation period must be very small in the order of λ_pump/2, that is to say roughly 500 nm for conventional 1 μm pump lasers, which is significantly more challenging to achieve than the QPM period for usual co-propagating OPO, typically ranging in the several tens of λ_pump (10 μm -100 μm for λ_pump =1 μm). The first successful BWOPO experimental demonstration was realized in 2007, within a periodically poled KTP (PPKTP) crystal, and a grating period of 800 nm²². In this pioneering work, two specific spectral properties of BWOPO could also be verified: i) pump wavelength tuning essentially affects the co-propagating beam wavelength while the couterpropagating beam wavelength remains almost fixed, and ii) the pump spectrum is essentially imprinted on the forward travelling wave while the backward wave linewidth is significantly narrower (two orders of magnitude narrower in²²). Since this first demonstration, most of the experimental work has been carried out with sub-ns pulses in order to reach very high threshold intensities while avoiding optical damaging. Recent progresses on sub-μm QPM structures fabrication in PPKTP have allowed for BWOPO pumping with 10 ns Q-switched pulses from an injection seeded Nd:YAG pump laser²³, which further opens the path toward remote gas sensing applications. The present study follows this path by employing a tunable single frequency laser as the pump for a similar BWOPO device as in²³.

2.2

BWOPO phase matching and tuning

The geometry and QPM configuration of the BWOPO studied in this paper is shown in Figure 1.

Figure 1:

Schematic principle of the BWOPO in a periodically poled nonlinear crystal. The first order QPM condition with a 580 nm grating period and a 1030 nm pump wavelength result in a forward signal wave around 1981 nm.

The wavelength tuning of forward and backward waves can be achieved by modifying the quasi-phase matching condition k_f + K_g = k_p + k_b. In BWOPO, this could be achieved by changing the QPM grating period either through mechanical translation to switch from one crystal grating to another or through crystal rotation for angular tuning as in²⁴. Conversely to conventional co-propagating OPOs, temperature tuning is a very weak lever as it is inversely proportional to the sum of forward and backward refractive index instead of the difference, which result in a temperature tuning rate several orders of magnitude smaller for the BWOPO²². As a consequence direct pump tuning is a very attractive feature in the perspective of gas remote sensing applications since it may provide fast tuning functionalities to probe the targeted molecules absorption features, without misalignment disadvantages.

As illustrated in Table 1 the specific phase matching condition in BWOPO results in very different tuning rate of the forward and backward waves with respect to that of the pump. For the forward wave (signal wave in our case) the tuning rate is almost equal to 1, while the backward wave tuning rate is close to zero, meaning that pump wavelength variation are almost entirely imprinted on the forward wave.

Table 1.

BWOPO tuning rates with respect to pump wavelength tuning, calculated by first-order expansion of the phase matching condition. ωp, f, b and νp, f, b designate the angular frequencies and group velocities for the pump, forward, and backward waves, respectively.

2.3

Threshold and efficiency

Since there is no feedback assistance from a cavity resonator, one experimental challenge is to reach BWOPO threshold with pump intensities significantly smaller than the optical damage threshold at the crystal interfaces. The theoretical expression for the BWOPO threshold intensity in CW regime (assuming plane wave interaction) is given by the following expression²⁵:

Where ∊₀ is vacuum permittivity, c the speed of light, d_eff the effective nonlinear coefficient of the crystal, L the grating length, n_{p, f, b} the refractive indices of pump, forward and backward waves, and λ_{f, b} the forward and backward wavelengths. With the parameters from Figure 1, the CW threshold intensity corresponding to the experimental cases exposed in part 3 are approximately 85 MW/cm² and 15 MW/cm² for the 7 mm and 17 mm PPKTP crystal, respectively, assuming a nonlinear coefficient of d_eff = 7 pm/V. As illustrated by these numbers, the fabrication of long nonlinear crystals with a homogenous grating periodicity, which is highly challenging for sub-μm periods, is the key to achieving a BWOPO configuration with manageable pump intensities.

In the pulsed regime, the oscillation threshold peak intensity is higher than the CW theoretical threshold due to the parametric oscillation build-up time. This is all the more pronounced when the pump pulse duration is short i.e. comparable to the pump travelling time in the nonlinear crystal τ = L/v_g (with v_g the pump group velocity, and L the crystal length). However, for pulse durations significantly longer than this travelling time, the CW calculation gives a valid order of magnitude of the threshold intensity. This is for example the case in reference²³, where the nonlinear travelling time is approximately 44 ps (with a 7 mm long PPKTP), and the pump pulse duration 13 ns. This is also the case in our present experimental configuration where the travelling time are 44 ps and 106 ps (7 mm and 17 mm length PPKTP respectively) and the pump pulse duration is 15 ns. As illustrated later in part 3.2, the experimental threshold intensities were estimated to be ~ 100 MW/cm² and ~ 20 MW/cm², in line with the estimation from equation (3). We refer the readers to the theoretical study published in²⁵ for a full detailed and complete description of BWOPO in pulsed regime, where analytical formulas are derived to take into account the OPO build-up time influence on threshold and conversion efficiency.

One other attractive aspect of BWOPO is that the parametric conversion efficiency presents a monotonic growth without the occurrence of the detrimental back conversion effects that are observed in co-propagating OPO for high pumping intensities. This relates to the fact that counter propagating signal and idler waves impose maximum intensities for both waves to be reached at the opposite ends of the nonlinear crystal^21,25. In CW plane wave approximation theory, the conversion efficiency can even get close to 100 % provided sufficient pump intensity. In practical experiments, although the conversion efficiency is reduced because of transverse phase and intensity inhomogeneity plus OPO build-up time, high conversion efficiencies superior to 50 % as well as high energy extraction > 1 mJ in both signal and idler beams have been demonstrated in the nanosecond regime²³.

3.1

Pump laser

In order to pump and tune the BWOPO into the mid-infrared, we used a high power frequency agile Ytterbium MOPA that has been previously developed for tunable OPA experiments¹⁸. This laser source consists in a hybrid combination of fiber & bulk amplifiers respectively pumped at 976 nm and 940 nm. The general MOPA properties are summarized in the Figure 2 below. This configuration enables to produce a high power laser beam (3.5 mJ, 15 ns pulses at 5 kHz), with a very good beam quality (M²<1.2), while directly benefiting from the spectral agility of the CW seed laser with a continuous 10 GHz fast frequency tuning through piezoelectric modulation. These properties are well in line with the requirements to reach the BWOPOs oscillation threshold, and to produce a narrowband tunable forward signal wave. As illustrated in Figure 2, this pump laser is currently a laboratory experimental bench, and characteristics such as pulse duration could be adjusted for future parametric studies.

Figure 2:

General architecture and characteristics of the Ytterbium MOPA pump laser (a), and overview of the experimental implementation of a fiber amplification stage and a bulk amplifier stage (b). We refer the reader to paper¹⁸ for a detailed description and characterization of the set-up. SBS stands for Stimulated Brillouin Scattering.

3.2

BWOPO characterization

The pump laser beam is shaped in order to reach the hundreds of MW/cm² required to reach and exceed the BWOPO oscillation threshold. It was focused on 140 μm radius (1/e²). Two PPKTP crystals of 7 mm and 17 mm length, with a 580 nm poling period were tested. The crystals are placed on a thermalized plate stabilized at slightly above ambient temperature at 27°C. The generated 1981 nm forward wave and the 2145 nm backward wave were separated from the pump beam with dichroic mirrors and characterized in power and central wavelength (Figure 3). All three beams were characterized with high finesse wavemeters; the pump beam with a WSU 10 ultimate, the forward wave with a WS/6 IR2, and the backward wave with a WS/6 IR3, all with frequency resolutions better than 100 MHz.

Figure 3:

Experimental set-up schematic (a), and laboratory implementation (b) of the BWOPO

The pump tuning of the BWOPO is consistent with what is theoretically expected from the tuning rates in Table 1. As illustrated in Figure 4, when the pump wavelength is continuously tuned over a 10 GHz span, the BWOPO forward frequency follows proportionally with a ratio close to 1, while the backward idler frequency shift (theoretically within a few MHz) remains undetected below the wavemeter resolution. BWOPO thus acts as a direct frequency shift translator in the mid-infrared. This is a useful property for remote gas sensing applications such as spaceborne IPDA lidar, where fast ON and OFF absorption line wavelength tuning over several GHz is required. For instance, in the present work our wavelength modulation rate is limited to ~0.1 Hz by the measurement integration time on the backward beam wavelength-meter. In a future work spectral characterizations through beat note analysis with an ancillary CW laser would give access to higher sensitivity and speed measurement up to pulse to pulse (at a 5 kHz repetition rate) frequency and linewidth characterizations of the BWOPO.

Figure 4:

Experimental pump wavelength tuning with a progressive increasing optical frequency excursion over 10 GHz (a), corresponding BWOPO frequency tuning for the forward (b) and backward (c) waves.

Finally, Figure 5 gives the output power characteristics for both 7 mm and 17 mm nonlinear crystals. The oscillation threshold is 370 μJ and 70 μJ for the short and long crystal respectively, corresponding approximately to 100 MW/cm² and 20 MW/cm² intensities. The pulse duration of the parametric waves was about 12 ns. In the current experiment up to 0.60 mJ of forward signal wave and 0.36 mJ of backward idler wave could be extracted from the 7 mm crystal and 1.9 mJ of pump energy input. This corresponds to an optical conversion efficiency of approximately 50 %. As introduced in part 2.3, the conversion efficiency follows a monotonic trend even for high pumping rates as illustrated in Figure 5(b) in the 17 mm crystal case, where total conversion efficiency reaches ~70 % around 10 times above the threshold. These power and efficiency characteristics are comparable with what may be obtained in high power copropagating OPOs based on similar nonlinear crystals, but with a much simpler arrangement and very limited detrimental backconversion effects that tend to degrade the beam and spectral quality in conventional OPOs.

Figure 5:

Power characteristics, with the total forward + backward extracted energy from the BWOPO respect with pump energy (a), and the corresponding total optical to optical conversion efficiency (b) for two different PPKTP crystal lengths. The inset in (a) is an intensity profile of the 1981 nm forward beam.