The idea of the mirrorless optical parametric oscillator (MOPO), where a pump beam is down-converted into counter-propagating signal and idler waves, was first suggested in 1966 [1]. The counter-propagating geometry of the second-order nonlinear interaction provides unique spectral, tuning, and coherence properties to the parametric waves [2,3] and ensures efficient frequency conversion through the distributed nonlinear feedback mechanism, without an external optical cavity. These unique properties make the MOPO a remarkably simple single-pass source of parametric waves with high temporal coherence and low sensitivity to variations in temperature or excitation geometry, in contrast to conventional optical parametric oscillators (OPOs), where more complex designs and special optical components must be involved in order to achieve similar features [4]. Thus, in combination with well-established single-frequency nanosecond pump lasers operating at 1 μm, the MOPO can potentially provide mJ-level transform-limited pulses in the 1.5–3.4 μm spectral region. This would be of great interest for applications where spectral purity, efficiency, and robustness of the optical arrangements are of key importance, including remote sensing, airborne and space-based LIDAR, spectroscopy, and quantum communication.

For the MOPO, the large momentum mismatch between the counter-propagating photons would demand an extraordinarily large material birefringence, which places the quasi-phase matching (QPM) approach as the only viable alternative to achieve phase matching in this spectral region [5]. The QPM condition for a counter-propagating-idler MOPO reads:

${\mathrm{KTiOPO}}_4$ (KTP) isomorphs have so far been the best candidates for fabrication of sub-μm QPM structures through periodic poling due to their quasi-one-dimensional crystal structure and large anisotropy in the ferroelectric domain propagation [6]. Bulk Rb-doped KTP (RKTP), with less than 1% of ${\mathrm{K}}^{+}$ ions replaced by ${\mathrm{Rb}}^{+}$, presents two orders of magnitude lower ionic conductivity than regular flux grown KTP, which is beneficial for fabrication of fine-pitch QPM gratings [7]. Moreover, the low dopant concentration warrants the same linear and nonlinear optical properties as those of undoped KTP, making this material an excellent choice for MOPO implementation. Indeed, a highly efficient MOPO with relatively broadband picosecond pulses was recently demonstrated based on sub-μm periodically poled RKTP (PPRKTP) [8]. A high-efficiency MOPO operating in the nanosecond-pulse regime, well below the optical damage threshold, requires a long sub-μm period QPM structure, while output energy scaling to mJ level mandates a homogeneous structure with large aperture.

In this Letter, we demonstrate, to the best of our knowledge, the first MOPO realized with ns-pumping. High-quality QPM devices with sub-μm periodicity were implemented in RKTP via coercive-field engineering and periodic poling. The PPRKTP crystals were used as a MOPO, pumped by a narrowband, 10 ns, $Q$-switched laser operating at 1.064 μm, and demonstrated highly efficient mJ-level parametric output at 1.74 μm and 2.741 μm with an inherently narrow spectral width.

For our experiments, we have used commercial, flux-grown, $c$-cut RKTP samples with dimensions $11\mathrm{mm}\times 6\mathrm{mm}\times 1\mathrm{mm}$, along the $a$, $b$, and $c$ crystallographic axes, respectively. In order to achieve consistent periodic poling with sub-μm periodicity, we take advantage of a recently developed technique based on coercive-field engineering by local crystal composition control [9], providing precise control of the lateral domain growth. This allows poling with planar electrodes, which substantially reduces the domain broadening associated with the fringing fields from the periodic electrodes. First, an aluminum grating with a period of 755 nm was created on the $c^{-}$ faces of the crystals using photolithography with an in-house-built UV-laser interferometric setup, similar to that reported in Ref. [7]. Additionally a planar ion-diffusion stop-layer was created on the $c^{+}$ faces by oxygen plasma etching. The crystals were then placed in a molten nitrate salt bath containing 20% ${\mathrm{KNO}}_3$, 73% ${\mathrm{RbNO}}_3$, and 7% $\mathrm{Ba}{({\mathrm{NO}}_3)}_2$ for a duration of 4 h at a temperature of 330°C, inducing ion exchange through the metallic grating mask. The ion exchange resulted in a coercive-field increase of $\mathrm{\Delta }{E}_c\approx 1.5\mathrm{kV}/\mathrm{mm}$ in the ion-exchanged areas, compared to the non-exchanged regions. Thus, by appropriately choosing the electric-field magnitude, domain switching could be induced in the non-exchanged regions, while the ion-exchanged ones remain un-switched. After removing the Al-grating, the crystals were poled using 5-ms-long triangular electric-field pulses with a peak magnitude of $6.0\pm 0.3\mathrm{kV}/\mathrm{mm}$. The poling volume was approximately $7\mathrm{mm}\times 3\mathrm{mm}\times 1\mathrm{mm}$. Figure 1(a) shows the domain structure on the non-polar $b$face of one of the crystals imaged by piezoforce microscopy (PFM) at a depth of (a) 100 μm, and (b) 900 μm, from the patterned face. The duty cycle of the inverted domains is approximately 44% and remains constant over the whole crystal thickness.

 

Fig. 1. PFM images of the domain structure on the non-polar $b$ face of a representative PPRKTP crystal. The images have been scanned at (a) 100 μm, and (b) 900 μm below the patterned face, respectively.

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Next, we evaluated the performance of one of our samples as a MOPO device. Figure 2 depicts the experimental setup. The uncoated crystal was pumped by an injection-seeded, diode-pumped, single-longitudinal-mode, $Q$-switched Nd:YAG laser (Innolas GmbH) that provides 80-mJ, 10-ns-long, linearly polarized pulses at 1064.4 nm at a repetition rate of 100 Hz. The pump energy was controlled by a half-wave plate and polarizer arrangement. The pump beam was polarized along the crystal $c$ axis launched parallel to the crystal $a$ axis and confocally focused in the crystal with a ${\mathrm{CaF}}_2$ lens, to approximately 200 μm beam size (estimated with the knife-edge technique). The crystal temperature was kept at 22°C with a thermoelectric element. In this configuration, the PPRKTP crystal generated a signal at 1740.1 nm co-propagating with the pump, and a backward-propagating idler at 2741.4 nm. In order to characterize the performance of the MOPO, the signal and residual pump were separated by a dichroic mirror (99% transmission and reflection for the signal and pump, respectively), whereas the idler was separated from the pump path by a partially reflecting mirror (99% transmission for the pump, approx. 20% reflection for the idler) that was placed before the focusing lens.

 

Fig. 2. Schematic illustration of the experimental setup. HW, half-wave plate; POL, polarizer; PR, partially reflecting mirror for the idler wave; L, lens; DM, dichroic mirror.

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The MOPO threshold was reached at a pump energy of 0.76 mJ, corresponding to a threshold intensity of $660\mathrm{MW}/{\mathrm{cm}}^2$. The conversion efficiency and pump depletion versus pump energy are shown in Fig. 3(a). Here the pump depletion and the signal efficiency were obtained directly from the signal output and the incident and transmitted pump energies, whereas energy of the idler wave was calculated using the Manley–Rowe relations.

 

Fig. 3. (a) MOPO conversion efficiency and pump depletion as a function of pump energy. (b) MOPO signal-conversion efficiency distribution across the optical aperture of the PPRKTP crystal.

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At a pump energy of 6.75 mJ, the signal energy reached 1.95 mJ, corresponding to the signal energy conversion efficiency of 29%, while the combined signal-and-idler energy conversion efficiency was 47%. The maximum pump energy was chosen below the expected laser-induced damage threshold of $10\mathrm{J}/{\mathrm{cm}}^2$ for RKTP [10].

It should be noted that for MOPOs the efficiency does not exhibit saturation or roll-off, which typically happens in ordinary OPOs with co-propagating interactions, caused by back-conversion of the signal and idler to the pump. Owing to the spatial separation of the signal and idler peak intensities, the back-conversion process is very inefficient for MOPOs [11].

In order to evaluate the homogeneity of the QPM grating over the optical aperture, the crystal was scanned in steps of 300 μm in the two directions ($b$ and $c$) perpendicular to the pump beam, while the signal energy was recorded and the pump energy was kept constant at two times above threshold. The normalized conversion-efficiency distribution over the crystal aperture is shown in Fig. 3(b). Note that the drop in efficiency at the edges in the $b$ direction is due to the fact that part of the pump beam propagates outside the periodically poled region. As can be seen, the grating is quite uniform across the $1\mathrm{mm}\times 1\mathrm{mm}$ central section of the scanned area, with a standard deviation for the signal efficiency of only 0.12. The calculated $d_{\text{eff}}$ for our crystals was 9. 77 pm/V [8], which is close to the expected theoretical value of 10.7 pm/V [12]. Thus, taking into account the high quality of our QPM device, it would be possible to increase the signal and idler energies by about two times by using a larger beam and exploiting the full aperture of the QPM structure.

One of the striking features of MOPO is the narrow spectral width or high spectral brightness. Figure 4 shows the spectra of (a) the pump, (b) the co-propagating signal, and (c) counter-propagating idler waves.

 

Fig. 4. Measured spectra of (a) the pump, (b) forward-propagating signal, and (c) backward-propagating idler waves.

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The pump and signal spectra were measured with a resolution of 0.05 nm using an ANDO (AQ6315A) optical spectrum analyzer (OSA), whereas the idler was recorded with a resolution of 0.1 nm using a spectrometer with mid-IR sensitivity (Yokogawa AQ6376). The measured bandwidths of the signal and idler waves were 14.4 GHz and 16 GHz, respectively. Note that both the parametric waves present narrow bandwidth. For comparison, one could consider conventional co-propagating parametric down-conversion in the same spectral region with PPRKTP. This would give a full width at half-maximum (FWHM) parametric gain bandwidth of about 4.8 THz in 7-mm-long crystal with a period of 37.9 μm, i.e., approximately a 300-times broader spectrum [13].

Indeed, it is the counter-propagating nature of the interaction that gives the MOPO its unique spectral features. For a MOPO, the phase modulation of the pump is mainly transferred to the forward wave, meaning that the forward wave is a spectrally shifted replica of the pump, while the phase of the backward wave remains essentially constant [3]. Thus, it is expected that the spectral width of the signal wave should be transform limited for a single-longitudinal-mode pump, while the bandwidth of the idler would be automatically transform limited, thanks to the counter-propagating geometry. Signal and idler pulse lengths of 6.7 ns were measured with a fast photoelectromagnetic detector (PEM-10.6, VIGO System) at pump power two times above threshold. The signal and idler spectra were in fact somewhat broader than the transform limit. We attribute this broadening to slightly noncollinear pumping as a result of the non-ideal pump beam intensity profile [2].

The transverse intensity profiles of the undepleted pump, signal, and idler beams were characterized with a pyroelectric array camera (Spiricon Pyrocam III). The beam profiles of the parametric waves were recorded at a pump energy two times above the MOPO threshold, while the residual pump light was removed using a long-pass filter with the cutoff wavelength at 1.5 μm. As shown in Fig. 5, the pump beam is astigmatic and contains two high-intensity regions as a result of the thermal lensing properties in the Nd:YAG amplifier. The separation between the areas is about 2.6 mm at the position of the focusing lens. In the crystal, placed in the focus of the lens, the maximum noncollinear angle would be about 0.4 deg, sufficiently large to increase the signal and idler spectral bandwidth to the values observed in the experiment [2]. This shows that in order to obtain transform-limited spectra for a nanosecond MOPO, the device must be pumped with a well-collimated ${\mathrm{TEM}}_{00}$ pump beam. Regardless of the somewhat poor intensity profile of the pump beam, the signal and idler beams had significantly better mode profiles. Indeed, it is expected that the signal and idler self-establish strictly counter-propagating oscillation even for noncollinear pumping, due to the MOPO characteristics [2]. Moreover, as discussed before, the suppression of the back-conversion cascading process in MOPO should also prevent deterioration of the signal and idler beam quality.

 

Fig. 5. Far-field intensity profiles of (a) incident pump, (b) signal, and (c) idler beams at a pump energy two times above the MOPO threshold.

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In conclusion, we have demonstrated, to the best of our knowledge, the first nanosecond-pumped MOPO. It consisted of a 10-ns, 100-Hz, 1064-nm, single-frequency pump laser and a PPRKTP crystal with a poling period of 755 nm. A maximum signal energy of 1.95 mJ was achieved at a pump energy of 6.75 mJ, corresponding to the combined signal-and-idler conversion efficiency of 47%. It should be stressed that the MOPO operation was possible due only to the high quality of the QPM grating throughout the full 7-mm length. This gave a sufficiently large margin for reaching the counter-propagating parametric oscillation threshold and safe operation well below the optical damage threshold. Increasing the length of the QPM structure to 10 mm would decrease the MOPO threshold by two times. The strong suppression of back-conversion and absence of any competing parasitic processes in the MOPO allow reaching high efficiencies and maintaining good beam quality. The spectral width of the generated parametric waves is indeed orders of magnitude narrower than what would be obtained from a co-propagating OPO. However, in order to generate fully transform-limited nanosecond pulses, the MOPO should be pumped with a well-collimated fundamental transverse mode beam. Note that single-mode pumping is required to obtain the narrowest bandwidth. However, MOPO can efficiently convert when it is pumped with a multimode and spectrally broad pump [8].

The high conversion efficiency and favorable spectral properties make this device an attractive single-pass source for generating near- and mid-infrared transform-limited mJ-level pulses in a very simple, compact, and robust arrangement.