1. Introduction

Optical parametric coherent light sources delivering narrowband, tunable radiation in near and mid-infrared are extremely useful in LIDARs, ranging, and remote sensing. LIDARs for remote sensing of small molecules, e.g., those comprising greenhouse gases, require transform limited nanosecond pulses with energies of several mJ [1]. These requirements can be satisfied by a master-oscillator power amplifier (MOPA) system consisting of an optical parametric oscillator (OPO) seeding an optical parametric amplifier (OPA). For narrowband seeder OPOs, especially those operating close to degeneracy, it is beneficial to use a type-II doubly resonant OPO configuration with separate resonators for the signal and idler in order to achieve Vernier tuning [2]. Quasi-phase-matched (QPM) crystals offer wavelength flexibility, noncritical interactions, and high nonlinearities, which are critical for realizing efficient high-energy nanosecond OPA stages [3]. Doubly resonant nanosecond OPOs are low threshold oscillators [4] and, by nature, are highly sensitive to feedback, as well as the phase of the pump [5–7]. Nevertheless, when carefully designed and properly stabilized, they can produce µJ-level transform-limited nanosecond pulses when pumped with single longitudinal mode lasers [8]. For scaling the output energy, as required in remote sensing LIDARs, at least two amplification stages are needed. These OPA stages are commonly pumped by high-energy Q-switched Nd:YAG lasers utilizing unstable cavity design [9,10] that typically have a non-Gaussian radiation mode profile [11,12]. Moreover, such multi-transversal mode OPO pumping would lead to strong spectral broadening and a decrease in spatial coherence associated with noncollinear parametric interactions [13,14].

The backward-wave optical parametric oscillator (BWOPO) [15,16] is an oscillator where the positive feedback for oscillation is established by a counter-propagating geometry of second-order interaction without needing an external cavity. A BWOPO requires a QPM structure with sub-wavelength periodicity to compensate for the substantial momentum mismatch in the counter-propagating nonlinear interaction. The most remarkable property of the BWOPO geometry is the generation of the narrowband backward wave, even for broadband pumping [17,18]. We have shown that a BWOPO realized with periodically poled Rb:KTiOPO₄ (PPRKTP) has a low oscillation threshold in the nanosecond pulse regime, allowing high-efficiency generation of mJ-level narrowband pulses [19]. PPRKTP has a large optical damage threshold in the near-infrared [20] and a large nonlinear coefficient. The crystal structure is beneficial for fabricating high-aspect-ratio domain structures throughout the bulk [21]. These properties are prerequisites for realizing efficient nanosecond BWOPO with mJ-level energy output. Recently, Godard et al. [22] published the theoretical aspects of the threshold and subthreshold linewidth of the BWOPO. Plane-wave theory predicts strong spectral narrowing of the BWOPO backward wave when the pump intensity approaches the oscillation threshold. The analysis indicates the backward wave for nanosecond BWOPO should be close to transform-limited.

In this work, we experimentally determine the bandwidth of the backward wave for a BWOPO pumped by a nanosecond, single-longitudinal, but multi-transversal mode (M² > 4) high-energy laser at 1064 nm. The laser is of the type that is often used in LIDARs for remote sensing. At 2.5 times above threshold, the BWOPO generated about 1 mJ parametric output with the backward-generated signal at 1855nm and the forward-generated idler at 2495 nm. Although pumped with close to transform-limited pump pulses (time-bandwidth product of 0.63), the BWOPO backward wave experiences spectral broadening to a time-bandwidth product of 1.73. The spectral broadening is attributed to the contributions of the noncollinear BWOPO modes, which arise from the nonlinear interaction of the multimode beams. Note that the effect of noncollinearity in BWOPO is much smaller than in nanosecond PPRKTP OPOs employing co-propagating nonlinear interactions in the same spectral region. The BWOPO temperature tuning is also an order of magnitude smaller than that in regular OPOs, allowing for precise tuning of the generated narrowband backward wave with a tuning rate of 2.48 GHz/K. Finally, the BWOPO backward signal wave was used as a seed in a single-stage PPRKTP OPA to generate 20 mJ narrowband pulses.

2. Experimental results

The BWOPO was realized using a PPRKTP crystal with a QPM periodicity of 500 nm. It was designed to generate a backward signal at 1855nm and a forward idler at 2495 nm when pumped at 1064 nm employing type-0 phase matching. The 7 mm long BWOPO sample had an optical aperture of 3 × 1 mm² along the y- and z-crystal axes, respectively. The crystal was fabricated using deep-UV interferometric laser lithography and electric field poling [23]. The BWOPO characterization arrangement is shown in Fig. 1. The pump laser for all the measurements was a single-longitudinal mode, injection seeded, 100 Hz, 10.5 ns, Q-switched diode-pumped Nd:YAG laser power amplifier system (InnoLas Spitlight) operating at 1064 nm with a maximum output energy of 110 mJ. The laser was designed as an unstable cavity oscillator with a Gaussian reflectivity profile output coupler. The pump beam passed through an arrangement of half-wave plates and two polarizing beam splitters. This way the pump energy was divided between the OPA and the BWOPO. The largest part of the pump energy passed through the beamsplitter and was used for OPA pumping. A small portion of the pump was routed to a Fabry-Perot interferometer (FPI, Toptica, FSR 1 GHz, Finesse 500) for bandwidth measurements. The same FPI was used for the BWOPO backward signal bandwidth characterization. The 1855nm backward wave was collected using a dichroic mirror, and a long pass (LP) filter removed reflected pump radiation. It was then frequency-doubled to 927 nm, and residual 1855nm radiation was filtered out prior to the FPI. The frequency doubling was done in a 5 mm BBO crystal (ϕ=90°, θ=20.4°). Lower-resolution spectral measurements of the pump and BWOPO waves were done using optical spectrum analyzers (OSA, ANDO AQ-6315A and Yokogawa AQ6374, respectively).

 

Fig. 1. Setup for linewidth measurement. A diode-pumped solid-state (DPSS) Q-switched Nd:YAG Laser system (Innolas Spitlight) is the pump of the BWOPO. Inset shows pump and BWOPO intensity profiles. Spatial filters (pinholes) were used to mode-match to the FPI. Positions of power measurements are indicated with arrows for the pump and signal, dotted lines indicate image positions. The power meter is moved in and out of the beam path for the pump power measurements.

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We measured the M² factor of the pump at the position of the BWOPO crystal with a beam profiler (Thorlabs M2MS). Due to thermal lensing in the pump laser system, the beam had rather different M² along the BWOPO crystal axes: along y-axis, $M_y^2 = 6.1$, and along z-axis $M_z^2 = 2.8$. In order to achieve similar pump diffraction angles in both directions, we used an astigmatic focusing arrangement (not shown in Fig. 1). The inset shows the BWOPO beam close to focus in the M² measurements, and the pump as measured before focusing. The pump beam waist radii in the BWOPO crystal were 150 µm and 415 µm along the crystal z- and y-axis, respectively.

The BWOPO reached the oscillation threshold at 1.8 mJ pump energy, as shown in Fig. 2. The positions of the output measurement can be seen in Fig. 1. At the pump energy of 4.7 mJ, the forward idler energy reached 0.54 mJ (1.27 mJ combined signal + idler energy, red data points in Fig. 2). On the one hand, this corresponds well to the measured depleted pump when calculating the backward signal energy from the Manley-Rowe condition (red data points in Fig. 2). On the other hand, when adding the actual measurements of the signal to those of the measured forward idler, the total energy is lower than the measured pump depletion (yellow data points in Fig. 2). We attribute this discrepancy in the measured signal power to the water vapor absorption in air and the loss at the dichroic mirror [24].

 

Fig. 2. Measured depleted pump energy (blue circles); the sum of the measured BWOPO idler energy and the calculated signal from Manley-Rowe relations (red circles); The sum of the measured signal and the measured idler energies (yellow circles) as a function of the incident pump.

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The spectrum of the backward wave for a BWOPO is essentially insensitive (-10⁻³Hz/Hz) to any spectral changes in the pump as it translates almost completely to the forward wave (1.001 Hz/Hz) [16]. In order to demonstrate the BWOPO forward wave tuning, we varied the wavelength of the Yb:fiber DFB laser, which was seeding the pump laser system. The pump could be tuned by a maximum of about 7 GHz without losing its single-longitudinal mode lock. The OSA measurements are shown in Fig. 3. The BWOPO forward idler tuned by a very similar frequency range with the accuracy of the measurement being limited by the resolution of the spectrometers. The change in the backward signal wavelength was below the resolution limit of the OSA or FPI.

 

Fig. 3. Measurement of pump tuning (a) by changing the seed wavelength and corresponding change in the BWOPO forward idler (b).

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For the FPI measurements we alternated between the pump and the frequency-doubled BWOPO signal beams. The average linewidths were obtained from 50 FPI scans using a single Gaussian fit. The Fabry-Perot spectral measurements of the frequency-doubled BWOPO signal are shown in Fig. 4(a). A broadband photoelectromagnetic detector (Vigo) with <1 ns response time was used for the temporal trace measurements, see Fig. 4(b). The measurements were done at the maximum pump energy of 4.7 mJ. The pump and BWOPO had pulse lengths of 10.5 ns and 6.3 ns (FWHM), respectively. The pump bandwidth was measured to 60 MHz, giving the time-bandwidth product of 0.63. The trace of the BWOPO frequency-doubled signal had a FWHM of about 4.5 ns. Numerical simulations using SNLO software show that the second harmonic spectral width should be 1.5 times broader than the fundamental signal spectrum. Taking that into account, we deduce the BWOPO signal spectral width of 274 MHz. That gives a time-bandwidth product for the BWOPO signal of 1.73, about 2.7 times broader than expected for transform-limited pulses. Due to energy conservation, and since the broadening comes from non-collinearity, the forward idler wave should have similar spectral width as the backward signal.

 

Fig. 4. (a) Linewidth measurement of the 927.5 nm frequency-doubled backward wave. The linewidth, 274 MHz (FWHM), at 1855nm, is 1.5 times smaller than measured at 927.5 nm (b) Temporal measurements of the Idler, Signal, Pump, and SHG of the Signal.

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This small broadening can be attributed to noncollinear counter-propagating interactions that are enabled due to the imperfect spatial coherence of the pump. It was instructive to measure the M² values in the y- and z-directions of the BWOPO backward signal. Contrary to the pump, which was astigmatic, the BWOPO signal was, within the measurement accuracy, a radially symmetric (see Fig. 1), with M² = 4.9 along the crystal y- and z-axes, respectively. Such a beam, with reduced spatial coherence, can be looked upon as a sum of contributions of separate BWOPO channels propagating at slightly different angles. This noncollinearity is determined by the small divergence of the pump beam in the PPRKTP structure. The divergence in the near field was estimated to be 0.66-0.82 mrad. Using the expression from [25] with a small noncollinear angle approximation leads to spectral broadening in the 216-333 MHz range for the BWOPO used in this work. One might suspect that imperfections of the QPM structure could also cause the observed spectral broadening. In our sub-µm PPRKTP the periodicity is established interferometrically. Therefore, the main error is in duty cycle variations. However, it has been shown [26] that this type of error does not lead to spectral broadening, and only affects the effective nonlinearity of the structure.

Smooth, precise, and continuous tuning of the BWOPO wavelength is possible by controlling the temperature of the nonlinear crystal. The BWOPO sample rested on a temperature-controlled copper block in our experiments. Figure 5(a) shows the resulting wavelength tuning as a function of temperature in range between 15 and 60 °C. The equation for tuning of the BWOPO backward-wave frequency is:

 

Fig. 5. (a) Spectra of the backward wave from the BWOPO at different temperatures. (b) Comparison of temperature tuning of the OPO (black lines, right vertical axis) and the BWOPO (red lines, left vertical axis). Data points: BWOPO measurement data. Dotted lines:calculations without (α=0) thermal expansion.

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Here n is the refractive index, c is the speed of light in vacuum, Λ is the QPM period, and α is the thermal expansion coefficient. The subscripts p, f, b, refer to the pump, the forward and the backward waves, respectively. As there are no longitudinal cavity modes, the BWOPO tuning is continuous with temperature, and its tuning is ${{\partial {\nu _b}} / {\partial T}} ={-} 2.48$ GHz/K. The measurements fit very well by using the refractive index data from Fradkin [27], thermo-optic coefficients from Emanueli [28], and thermal expansion coefficient from Pignatiello [29].

In Fig. 5(b), we compare the temperature tuning of the BWOPO (Eq. (1)) with a co-propagating PPRKTP OPO pumped at 1064 nm and operating in the same spectral range. Here the PPKTP grating periodicity is $38.5\; \mathrm{\mu}\textrm{m}$, and we disregard cavity mode-hoping in the OPO. The BWOPO, which is intrinsically mode-hop free, tunes one order of magnitude slower with temperature than the OPO. That is beneficial for the overall wavelength stability of the BWOPO and gives a useful precise tuning method, as required in spectroscopic applications.

The short QPM period required for momentum conservation in counter-propagating interactions strongly increases the role of thermal expansion to the overall wavelength tuning. We calculate Eq.1 with (solid lines, $\mathrm{\alpha } = 7 \cdot {10^{ - 6}}$) and without (dotted lines, $\mathrm{\alpha } = 0$) thermal expansion in Fig. 5 (b). For a BWOPO QPM grating period of 500 nm, the thermal expansion (the last term in Eq.1) is responsible for about 46% of the overall frequency tuning. This contrasts the co-propagating processes, where the thermal change of the QPM period has considerably less impact (∼10%), and the thermo-optic effect plays a larger role.

Finally, the BWOPO backward signal was used as a seed for the OPA which was pumped with the remaining pump laser energy of 105 mJ. The single-stage OPA was realized using three consecutive uncoated PPRKTP samples with 12 mm long gratings with a QPM period of 38.5 µm and an aperture of 5 × 5 mm² [30]. Here single stage means that there was no refocusing, or rejection of beams in the OPA. The OPA was seeded with 0.21 mJ of the BWOPO signal temporally and spatially overlapped with the pump. A maximum of 20 mJ (2W of average power) of the signal and idler was generated (see Fig. 6(a)). That consisted of 11.5 mJ of signal and 8.5 mJ of idler at 1855nm and 2495 nm, respectively. The OPA signal spectrum is shown in Fig. 6(b). The OPA gain bandwidth without changing the OPA crystal temperature was about 900 GHz, so it can readily accommodate the BWOPO tuning range. The non-seeded parametric wavelength adjusts to match the seed wavelength as the BWOPO temperature changes.

 

Fig. 6. (a) The seeded OPA energy measured as a function of pump energy. (b) output spectrum for the seeded OPA.

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3. Conclusions

It is known that the fundamental properties of momentum conservation in the counter-propagating interactions, that are necessary for positive feedback and self-established oscillation in a BWOPO structure, make the backward-generated wave narrowband. The plane wave picture suggests that transform-limited nanosecond pulse pumping would result in a transform-limited backward wave. We here show that with multi-transversal mode pumping the noncollinearity can introduce weak coupling between spatial and temporal degrees of freedom, that leads to spectral broadening. In particular, we demonstrated that a nanosecond pumped BWOPO backward wave resulted in a bandwidth of 274 MHz at 1855nm for a 1064 nm pump with 60 MHz linewidth. That is about 2.7 times broader than what could be expected for transform-limited pulses. The bandwidth of the BWOPO forward idler at 2495 nm should be the same as that of the backward signal, based on the energy conservation condition. It can be expected that a pump source with higher spatial coherence (M²≈1) and transform-limited pulses would result in a transform-limited BWOPO bandwidth. The BWOPO generated mJ-level output that is beneficial for seeding an OPA, reducing the number of required amplification stages. We used the backward signal to seed a single-stage PPRKTP OPA, and generated a combined signal and idler output of 20 mJ. The slow temperature tuning of the BWOPO signal (and idler) (2.48 GHz/K), makes the BWOPO much easier to stabilize than the standard narrowband OPO, and the crystal temperature can for example be used for precisely targeting specific absorption lines. With minor modification in the QPM-grating period, our system could be used to measure greenhouse and atmospheric gases, e.g., CH₄, CO₂, H₂O, and DHO at 2280.90 nm, 1982.78 nm, 1982.45 nm, and 2051nm, respectively [1]. Implementation of the cavity-free BWOPO in systems for ranging, LIDAR and remote sensing could improve the ease of handling, streamline the design, and reduce susceptibility to vibrations - making them attractive for mobile systems such as, air- or space-borne application.