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We demonstrate with simulations and experiments that an optical parametric oscillator using two different crystals with orthogonal walk-off planes can generate a symmetric, high-quality beam even if the resonator has a high Fresnel number. In the experiments we used KTA and BBO crystals to convert 5 ns pulses at 1.06 μm to 1.7 μm pulses with more than 10 mJ energy and beam quality M2 ≈2.
©2010 Optical Society of America
1. Introduction
Designing an optical parametric oscillator (OPO) with both high energy and beam quality leads to conflicting demands. First, high energy operation implies that the beams must be wide in order to avoid optical damage. Second, the nanosecond pump pulses available from high energy, Q-switched lasers require a short resonator to allow rapid signal buildup for efficient conversion. However, a short resonator with wide beams has high Fresnel number and poor suppression of higher-order transverse modes. This leads to poor beam quality unless a method can be found to restrict the divergence of the generated beams.
Walk-off is normally considered a detrimental process in nonlinear crystals because it reduces the overlap between the beams. However, walk-off between the signal and idler beams increases the spatial coherence, and hence the beam quality, in the walk-off plane. The angular acceptance interval for two interacting beams of orthogonal polarization is inversely proportional to the walk-off distance [1]. In collinear, critically type 2 phase matched OPO’s, the beam quality therefore tends to be asymmetric since the angular acceptance interval of the nonlinear interaction is very different in the critical and noncritical direction [2].
Several approaches to reduce the asymmetry exist, for example using a prism reflector to flip higher-order beam components out of the noncritical plane [3,4], intracavity image rotation [2,5], or employing a confocal unstable resonator [2,6].
2. OPO with orthogonal critical planes
Our approach to attain a symmetric, high-quality beam in an OPO with large Fresnel number is to employ two different nonlinear crystals with orthogonal critical planes. Both crystals are critically, type 2 phase matched, so that either the signal or the idler beam has walk-off. The polarization of the pump does not matter in principle, but to avoid the need for waveplates it is important that each beam can have the same polarization direction in both crystals. Because the pump must always have the fast polarization (for phase matching in crystals with normal dispersion), one crystal must have walk-off for the slow polarization (e.g. positive uniaxial crystal) and the other must have walk-off for the fast polarization (e.g. negative uniaxial crystal). Biaxial crystals can of course also be used; the important point is only to have walk-off for the slow polarization in one crystal and for the fast polarization in the other. The proposed OPO configuration is shown in Fig. 1 .
Fig. 1 Sketch of directions of polarization in the OPO with orthogonal critical planes for collinear type 2 phase matching. The walk-off direction in crystal 1 is perpendicular to the walk-off direction in crystal 2. This leads to increased beam quality for the beams generated in a resonator containing both crystal types compared to a resonator with only one type of crystal.
This design has the advantages that it requires mirrors and crystals only, and it allows for simple angle tuning of the crystals. Although walk-off is essential for limiting the angular acceptance interval, a walk-off distance comparable to the beam width can also reduce the gain severely. The optimal walk-off distance is a compromise between beam quality and efficiency, and it depends on beam width and gain. In some cases, a single, long crystal of each type may be optimal, in other cases walk-off compensating pairs. The two types of crystals will in general have different walk-off angles and nonlinear coupling coefficients. Both these parameters must be taken into account to find a length ratio that leads to a symmetric beam.
A similar configuration was proposed in [2], however, the OPO was based on two equal crystals separated by a retarder plate which rotates the polarizations (but not the field intensity pattern) of all beams by π/2.
3. Simulations
In order to study the effects of orthogonal critical planes, an OPO was first simulated with parameters which were not restricted to those of existing crystals. We assumed two materials which differed only in the direction of walk-off and had otherwise identical parameters. A simulation model accounting for all relevant effects [7,8] was used, and the pump beam was modeled as a 6th order super-Gaussian single-longitudinal-mode (SLM) beam, corresponding to M2 ≈1.3.
We simulated a single-pass pumped, singly resonant, linear OPO containing four crystals. The first and second crystal pairs correspond to crystal 1 and 2 in Fig. 1, and each of the crystal pairs is configured for walk-off compensation, which suppresses beam tilt and angular dispersion [9]. The parameters for the simulated OPO are listed in Table 1 .
Table 1. OPO parameters used in the simulations.
Two configurations were simulated and compared: crystal pairs with either parallel or orthogonal walk-off planes. The energy and beam quality as functions of pump energy are shown in Fig. 2 .
Fig. 2 Energy (open circles) and beam quality in both directions (diamonds and crosses) for the OPO containing crystal pairs with parallel (red) and orthogonal critical planes (black).
The threshold and signal output energy are approximately the same for both configurations. The OPO with orthogonal critical planes generates an almost symmetric beam, in contrast to the OPO with parallel critical planes.
The walk-off distance through one of the crystals used in the simulations was only 0.2 mm, corresponding to 7% of the beam diameter. A greater walk-off distance leads to improved beam quality by reducing the acceptance angle. This effect was studied by varying the walk-off angle in the simulations, while the other parameters were chosen to keep the nonlinear coupling constant. Figure 3 shows the calculated pulse energy and beam quality as functions of walk-off distance relative to the beam diameter for an OPO with orthogonal walk-off planes.
Fig. 3 Simulated performance of the OPO with orthogonal critical planes as function of the walk-off distance relative to the beam diameter. The pump energy was 70 mJ.
We notice that the walk-off distance relative to the beam size has significant effect on the beam quality. Therefore, in an actual experiment, it is important to choose crystal type and length to get a suitable walk-off distance compared to the beam size.
The crystals in our experimental realization of the OPO have some idler absorption, which can reduce back conversion [10] and therefore affect the beam quality. In order to study the effects of orthogonal critical planes and idler absorption independently, we also simulated both OPO configurations with idler absorption 150 m−1. The results in Fig. 4 show that both idler absorption and orthogonal critical planes contribute to improved beam quality, and they work well in combination. The effect of idler absorption is investigated in detail in a separate paper [11].
Fig. 4 The effect of idler absorption at 70 mJ pump energy (3.5 times threshold) for the two OPO configurations. Near and far fields for parallel critical planes without idler absorption are shown in (a) and (e) respectively, whereas the same case including idler absorption at 150 m−1 are shown in (b) and (f). Near and far fields for orthogonal critical planes without idler absorption are shown in (c) and (g), whereas the orthogonal critical planes configuration including idler absorption at 150 m−1 are shown in (d) and (h).
4. Choice of crystals
Table 2 compares the most common nonlinear materials that can be used in an OPO for conversion from 1.064 µm to about 1.7 µm with type 2 critical phase matching.
Table 2. Materials for type 2 phase matched OPO for 1.06 μm to 1.7 μm conversion. S/F wo lists whether slow or fast beam has walk-off, U/B lists whether the material is uniaxial or biaxial, L∙Δθ2 is the product of crystal length and acceptance angle for the signal, and WO is the walk-off angle. The crystal data and acronyms for the crystal names are given in [12].
To have orthogonal walk-off directions, we need one crystal where the slow beam has walk-off and another crystal with walk-off for the fast beam. We note that while there are several good materials with walk-off for the slow beam, there are fewer and less obvious candidates with walk-off for the fast beam. BBO has high idler absorption, YCOB has low walk-off, and LNO has a small effective nonlinearity for type 2 phase matching. As discussed in the previous section, some idler absorption may in fact be advantageous for the OPO performance, so we chose to use BBO. The idler absorption varies rapidly with wavelength, so by tuning the OPO we can effectively adjust the absorption to a suitable value. We used a signal wavelength of 1.68 μm, corresponding to an idler wavelength around 2.9 μm and an approximate absorption of 250 m−1. We used KTA for the crystal with walk-off for the slow beam. It was chosen because of its higher nonlinearity, but it is likely that both KTP and BiBO would perform similarly.
5. Experiments
A sketch of the experimental setup including mirror specifications is given in Fig. 5 . The resonator is not perfectly singly resonant because of the considerable idler reflection at the input mirror. The effect of the idler reflection is reduced by the idler absorption and the use of multi-longitudinal-mode (MLM) pump pulses [13]. The Fresnel number of the experimental setup was approximately 50.
Fig. 5 The experimental setup. The half wave plate and polarizer were used to attenuate the pump energy. The telescope reduced the pump beam diameter to 4 mm. KTA and BBO crystals were 15 mm and 10 mm long, respectively. Wavelength tuning was accomplished by rotating the KTA crystals about an axis normal to the plane of the paper, and the BBO crystals about an axis in the plane of the paper, as indicated above the crystals. Mirror reflectances at pump, signal and idler wavelengths are shown in the table.
5.1 Pump beam
The pump source was a Quantel Brilliant b Q-switched Nd:YAG laser operating in MLM at 10 Hz pulse repetition rate. The pulses were approximately 5 ns long, and had 20 GHz bandwidth. The beam diameter out of the laser was approximately 8 mm, and after the telescope it was measured to 4 mm at 1/e2 of the peak fluence. The pump energy was limited to 70 mJ in order to keep total fluence (pump plus signal and idler) below 2 J/cm2. The near and far fields were measured using a CCD camera. The beam quality was estimated to (Mx 2, My 2) = (1.8, 1.4) after removing the noise as explained in the subsequent section.
5.2 OPO
Two different OPO configurations with equal resonator length were tested:
- • Two KTA crystals in walk-off compensating configuration (denoted KTA-KTA’)
- • Two KTA crystals in walk-off compensating configuration and two BBO crystals without walk-off compensation (denoted KTA-BBO-KTA’-BBO). The reason for not orienting the BBO crystals for walk-off compensation is that the available BBO crystals were identically cut with respect to the crystallographic axes, so for an interaction with two extraordinary waves, walk-off compensation would reverse the sign of the nonlinear coupling coefficient [14].
First, the KTA-KTA’ OPO was tuned to 1.68 μm signal wavelength and optimized with respect to output signal energy. Then the BBO crystals were inserted and tuned without tuning the previously installed crystals. The near and far fields of the signal beam were measured with a pyroelectric camera with 100 μm pitch, at 60 mJ pump energy. The pump energy was monitored behind the final folding mirror by a thermopile detector and the signal pulse energy was measured by another similar detector placed behind a filter removing idler and residual pump. The experimental OPO configurations were also simulated using the same parameters as in the experiments, except for the pump beam which was modeled as a 6th order super-Gaussian MLM beam. Figure 6 shows measured and simulated energy curves for both OPO configurations.
Fig. 6 Measured (red) and simulated (black) signal energy as function of pump energy for the OPO-configurations investigated: KTA-KTA’ (a), and KTA-BBO-KTA’-BBO (b). The pump energy is the energy at 1.06 μm impinging the first crystal.
The measured and simulated near and far field beam profiles for both OPO-configurations are shown as contour plots in Fig. 7 .
Fig. 7 Images of the signal beam. Measured near (a) and far (e) fields for the KTA-KTA OPO. Corresponding simulated near (c) and far (g) fields. Measured near (b) and far (f) fields for the KTA-BBO-KTA’-BBO OPO. Corresponding simulated near (d) and far (h) fields. The far field measurements are carried out in the focal plane of an f = 1.00 m lens.
The qualitative features agree with those in Fig. 4. The M2 beam quality measure is based on the second moments of the fluence distributions, which are very sensitive to noise. The data were filtered by an aperture at least twice as wide as the beam and the resulting estimates of M2 are also shown in Fig. 7. We have used the same apertures for the two OPO configurations, so even if the M2 estimates are inaccurate, they should at least give a fair comparison of the beam quality from the two OPO's. We notice that inclusion of the BBO crystals strongly reduces the asymmetry of the generated signal beam.
6. Conclusion
We have demonstrated the generation of nearly symmetric, high-quality, high-energy nanosecond pulses using a linear, singly resonant optical parametric oscillator with Fresnel number > 50. The beam quality is achieved by means of nonlinear crystals with orthogonal walk-off planes. Idler absorption also contributes to improved beam quality in the experiment, but the simulations show that the orthogonal critical planes represent the most important mechanism.
Acknowledgments
The authors would like to acknowledge Knut Stenersen, FFI, for valuable comments and discussions concerning the manuscript.
References and links
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