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We report on efficient cw high-power second harmonic generation in a periodically poled LiTaO3 crystal placed in a resonant enhancement cavity. We tested three configurations, differing in the coupling mirror reflectivity, and a maximum conversion efficiency of about 76%, corresponding to 6.1 W of green light with 8.0 W of fundamental power, was achieved. This is, to the best of our knowledge, the highest cw power ever reported using a periodically-poled crystal in an external cavity. We observed photo-thermal effect induced by photon absorption at the mirrors and in the crystal, which however does not affect stable operation of the cavity. A further effect arises for two out of the three configurations, at higher values of the input power, which degrades the performance of the locked cavity. We suggest this effect is due to the onset of competing nonlinearities in the same crystal.
©2010 Optical Society of America
1. Introduction
Optical frequency conversion in nonlinear crystals is a useful technique for generation of new frequencies in spectral regions where lasers are inefficient or unavailable at all. Quasi Phase-Matching (QPM) in periodically poled ferroelectric crystals has become a well assessed and versatile technique for efficient nonlinear generation and engineering of new optical devices [1]. Indeed, with respect to conventional birefringent materials, a wider range of phase matching conditions can be achieved by properly engineering antiparallel ferroelectric domains into the crystal, virtually limited by the transparency range of the material and by the technical ability to obtain smaller periods. To date, different materials have been used for Second Harmonic Generation (SHG) in QPM crystals, for frequencies from the IR to the UV range, in different configurations and emission regimes (pulsed or cw).
Efficient cw SHG requires high power pump sources and long interaction lengths [2–7]. In single-pass generation optimal efficiency requires tight focusing condition, depending on the length of the crystal [8], which combined with high input power can result in high power density. As a consequence, severe thermal effects can occur due to absorption in the crystal, such as thermal lensing, dephasing or even permanent damages [9]. However, conversion efficiency can be significantly improved by means of power enhancement using the same laser cavity [10–12], or external cavities [13, 14]. The use of a cavity relaxes the requirements concerning pump power, crystal length and focusing parameters. Indeed, final efficiency is given by a balance between single-pass efficiency and mirrors reflectivity. So, it is possible to loosen focusing condition in the crystal, which determines single-pass efficiency, and recover final efficiency by properly choosing mirrors reflectivity. Thermal effects can however be even more critical in case of resonant cavities, for which optical stability can be dramatically compromised [15], and their use with periodically poled crystals has been restricted to moderate input powers [16–21], while higher input powers have been successfully used with bulk crystals in external cavities, generating tens of SH power [22–24]. Improvements in crystal growing techniques give better-quality materials which can withstand higher power levels, extending the power range of generation. Recently, MgO-doped stoichiometric lithium tantalate (LiTaO3) has shown improved performance in terms of low absorption, high photorefractive-damage resistance, and high thermal conductivity [9,25–27], which makes it suitable for high power applications.
In this paper, we demonstrate efficient high-power SHG of green light at 532 nm in periodically poled LiTaO3, with the use of an external enhancement ring cavity, with different reflectivities for the coupling mirror. The use of different coupling mirrors can realize different final efficiencies. In particular we were interested in the design of a cavity-enhanced SHG to be used in a successive sum frequency generation process, giving the third harmonic of the fundamental radiation at 1064 nm [28]. In this case the optimal condition for SFG input powers requires a 50%-efficient SHG. We investigated the presence of effects which can compromise the correct operation of the locked cavity at high powers. In particular, we observed a dynamic photothermal effect due to absorption at the mirrors surface and in the crystal which, however, does not affect stable operation of the locked cavity. Moreover, for some of the tested optical configurations and for higher levels of input power, a second effect occurs, which we suggest can be due to the onset of competing nonlinearities, affecting proper cavity operation. Nonetheless, we achieved a maximum stable generation of 6.1 W of second harmonic with 8.0 W of fundamental power, with an efficiency of 76%. To date, this result represents the highest value obtained for cw SHG in periodically-poled crystals using an external cavity.
2. Experimental setup
The pump source is an Ytterbium-doped fiber laser emitting up to 10 W of cw radiation around 1064 nm, with a linewidth of less than 200 kHz. A Faraday isolator avoids back-reflections. The QPM crystal is a periodically poled sample of 1%-MgO-doped LiTaO3, 15 mm long with a period of 7.97 μm. The crystal is embedded in a copper oven and placed in an enhancing ring cavity. The oven temperature can be stabilized within 0.1℃ by means of a Peltier element driven by an active control. QPM condition was obtained at 45.2℃.
Fig. 1. Schematic view of experimental setup. OI, optical isolator; L#, coupling lens; SM, steering mirror; M#, cavity mirror; PPSLT, temperature stabilized periodically poled lithium tantalate crystal; A, beam attenuator; QWP, λ/4 waveplate; PBS, polarizing beam splitter; PD#, photodetector; PZT piezo actuator.
The setup is sketched in Fig. 1. The cavity is made by four mirrors in a bow-tie configuration, using two curved mirrors (M1 and M2), having 200 mm radius of curvature, and two plane mirrors M3 and M4. The total length of the cavity is ~ 1.17 m, and the free spectral range is about 256 MHz. The crystal is placed between the curved mirrors, where the smallest waist of 63 μm occurs. The pump radiation is coupled into the cavity through the coupling mirror M1, passing through the crystal and then reflecting off mirrors M2, M3, and M4, in the order. Second harmonic (SH) is generated in the first section of the folded intracavity path and is coupled out of the cavity through mirror M2. The reverse path is possible as well, entering the cavity through mirror M1, but reflecting off mirrors M4, M3, and M2, in the order, and then passing through the crystal. In this case, the generated light is coupled out of the cavity through mirror M1, collinear to the reflected pump radiation. These collinear beams can be used, for instance, as inputs for a further sum frequency generation stage [28], for which an optimal SHG efficiency of 50% is required. We used three coupling mirrors, with different reflectivities at the fundamental wavelength, namely 88, 94 and 97%. The remaining mirrors are high-reflection (HR) coated (99.98%) at the fundamental wavelength. All the remaining surfaces of mirrors substrates are antireflection coated at the fundamental wavelength, while mirrors M1 and M2 are also antireflection coated at the SH wavelength. A plane mirror is mounted on a PZT actuator which is used to actively control the cavity length and keep the cavity resonant with the laser frequency. The laser beam is spatially coupled to the fundamental cavity mode by means of lenses L1 and L2. A dichroic mirror is used to completely separate SH from the residual fundamental power transmitted through mirror M2. A small, calibrated fraction (< 10 mW) of the generated light is sampled and monitored by a Si photodiode. A second photodiode is used to monitor the transmission of the fundamental frequency through mirror M3.
The cavity is locked according to the Hänsch–Couillaud scheme [29], that was already successfully used for SHG [30]. To this purpose, light reflected from the cavity is attenuated and polarization analysed by a quarter-wave retardation plate and a polarizing beam-splitter. The transmitted and reflected beams are intensity balanced by rotating the waveplate and collected by two twin photodetectors. The amplified signals from photodetectors are subtracted and fed to the servo electronics which drives the PZT-mounted mirror.
Fig. 2. Experimental evidence of photothermal effect when scanning a cavity resonance, with the laser approaching the resonance from (a) lower and (b) higher frequencies, for three different input powers: (i) 0.05 W, (ii) 4.5 W, and (iii) 8.0 W.
The locked cavity usually operates in a quite stable regime, except for the cases discussed in Sec. 3. The dynamic range of the correction signal, corresponding to about two free spectral ranges, is sufficient to keep the cavity locked for several minutes. Unlocks of the cavity are usually caused by environmental perturbations, as mechanical shocks (road traffic) or by long term mechanical deformation due to temperature drifts.
3. Discussion of results
The second harmonic power P SH generated in a ring cavity is related to the intracavity fundamental power P c entering the crystal:
By imposing the self-consistent equations for the field amplitudes of the cavity, an implicit expression can be derived for the circulating power P c, at resonance [14], as
where R 1 and T 1 are the reflectance and transmittance of the coupling mirror, respectively; R 2 is the light left in the cavity after a round-trip, which accounts for transmission through the other mirrors and any other loss in the cavity, except the loss of fundamental power converted to second harmonic, given by the term (1 − γ SH P c).
We preliminarily measured the single pass conversion efficiency γ SH for the focusing condition realized between the curved mirrors M1 and M2. To this purpose, we removed mirror M2 and measured the generated second harmonic as a function of the impinging power at the fundamental frequency. We finally obtained γ SH = 0.0035 W-1. Also, from the light reflected by the coupling mirror we estimated the total loss of the cavity, Γ = 1 − R 2, with the crystal inside but far from the QPM condition, obtaining Γ = 4%.
Thermal effects are a critical issue for stable operation of cavities with high circulating power. They are due to the unavoidable absorption of light at the mirrors surface or into the crystal, which induces a local heating of optical components. These effects are proportional to the circulating power and can dynamically affect the cavity stability. Local heating of mirrors and crystal can have the following effects: change the effective optical path in the cavity; induce a thermal lensing which strongly modifies the geometry and stability of the resonator, deteriorating the coupling of the input beam into the fundamental TEM00 mode, or even making the resonator unstable; moreover, it can change the QPM condition, degrading the efficiency of the nonlinear process.
An evidence of thermal lensing is usually given by a change of the radiation coupled in the different transverse modes of the resonator. Hence, we carefully aligned the cavity at low input power, typical by coupling more than 95% of the power in the fundamental TEM00 cavity mode. By increasing the input power, we did not appreciate any significant relative change of the coupled radiation, suggesting that thermal lens effect is unnoticeable over the whole range of input power.
A photothermal induced change of the effective cavity length is evident by scanning the cavity length across a resonance, as observed for free space cavities [16, 17, 31], and more recently even for fibre cavities [32]. There is a clear push-pull effect due to the dynamic change of the optical path, depending on the laser detuning with respect to the cavity resonance, as the laser and the resonance frequencies approach each other. The dynamical response depends on the timescale of thermal diffusion over the beam dimension [33, 34]. So, the effect is stronger when the resonance crossing time is longer than the thermal diffusion time, rapidly decreasing for faster scanning velocity. As shown in Fig. 2a, when the laser approaches the resonance from lower frequency, the photothermal effect dynamically reduces the optical path and the peak slips towards higher frequency; after the laser overtakes the top of the resonance, this slips back to lower frequency, resulting in an increased resonance crossing time. When the laser approaches the resonance from higher frequency, Fig. 2b, the peak moves towards the laser, now reducing the crossing time. In this case, when the crossing time is lower than the cavity buildup time, a reduction of the peak power can be observed. This effect was observed even for the cavity without the crystal and clearly corresponds to an effective decrease of the optical path when the laser approaches the resonance. The effect increases with the crystal placed inside in the cavity and is proportional to the impinging power. No difference was appreciated in case of quasi-phase matched or unmatched conditions. Nevertheless, the occurrence of photothermal induced change of effective intracavity path does not affect stable operation of the cavity when locked to the laser for input powers up to 8 W.
We also verified that heating of the crystal did not significantly modify the QPM temperature. Usually, we set the QPM temperature for low input power. For higher values of input power, we observed no difference between the peak value of green power measured when rapidly scanning the cavity and the stable green power with the cavity locked to the laser. Besides, with the cavity locked to the laser, we changed the oven temperature by small steps around the initial QPM temperature, measuring the corresponding SH power. Again, we did not appreciate any change of QPM temperature.
Recent experiments on high power single-pass SHG in periodically-poled LiTaO3 report evidence of thermal dephasing and lensing [5–7]. Sinha et al. [5] used an undoped crystal, which is more sensitive to green-induced IR absorption of fundamental, compared to our MgO-doped crystal. A closer comparison can be made with Ref. [6, 7]. They use a MgO-doped crystal, with input power (29.5 W) comparable to our typical intracavity powers. A detailed study of dephasing for different focusing conditions shows that dephasing is clearly evident for tight focusing, i.e., greater thermal load. Dephasing strongly reduces For waist sizes (and thermal loads) similar to our.
Fig. 3. Power profiles observed by scanning the cavity across a resonance: (a) SH profiles for 94%-reflectivity coupling mirror and for three different values of input power, P 1 = 4.4 W, P 2 = 6.3 W, and P 3 = 8.0 W; (b) syncronous profiles for fundamental (F) and second harmonic (SH) above threshold, for 97%-reflectivity coupling mirror and 5.4 W of input power. The scale of fundamental power indicates the intracavity circulating power.
A further effect was observed by scanning the cavity resonances, when the QPM condition is satisfied. It causes a distortion of the shape of the scanned resonance peaks, both for fundamental and SH. Unlike the photothermal effect, this effect neither depends on the scanning velocity, nor on the scanning direction. Moreover, it does not occur at the highest conversion efficiency, which also implies the highest circulating power. Finally, it appears when input power exceeds a threshold value, which depends on the reflectivity of the coupling mirror —the higher is the reflectivity, the lower is the threshold. Figure 3(a) shows the second harmonic power exiting the cavity around a resonance, for three different values of the input fundamental power. For the lowest input power, P = 4.4 W, the resonance has the usual symmetric lorentian shape. For increasing values of input power, P = 6.3 W and 8.0 W, around zero detuning, SH power suddenly decreases, setting to a constant level for a small interval of positive detuning. This constant value is the same for all the input powers above the threshold, at least within the experimental fluctuations. For larger detuning, the SH power decreases again. Figure 3(b) shows power profiles of both fundamental and second harmonic, exiting the cavity around a resonance, for 5.4 W of input power. The scale of fundamental power indicates the intracavity circulating power, estimated dividing the transmitted power by the M3 mirror transmittivity. We notice that zero-detuning point is difficult to determine for the deformed profiles. For negative frequency detuning both fundamental and second harmonic power increase monotonically. Next to the sudden decrease of the second harmonic power, the fundamental power displays a sudden change of the increasing rate, continuing to increase up to a maximum value, then decreasing without further discontinuities in the derivative.
We believe that this behavior is due to the onset of a competing χ (2) nonlinear process [35]. Specifically, in the SHG cavity pumped at frequency ν, the generated second harmonic, at 2ν, can act as a pump for a nondegenerate resonant OPO with signal and idler frequencies ν ± = ν ± Δ, provided that: (1) both signal and idler are resonant with the cavity; (2) ν ± and 2ν satisfy the QPM condition for OPO at the operating temperature; (3) the second harmonic power is higher than the OPO threshold. White et al. showed that threshold depends only on cavity linear losses and detuning, and on nonlinear interaction rates of both SHG and OPO (Eq. (2) of Ref. [35], more details in Ref. [36]). Detuning from resonance increases the effective cavity decay rate, increasing the threshold for parametric oscillation. So, during frequency scan, OPO actually starts where SH profile suddenly decrease and fundamental profile changes its increasing rate. As the detuning decreases, the threshold decreases as well, reaching the minimum value at resonance. However, during cavity scan signal and idler can even hop to different frequencies, if more favorable conditions for parametric oscillations are satified. Moreover, photothermal effect is present as well and leads to asymmetric cavity dynamics for negative and positive detuning (Fig. 2). Around resonance, the competing OPO remains active for a small interval around the centre of the resonance (zero detuning); here the SH power remains fixed at the threshold level (power clamping), irrespective of the input power, and all the excess SH power is converted to the OPO signal and idler. These two are both resonant and are detected together with the transmitted fundamental power. Their frequencies are presumably very near to fundamental frequency, well within the SHG acceptance bandwidth (HWHM ≃ 0.2 nm), and a high-resolution spectrometer is needed to resolve them.
The input power threshold values for the onset of the assumed competing OPO were estimated as about 3 and 5 W for input mirrors with reflectivity 97% and 94%, respectively. Just after the onset of the competing nonlinearities regime, the cavity can still be locked to the laser, but the SH power at resonance is clamped at the OPO threshold. In fact, residual fluctuations of frequency locking, due to finite gain and bandwidth of the servo electronics, result in a noisier amplitude (i.e., increasing r.m.s.) output around an average value higher than the threshold values. Further increase of the input power makes the locking unstable. An accurate characterization of the observed effect requires a substantial modification of the setup and is out of the scope of the present work. However, for the configuration with optimum efficiency, using the coupling mirror with 88% reflectivity, OPO does not take place and the maximum conversion efficiency (76%) is achieved, generating 6.1 W cw at 8.0 W of input power. With coupling mirror reflectivity of 97% (94%) the cavity operates with stable locking up to about 4 (4.7) W of input power, generating a maximum SH power of 1.4 (2.7) W with efficiency of 35% (57%). Figure 4 shows the results obtained for the three different configurations. Increasing the reflectivity of the coupling mirror reduces the efficiency of the frequency conversion, while the range of input powers is limited by the onset of competing nonlinearities, which rapidly degrade the performance under cavity locking conditions. For the most efficient and stable configuration we also show, see the inset of Fig. 4, the experimental efficiency η = PSH/P in as a function of the input power, along with the efficiency η(P in) calculated by solving Eqs. (1) and (2), with the cavity parameters experimentally estimated. A comparison can be made with the optimal efficiency achievable in case of impedence-matched cavity [14]. For the present values of γ SH, Γ and R 1 = 88%, the cavity is impedence matched for 2.9 W of input power, for which the efficiency is about 70%. On the other hand, a maximum efficiency of 82% could be achieved, for 8 W of input power, with a 81%-reflectivity input mirror, corresponding to 6.5 W of SH power.
Fig. 4. Second harmonic power P SH as a function of the input fundamental power P in for three different values of input mirror reflectivity: 88%, 94% and 97%. The inset displays, for the configuration with the 88%-reflectivity coupling mirror, the experimental efficiency η vs. P in, along with efficiency predicted by Eqs. (1) and (2), with all the measured parameters.
4. Conclusions
We demonstrated stable operation of an enhancing cavity using a periodically-poled LiTaO3 crystal, generating up to 6 W of cw green power with 8 W of fundamental input power, with an efficiency of 76%. To our knowledge, this is the highest cw SH power generated in external cavities with periodically-poled crystals inside, with a significant improvement with respect to previous results.
Different values for the efficiency are obtained by simply changing the reflectivity of the input mirror. We did not notice any signature of thermal lensing through the crystal, nor a dephasing of the QPM condition. The observed photothermal effect due to absorption at the mirrors and in the crystal does not compromise correct operation of the cavity when it is locked to the laser. A comparison with recent results obtained in single-pass configurations shows the design versatility of external-cavity configurations with respect to single-pass ones. Moreover, we observed a second effect which appears in cavity configurations with higher reflectivity of the input mirror and for input powers above a threshold value, strongly affecting correct operation of the locked cavity. However, the configuration with the lowest mirror reflectivity does not suffer from it, at least in the range of input powers we investigated, and this latter is the configuration with the higher efficiency. We suggest this effect can be due to competition of χ (2)-nonlinearities. Confirmation of this hypotesis needs more investigations and substantial modification of the present experimental setup. In particular, a high resolution spectrum analyzer is required for spectral resolution of the signal and idler. Moreover improvement of locking electronics would allow static cavity detuning. Anyhow, its occurrence shows that there are different effect beyond thermal ones which can set a serious limit for power scaling of similar systems.
Finally, the demonstrated efficient operation of such a nonlinear cavity, generating several Watts of second harmonic power, can be of interest for other types of cavity-enhanced frequency conversion schemes and for generation of high power nonclassical states of light.
Aknowledgements
The authors thank Pasquale Poggi for technical assistance. This work was funded by Ministero degli Affari Esteri (Project UVICOLS).
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