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Abstract
We introduce a method to enhance the phase-locking quality and duration of an end-pumped laser array by precisely shaping its pump beam to overlap with the array. Shaping the pump beam results in a significant improvement in lasing efficiency and reduces the pump power required to reach the lasing threshold compared to a typical uniform pumping configuration. Our approach involves shaping a highly incoherent laser beam by addressing smaller segments of the beam with higher local spatial coherence. We demonstrate a remarkable increase in the laser array output brightness by up to a factor of 10, accompanied by a substantial extension in the phase-locking duration.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-brightness laser sources with high beam quality are highly sought after for a wide range of applications. One method to obtain such a source involves phase-locking an array of low-power lasers, each with high beam quality [1–5]. Phase-locking is advantageous since the maximum far-field intensity of a phase-locked laser array increases quadratically with the number of lasers, whereas that of an array of independent lasers that is not phase-locked increases linearly.
Laser arrays can be obtained by many means such as multi-core fiber lasers, arrays of solid-state lasers, and vertical cavity surface emitting lasers (VCSELs), where the uniformly pumped gain medium is typically shared by all the lasers. The use of a shared gain medium and uniform pumping is typically preferred to overcome fabrication difficulties, achieve compactness, and avoid the challenge of shaping a spatially incoherent pump source. However, uniform pumping results in redundant heating of areas between the lasers, leading to a temperature gradient that extends from the center of the pumped area outward. This, in turn, creates a refractive index gradient, which changes the effective cavity length and resonance frequency of the lasers across the array.
While the method of active optical phase-locked loops can be used to overcome the degradation of phase-locking, it is typically restricted to a small number of lasers in the array [6–9]. A more scalable method involves passive phase-locking with mutual light injection between the lasers in the array [10–13], and it has been successfully used to phase-lock over a thousand coupled lasers [14]. Yet, passive phase-locking of many lasers can be challenging due to the requirement that their frequency detuning be sufficiently small compared to their coupling strength [15–18]. Experimentally, the lasing duration and the maximal pumping power of phase-locked laser arrays are limited due to inhomogeneities in the array caused by thermal effects.
To address these challenges, we developed a novel approach where the incoherent pump beam is shaped with a spatial light modulator (SLM) so as to pump mainly the lasing regions of the gain media. Hence, the thermal load on the gain medium is lowered, thereby reducing the deleterious thermal effects (namely thermal lensing and bulging), which in turn increase the quality and temporal duration of the phase-locking. We found that the shaping can increase the laser array’s brightness (phase locking criterion) by up to a factor of ten compared to conventional uniform pumping. The shaped pump heats mainly the lasing regions, leading to a uniform temperature change across the array at short timescales. Moreover, we show that pump shaping reduces the lasing threshold by a factor of two as compared to uniform pumping, so correspondingly less pump power is required to obtain the same output intensities.
Our approach offers advantages beyond brightness enhancement and can have potential benefits for other applications of laser arrays. As gain-dissipative optical oscillators, laser arrays are promising candidates for spin model solvers [19–22]. They also play an important role in the study of physical phenomena such as synchronization [14,23], topological lasing [24,25] and non-Hermitian physics [26–28]. Since phase-locking is essential in these applications and depends on the array’s uniformity, our pump shaping method would allow the employment of larger laser arrays and the use of more efficient coupling schemes.
2. Experimental arrangement and procedure
Our experimental arrangement, schematically presented in Fig. 1, is comprised of two parts: a degenerate (self-imaging) cavity laser that forms an array of coupled lasers and a pump shaping configuration. The degenerate cavity laser includes two lenses in a 4-f configuration and two mirrors [29,30]. The left mirror is a reflective phase-only SLM (SLM1, Holoeye’s Pluto 2.1-NIR-149) that forms a programmable array of apertures [31,32], which in turn define a square array of 36 lasers. The distance between the lasers at SLM1 plane was set to 320${\mathrm {\mu }}$m and their diameter was set to 224${\mathrm {\mu }}$m, to optimize the output brightness (see Supplement 1). The right mirror, deposited on the surface of a 3mm thick c-cut Nd:YVO4 gain crystal, has high reflectivity coating for 1064nm (and very low reflectivity for 808nm). The telescope lens L1 is a plano-convex lens with focal length 75cm, and L2 is an achromat doublet lens with a focal length 25cm, resulting in a demagnification of 3 from SLM1 plane to the gain crystal plane. The lasers are dissipatively coupled by placing an aperture of diameter 7.3mm in the far-field (FF) plane, providing a relative coupling strength of 1% [33]. The FF aperture diameter was set to precisely transmit up to the first-order diffraction peaks of an in-phase square array.
Fig. 1. Experimental arrangement. (a) The degenerate cavity laser, comprised of two lenses (L1 and L2), two mirrors in a 4-f configuration, a gain medium and an aperture. The left mirror is SLM1, and the right mirror with high-reflective coating at 1064nm and anti-reflective coating at 808nm is directly deposited on the Nd-YVO4 gain crystal. A polarizing beam splitter (PBS1) serves as an output coupler to an imaging system. The lasers are coupled by an aperture (Ap) placed in the far-field plane of the cavity. (b) The pump shaping apparatus is comprised of a fiber-coupled 808nm pump laser, a magnifying telescope (lenses L3 and L4), a polarizer PL1, SLM2, and a de-magnifying telescope (L5 and L6).
The gain crystal is pumped at 1Hz repetition rate by a quasi CW (pulse duration of 8ms) diode laser of 808nm and maximal power of 150W. The low repetition rate was chosen to ensure that the gain crystal cools down to room temperature between subsequent pulses. The pump emerges from a high power fiber of 200${\mathrm {\mu }}$m diameter and NA=0.22, providing a highly spatially incoherent source with $1.5\cdot 10^{4}$ transverse modes ($M^{2} \approx 86$ in each direction). To shape the pump laser, the fiber’s output is first imaged onto a second SLM (SLM2, Holoeye’s Pluto 2.1-NIR-118) with a magnification of $\times 60$ (overall diameter of 12mm). SLM2 forms an array of square lenslets, each with programmable focal length ($f_{lenslet}$), size and period, so as to shape the pump beam into an array of 36 focused beams. Importantly, each lenslet is illuminated by only a tiny area of the pump beam, so the number of modes impinging on it is highly reduced, enabling a tight focus. The light from the focused array is then imaged with 10:1 de-magnification onto the Nd:YVO4 gain medium, to exactly overlap the light from the laser array defined by SLM1. A polarizer (PL1) matches the pump laser polarization with the polarization of SLM2, and the c-axis of the Nd:YVO4 crystal. An imaging system separately detects the shaped pump beam at the gain medium plane, as well as the lasers’ near-field (NF) and far-field (FF) intensity distributions. An intra-cavity adaptive optics algorithm [17] was applied to the degenerate cavity laser, to correct for misalignment and aberrations that result in frequency detuning between the lasers in the array.
While the use of SLMs allows digital control and precise tuning of system parameters, their low damage threshold limits the attainable total laser power. However, once the optimal system parameters are determined, both SLMs can be replaced by a metal amplitude mask and a glass lenslets array suitable for high-power applications.
The optimal lenslet focal length depends on the multimode beam size and its divergence within the absorption length of the gain medium crystal, and maximizes the overlap with the lasing mode. It was experimentally found to be $f_{lenslet} = 8$cm, for a square lenslet with sides of 1.07mm (see Supplement 1).
3. Results and discussion
Some typical experimental results of pump shaping are presented in Fig. 2. Figure 2(a) shows the intensity distribution of the pump at the gain medium plane for the case of uniform pump (UP), where SLM2 serves as a flat mirror. Figure 2(b) displays the intensity distribution of the pump for the case of the shaped pump (SP), where SLM2 serves as a lenslets array. The corresponding phase distribution on the SLM is shown in Fig. 2(c). Cross-sections of the pump beams for the two cases are shown in Fig. 2(d). The measured waist of the shaped pump beams on the gain crystal is $w_0=30\mu m$ (the radius at which intensity drops by $e^{-2}$), and their peak intensity is 4.5 times stronger than the average intensity of the UP beam. The measured laser power as a function of the pump intensity for the UP and SP configurations, presented in Fig. 3, shows a 2.3-fold reduction of the lasing threshold for the SP configuration. The disparity between the peak intensity ratio and the threshold ratio can be attributed to the rapid divergence of the pump beams within the gain medium.
Fig. 2. Pump shaping. (a) Pump intensity distribution at the gain crystal plane for a uniform SLM. (b) Pump intensity distribution at the gain crystal plane for a shaped SLM. The mean waist size is $w_0=30\mu m$. (c) The phase distribution set on the SLM to simulate a 6 by 6 lenslets array. (d) Cross-section profiles of the uniform and shaped pump intensity distributions, obtained with the same pump power.
Fig. 3. Lasing threshold measurements. The average laser output power as a function of the pump power impinging the SLM. Dashed black lines display the linear fit of each data set. The ratio of the pump power at the lasing threshold in the SP configuration over that in the UP configuration is 2.3.
To assess the effects of pump shaping on phase-locking, we measure and compare the FF and NF intensity distributions of the coupled lasers array for the UP configuration (Fig. 4(a)), and the SP configuration (Fig. 4(b)). The pump power was set to yield the same total lasing power for both configurations at the beginning of the lasing pulse (13W and 6W in UP and SP configurations, respectively). Panels (i) and (ii) display the FF intensity distributions at camera trigger times of 0${\mathrm {\mu }}$s and at 3600${\mathrm {\mu }}$s, respectively, after the beginning of the pump pulse. The exposure time of the camera was set to 70${\mathrm {\mu }}$s. The FF peaks, observed in panels (i) indicate high-quality phase-locking at short times for both pump configurations. Nevertheless, in the SP configuration, the central peak is two times stronger and the background is much weaker than in the UP configuration, indicating a significantly improved phase-locking. At 3600${\mathrm {\mu }}$s, the sharp FF peaks are completely smeared for the UP configuration and remain sharp for the SP configuration as shown in panels (ii), indicating a dramatically better phase-locking for the SP configuration. The corresponding detected NF intensity distributions, displayed in panels (iii) and (iv), are all similar, indicating that the intensities of the lasers in the array are essentially unchanged for both pump configurations.
Fig. 4. Typical measurements of the NF and FF intensity distributions for (a) uniform pump and (b) shaped pump. Panels (i) and (ii) display the FF intensity distributions at camera trigger times of 0${\mathrm {\mu }}$s and 3600${\mathrm {\mu }}$s, after the beginning of the pump pulse. Panels (iii) and (iv) display the corresponding NF intensity distributions of the lasing mode. The camera exposure time is 70${\mathrm {\mu }}$s. The colorbars represent the instantaneous intensities in W/cm$^2$.
Subsequently, we undertake a more systematic comparison between the lasing modes and phase-locking state in the two pumping configurations by assessing the NF and FF intensity distributions of the lasers. These measurements were performed by capturing images of the intensity distribution at different triggering times of the camera, and the results are shown in Fig. 5. Each data point in the figure corresponds to the average value of the NF or FF intensity distribution obtained from an image taken with an exposure time of 70${\mathrm {\mu }}$s. Therefore, the data point at a triggering time $t$ is the average value between time $t$ and $t+70\;{\mathrm {\mu }}$s since the initiation of the pump pulse. For each panel of Fig. 5, the pump power of the SP and UP configurations was adjusted to yield the same output power at $t=0$. To demonstrate the importance of pump shaping at high pump powers, we conducted two measurements- one with low pump power and another with high pump power. During the ’Low pump’ measurement, the pump powers used in the SP and UP configurations were 6W and 13W, respectively, and resulted in an output power of approximately 0.15W. In the ’High pump’ measurement, the pump powers used in the SP and UP configurations were 20W and 37W, respectively, and yielded an output power of approximately 0.52W. Figures 5(a) and 5(c) display the FF peak intensity over time for the SP and UP configurations at low and high pump powers. In both the low and high pump measurements, the FF peak intensity was greater in the SP configuration compared to the UP configuration. Moreover, we observed that the FF peak intensity decreases over time, almost from $t=0$, and that the decrease is much more rapid in the UP configuration.
Fig. 5. Improved phase-locking by pump shaping. Panels (a) and (c) display the max FF peak intensities for the SP and UP configurations as a function of time, at low and high pump powers. Empty and filled circles correspond to shaped and uniform pump configurations. Panels (b) and (d) display the ratio of laser array brightness in the SP and UP configuration as a function of time, at low and high pump powers.
The criterion we use to quantify the phase-locking quality is the brightness of the laser array, defined as the power contained in the full width at half maximum of the FF intensity distribution, divided by the product of the solid angle of divergence and the mode area. Since the laser intensity in both configurations is the same and is almost unchanged during the measurement, the brightness gives a direct indication of the coherence of the lasers in the array (see detailed results in Supplement 1). The ratio of the laser array brightness for SP and UP configurations as a function of time is presented in Fig. 5(b) for low pump powers, and in 5(d) for high pump powers. In the ’Low pump’ experiment, the brightness of the laser array with the SP configuration at $t=0$ is twice larger than with the UP configuration. The advantage of the SP configuration increases to a factor of 7 at t=2000${\mathrm {\mu }}$s, and then slowly decreases with time. In the ’High pump’ experiment, the SP configuration displays a factor 10 improvement in the brightness at t=100${\mathrm {\mu }}$s, which decreases gradually until t=3000${\mathrm {\mu }}$s, when the phase-locking is completely lost in both configurations.
Since the laser output power is similar in both pumping configurations, and remains approximately the same throughout the measurement, the brightness ratio indicates that for the SP configuration, the initial phase-locking is improved and the degradation rate is significantly slower relative to the UP configuration. The improved phase-locking at $t=0$ at low pump powers can be explained by an improved beam quality of the laser in the SP configuration, due to the better overlap of the pump beams with the TEM00 modes. The measured M$^2$ of a single laser is 1.06 in the SP configuration, and 1.43 in the UP configuration (see Supplement 1). As efficient coupling requires high beam quality, the phase-locking is expected to improve in the SP configuration. However, we see that the brightness ratio increases dramatically with time in Fig. 5(b), meaning that the phase-locking in the UP case deteriorates much faster than in the SP case. Furthermore, the brightness ratio at $t=0$ is much higher when high pump power is used. We attribute the difference in the phase-locking quality and laser pulse duration to the difference in the thermal loads of the pumping configurations. Such thermal loads can result in thermal lensing, and also strain and stress that lead to bulging, all of which are well known in solid-state lasers [34–38], and specifically in Nd:YVO4 gain crystals [39–41]. The thermal lensing and the bulging of the shared gain medium change the effective lengths of the laser cavities in a non-uniform manner. This in turn introduces frequency detuning between the lasers that increases during the laser pulse and degrades phase-locking. Therefore, by using less pump power in the SP configuration, the thermal load is reduced, slowing down the thermal effects and significantly improving phase-locking. In Supplement 1 we present results of a numerical simulation of the expected thermal lensing, and interferometric measurement of the optical distortion of the gain crystal during the pulse. The results of both simulation and experiment support the above conclusions.
4. Concluding remarks
We showed that a highly incoherent pump with more than $10^4$ modes can be accurately shaped with high resolution by dividing it into smaller segments that contain considerably fewer modes and address them independently. We demonstrated that by shaping the pump beam to overlap with the lasing mode it is possible to improve the pumping efficiency and reduce the lasing threshold. This results in slower heating of the crystal that leads to a brightness enhancement by up to a factor of 10, and a significant improvement in the phase-locking duration. The pump shaping can be further utilized for homogenizing a nonuniform pump beam and compensating for inhomogeneous losses of the laser array.
Funding
Minerva; Israel Science Foundation.
Acknowledgments
The authors thank Uri Rossman and Chene Tradonsky for valuable help and discussions.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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