1. Introduction

Laser beam combining is a practical technique to combine several laser beams into a single beam with a power exceeding that obtainable from a single laser [1–5]. A side-by-side beam combining is a simple way to obtain high output power in conventional diode-laser arrays, where no effort is necessary to control the phase or frequency of individual beamlet. The combined power and the size of the source aperture are both proportional to the number of beamlets, while the far-field divergence is that of a single beamlet, so the brightness of the combined beam from this simple side-by-side geometry can be no better than that of a single element diode laser [3]. The commonly used beam combiner includes dichroic mirror, prism or grating, which can combine beam arrays at different wavelengths into a single one, which is useful in the wavelength division multiplexing in optical communications [1]. Combining fiber or diode laser beams are of current interest for scaling lasers to obtain high average output power and good beam quality. Phase controlled elements are usually used in the beam combining approach, such as holographic grating, diffractive optical element (DOE), or spatial light modulator (SLM) [6,7]. In this case, each laser beam is phase locked to a reference beam and amplified independently, and the phases of all beamlets must be controlled with a precision of much better than the wavelength (2π) [8]. This phase control of collinear propagating waves can be made by a well designed DOE, SLM, or using other multi-beam phase locked technique [9,10].

As an alternative to the beam combining at the input beam frequency, beams can be combined at a new frequency. Nonlinear frequency conversion allows the non-collinear beams to be combined to generate a beam at a new frequency [11]. The nonlinear processes can be sum-frequency, difference-frequency generation, et al. We demonstrate in this contribution that multiple different laser beams can be combined to generate second-harmonic beams propagating along one direction. We show that by properly choosing the beam combining configuration as well as by controlling the phases for individual input beams, it is possible to obtain the second-harmonic generated (SHG) output with power greatly exceeding that obtainable by a single laser beam. We further show that the SHG output power is variable from a virtually zero background to a maximum value that is orders of magnitude higher than the SHG output from a single laser beam.

2. Design and experiment

The experimental setup for the SHG beam combining is shown in Fig. 1(a) . The system consisted of a programmable SLM, an image detector, a feedback servo device, and a computer for running the control algorithm and updating the SLM. A 127-pixel phase-only transmission SLM (Hex-127, Meadowlark Optics) and an amplitude mask were employed, as shown in Fig. 1(a). A femtosecond laser (Mode-locked Ti:sapphire laser, Newport Spectra-Physics) was employed as the excitation source with pulse width of 80 fs. The output of the Ti:sapphire laser with central wavelength at 800 nm passed through an amplitude mask and was divided into a maximum of 127 beamlets. The spatially patterned laser output is then sent to the SLM, which provided a continuously variable phase variation from 0 to 2π. A frequency doubling crystal (BBO, type-I, 5 mm × 5 mm × 2 mm) was employed for SHG. The optical axis of the BBO crystal was cut at 28° along the horizontal direction to the normal of the crystal surface. The generated laser pattern was recorded using a CCD, and the date was analyzed with a personal computer. To optimize the SHG output, a self-adaptive feedback system and control unit were applied to analyze the SHG signal and to update the phase for SLM, until the output pattern reached the target profile.

 

Fig. 1 (a) Experimental setup for phase controlled beam combining with nonlinear frequency conversion, (b) configuration of four beams for generating and combining two-SHG signals.

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The experiment was first aligned for a two-beam frequency doubling, and this two-beam frequency doubling is a configuration widely used for the second-order intensity correlation measurement of ultrashort laser pulses. If four beams were arranged with the configuration shown in Fig. 1(b), two on-axis SHG signals were generated, which were correlated by the first order. Experimentally we were able to control the SHG output from a virtually zero background to a maximum value enhanced by the first order correlation, as shown in 
Fig. 2(a) . Theoretically, the generated on-axis signal with the four-beam configuration at the central spot is given by Eq. (1) [12],

 

Fig. 2 Intensity output of the combined SHG beam with the phase delay of one beam. (a) Experimentally observed result and (b) numerical simulation result.

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While E denoting the electric field of the incident femtosecond laser pulse, E_shg and I are the electric field and intensity of the combined SHG signal, respectively. The delay time τcan be controlled with the phase in the SLM [13]. Numerical simulation shows clearly that the control of the output power is possible with the control of the phase delay for any of the beamlets, as shown in Fig. 2(b), where we assume the femtosecond laser as a standard temporal Gaussian pulse.

In this experiment, the SHG signal was produced with rather low intensity input. The continuous-wave mode-locked Ti:sapphire laser beam was expanded and then divided by a mask, with the diameter of each aperture at 0.8 mm. The power of a single beamlet is only about 5 mW, with power intensity at a 10⁵ W/cm² level. The obtained efficiency of a single beam in the propagation direction is about 0.04%. With four beams arranged with the configuration in Fig. 1(b), the power of combined central beam was enhanced by a factor of 10 compared with the single beam input.

Since the phase of each beamlet can be controlled independently by the SLM, we applied many different beamlets and combined them together to give an output at SHG. 4, 6 and 12 beamlets were applied, with the multi-spots output shown in the Fig. 3 .

 

Fig. 3 Intensity pattern of the combined SHG output with four, (b) six and (c) twelve input beamlets. The corresponding masks are also shown at lower right corner in each figure.

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SHG can be generated at certain wavevector directions (the range of the wavevectors is termed as acceptance angle), within which phase-matching condition can be satisfied. Within the acceptance angle, the multiple input beamlets can generate a large number of SHG beams after SHG crystal. For example, a SHG signal can be generated collinearly with the laser beam. Furthermore, each pair of the non-collinear fundamental propagating waves can generate a SHG at a new direction. The ideal beam combination will be such that only central beam contains the maximum power, while the power for the rest should be reduced as much as possible.

The mode in Eq. (1) is an example to show that the power of the combined beam can be changed by the phase shift of an individual beam. In the optimized process, the phases for all the interacting beams have to be manipulated. As more beams get involved for the SHG beam combining, it is difficult to assign the phases for individual beamlets for an optimized SHG output. Instead, a self-adaptive control algorithm can be applied to maximize the output, or to shape the beam to an ideal shape [14]. For an experimental test, a target beam profile approaching a standard Gaussian was assigned, and the recorded pattern was compared with the target. The deviation of the generated profile from the ideal Gaussian profile was then evaluated by a simulated annealing algorithm and new phases for each beamlets were updated [15]. This process was repeated many times until the deviation became stabilized and minimized. The same self-adaptive control algorithm can be also applied to maximizing the output power from the system.

Figure 4 demonstrates such a controlled outcome with (a) showing the clean output from the SHG, and (b) showing the maximum output power for the optimized phases for 12 input beamlets. As CCD is 10 cm away from SHG crystal, the recorded Gaussian field distribution showed that the Gaussian mode can propagate without wavefront distortion. Figure 5 shows the recorded beam profile under the best beam quality.

 

Fig. 4 Beam profile of (a) the clean SHG output, and (b) the maximum SHG-energy output for the optimized phases of 12 input beamlets.

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Fig. 5 The optimized beam profile of the combined beam for the second harmonic of the Ti:sapphire laser output.

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It should be pointed out that, using this beam combining with nonlinear frequency conversion, the intensity of the combined central beam can be much higher than the case of only one central beam. An enhancement of 16 times was observed by optimizing the phases of all 6 input beamlets, and this enhancement can exceed 30 times with 12 input beamlets.

It is difficult with the self-adaptive algorithm to obtain a single SHG output, while the power is simultaneously maximized. The maximized output is usually at the expense of multiple output spots, as shown in Fig. 4(b). On the other hand, the output pattern can be optimized to an almost single transverse mode but at the expense of a reduced power. For the 12-beam configuration, the power of the central beam with optimized beam quality is 40% of the maximized power at SHG. However, maximizing the SHG output with a single transverse mode might be possible with a careful control of the excitation scheme and the acceptance angle of the SHG crystal, while only the central portion of the multi-spot input should be optimized. Moreover, the overall conversion efficiency, which is proportional to the input field, is expected to be much higher when higher input field are applied to illuminate the frequency doubling crystal.

3. Conclusion

In conclusion, we demonstrated a phase controlled beam combining via nonlinear optical conversion. It is shown that the combined second-harmonic fields can be conveniently variable from zero to a maximum value that greatly exceeds the second-harmonic field generated by a single laser beam. It is necessary to point out that the beam combining technique with the nonlinear frequency conversion should have a rather general applicability when the combined beam is desired to be at other frequencies. Other nonlinear processes, e.g., difference frequency mixing, to generate longer wavelength radiation, can be applied with this technique. We believe that this technique is applicable to many different phase-matching higher-order nonlinear processes to combine multiple laser outputs at a new frequency.