We experimentally demonstrated coherent beam combining using optical parametric amplification with a nonlinear crystal pumped by random-phased multiple-beam array of the second harmonic of a Nd:YAG laser at 10-Hz repetition rate. In the proof-of-principle experiment, the phase jump between two pump beams was precisely controlled by a motorized actuator. For the demonstration of multiple-beam combining a random phase plate was used to create random-phased beamlets as a pump pulse. Far-field patterns of the pump, the signal, and the idler indicated that the spatially coherent signal beams were obtained on both cases. This approach allows scaling of the intensity of optical parametric chirped pulse amplification up to the exa-watt level while maintaining diffraction-limited beam quality.
© 2010 OSA
The development of high power solid-state lasers opens up new fields of research not only in scientific application, but also in industrial application. In development of the solid-state laser, one of the most critical issues to be considered is power scaling. Scaling to a higher average power with good beam quality is limited due to thermo-optic distortion of the solid-state gain media and laser-induced damage of the optical components. One possible approach to resolving this is the use of beam combining techniques in order to increase output power while retaining ideal beam properties. Several approaches for beam combining have been reported [1–3]. They can be categorized into two main types: coherent beam combining and wavelength beam combining .
In coherent beam combining, the relative phases of multiple beams of the same wavelength are adjusted so that beams are coherently combined as a single beam. However, this requires precise phase control with a substantial accuracy much smaller than the wavelength (2π rad), resulting in the complex feed-back system. Although the beam combining based on stimulated Brillouin scattering (SBS) is a promising approach with a simple optical arrangement , SBS cannot be applied for the broad-band lasers. On the other hand, in wavelength beam combining, multiple beams that operate at different wavelengths are overlapped to form a single beam . Although phase control is not required in wavelength beam combining, the spectral brightness of the combined beam is decreased. A pulsed output based on wavevlength beam combining was demonstrated using a three-channel fiber laser . Recently, a continuous-wave output power of 2 kW, and in the pulsed regime, an output energy of 3.7 mJ with an average power of 187 W were obtained by combining four fiber amplifier channels . However, the higher pulse energy output is limited to several milli-joules due to nonlinear property of optical fibers.
An alternative approach is to utilize optical parametric amplification (OPA) using a multiple-beam pump scheme  where the three pump beams were overlapped with different incident angles onto a nonlinear crystal. In the parametric amplification process, the phase difference between the pump and the signal pulses is transferred to the phase of the generated idler pulse. This allows amplification of the signal pulse while maintaining the initial phase condition of the signal pulse. In beam combining using OPA, multiple beams that fulfill the phase-matching condition can be used as a pump source. Even if each pump beam has a different phase, the phase of the amplified signal is not affected. In this paper, we experimentally demonstrate that beam combining using the OPA process can be successfully realized with a random-phased multiple-beam array.
2. Experimental results of OPA pumped by two-beam
The experimental setup is illustrated schematically in Fig. 1 . An injection-seeded diode-pumped Nd:YLF oscillator generated a signal pulse of 1053-nm wavelength with 1-mJ pulse energy for 24-ns pulse duration (FWHM) at 10 Hz repetition rate. The signal pulse had a near-diffraction-limited beam quality. The output from the oscillator was down-collimated to a diameter of 2 mm. A waveplate and a Glan laser prism were used to extract the horizontal polarization. As a pump source, we used a commercial Nd:YAG laser (SureliteTM II-10, Continuum,) with 5.4 ns pulse duration (FWHM) at 10 Hz repetition rate. The wavelength of the pump laser was 532 nm. A waveplate and a polarizer were used to control the laser pulse energy in the range of 13 to 15 mJ. The pump pulse with the vertical polarization was expanded by a Galilean telescope and split into two beams. One of the two pump beams served as a reference for a Mach-Zehnder interferometer. Another beam was used as the pump beam for OPA. In this experiment, we prepared two sets of pump configurations: a two-beam pump scheme and a random-phased multiple-beam pump scheme which will be described below.
In the two-beam pump arrangement (Experiment 1 in Fig. 1), the circular pump beam was spatially divided to two semicircular beams and combined to the circular beam by using a pair of fused silica prisms (P1, P2). The phase of one of the divided pump beams was adjusted by a pair of fused silica prisms (P3), one of which was mounted on the motorized actuator stage and moved in parallel to the other prism in order to change the optical path length so that the initial optical path would remain unchanged. The phase shift is expressed by Δϕ = 2π(n – 1)δ sinα / λ, where n is the refractive index of the prism, δ is the moving distance, α is the apex of the prism, and λ is the wavelength. The parameters used in this experiment were n = 1.46, α = 30°, and λ = 532 nm. Since the minimum step of the motorized actuator was δ = 30 nm, the phasing control resolution was λ/77. After compounding the divided two pump beams into one beam, the spatial profile behind the aperture with a 9-mm diameter was image-relayed onto a type-I BBO crystal by a telescope with a vacuum tube. The dimensions of the crystal used in this experiment were 5 mm (height) x 5 mm (width) x 18 mm (thickness), and the cutting angle was 22.8°. The beam diameter of the pump laser was matched to that of the signal. The signal and pump pulses were synchronized to achieve temporal overlap in the BBO crystal. A noncollinear geometry was chosen in order to extract an idler beam whose wavelength was 1075 nm. The external angle between the pump and the signal was set to about 2°. The energy of the pump beam was adjusted to be 14 mJ. The conversion efficiency from pump to signal was about 1%.
A series of interferogram of the compounded pump beam with a reference beam taken with the Mach-Zehnder interferometer and the far-field beam patterns of the pump, the idler, and the amplified signal pulse are shown in Fig. 2 . The relative phase of the right semicircular pump beam of interference pattern was adjusted by the prism pair (P3). First, the relative phase of the pump beams was set to be zero [Fig. 2(a)] resulting in a single focal spot as the constructive interference as shown in the far-field pattern (FFP). Then FFPs of the idler and the signal were a single spot. Secondly, the motorized actuator was adjusted at the relative phase of π/2, π, and 3π/2 [Fig. 2(b-d)]. The FFP of the pump beam was no longer a single spot as the two pump beams interfered destructively, causing reduction of the on-axis far-field intensity. However, the FFP of the amplified signal remained unchanged, indicating that the spatial phase of the amplified signal was not affected by that of the pump beam. Instead, the relative phase of the pump beam had been transferred to that of the idler beam as shown in Fig. 2. This is due to the conservation of phase relation in the parametric amplification processes, which is expressed as ϕ p - ϕ s - ϕ i = π/2, where ϕ is the phase and suffixes p, s, and i denote the pump, the signal, and the idler, respectively. Finally, as the relative phase of pump beams reached π [Fig. 2(e)], FFPs were equivalent to those shown in Fig. 2(a). We estimated the Strehl ratio S which is defined as the ratio of peak intensity of the FFP to that of an ideal case. Figure 3 shows the Strehl ratio with respect to the relative phase difference of the pump beams. It was found that the S of the pump and the idler decreased with increasing different relative phase, showing the same tendency, while that of the signal is kept at ≥93%. This proves that the energy of two pump beams can be coherently coupled to a single signal beam without losing beam quality. The OPA efficiency is not affected by the phase conditions (in-phase or out-of-phase) between two beamlets. The next section addresses the deduction that makes it possible to use this concept for beam combining with a number of pump beams.
3. Multiple-beam combining with a random phase plate
In order to produce multiple beams (Experiment 2 in Fig. 1), a random phase plate (RPP)  was introduced to the pump beam. The RPP has a two-dimensional pixel of some basic element shape and the phase of each element is randomly chosen to be 0 or π rad. The RPP used in this experiment was 40 mm x 40 mm containing hexagonal elements with a maximal diameter of about 1.5 mm. Then the pump beam is divided into small beamlets having random phases. Figure 4(a) and (b) show the near-field pattern of the random-phased pump beam and the interference pattern showing 0/π phase distribution, respectively. The focusing spot is the superimposition of all the beamlets diffracted from each pixel, causing a high spatial frequency speckle pattern as shown in Fig. 4(c). The measured FFP of the idler has a speckle pattern [Fig. 4(d)] as the phase distribution of the pump beam is transferred to that of the idler. We observed the change in the speckle patterns of the idler and the pump beams as we moved the RPP to form a different pattern of hexagonal elements. However, the FFP of the amplified signal remained a single spot.
In order to characterize the beam quality of the amplified signal beam, we estimated the encircled energy of the amplified signal with respect to the aperture diameter measured in a unit of Fλ where F and λ are the F–number of focusing optics (929-mm focal length and 2-mm beam diameter) and the wavelength (1053 nm), respectively, as shown in Fig. 5 . In Fig. 5, the encircled energy for the amplified signal beam with two-beam pumping (Fig. 2(a)) and that of seeded signal are also presented for the comparison. An output energy of over 80% was contained within the diffraction-limited area of 2.4 Fλ, assuming a Gaussian beam profile, and the estimated Strehl ratio of the signal beam was 0.96. These results show that the signal beam can be amplified by a number of pump beamlets even with random phase distribution while keeping the beam quality of seeded signal.
The conversion efficiency from pump to signal was slightly (~10%) lower than that measured without the RPP. This is most likely due to the increased beam divergence of the pump beam. Since the beam size of the small beamlets of the RPP was about 0.4 mm on the crystal, the divergence angle was 1.6 mrad. On the other hand, the acceptance angle of the BBO crystal used in this experiment was calculated to be 0.16 mrad. But this effect of beam divergence is relaxed in the actual case using >cm scale pump beams. For scalability of high-energy OPA, a nonlinear crystal with a large size is required. For example, KDP and DKDP (or partially deuterated KDP) crystals are available in much large sizes than BBO crystals . The acceptance angles of 5-mm thick KDP and DKDP are 1.3 mrad and 1.4 mrad respectively. The relatively low pump intensity (< 50 MW/cm2 in this experiment) that results in a low gain is also attributed to low efficiency. However, higher efficiency over 10% can be achieved in a saturated regime with intense pump beam and optimized signal intensity even for KDP, DKDP and partially deuterated KDP crystals .
In summary, we have experimentally demonstrated beam combining by using an OPA process pumped by a random-phased multiple beams. We measured the FFPs of the amplified signal, the pump, and the idler, while controlling and randomizing the relative phase of the multiple pump beams. It was found that the spatial phase uniformity of the amplified signal was not affected by that of the pump beam. Our approach is applicable for more general case that uses a mutually incoherent spatial array of multiple beams as a pump source for OPA, and is very simple because the phase measurement and feed-back control system are not necessary. This scheme provides a significant benefit especially for the development of short pulse generation based on OPA. Since KDP, DKDP and partially deuterated KDP crystals with large apertures are available , a chirped signal pulse can be parametrically amplified by a number of pump beams, while keeping its own phase unchanged. This approach can be applicable for generating a femtosecond laser pulse with an even higher intensity of exa-watts while maintaining good beam quality by increasing the number of pump beams with moderate energy produced by diode-pumped solid-state lasers.
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