Phase Conjugate Laser Optics

Chapter 5.5.3.2 - Phase-locking performance

5.5.3.2   Phase-locking performance   A straightforward way of visualizing
the phase locking process for the four separate amplifier beamlets incident on the
SBS mirror is to consider them as one beam having abrupt phase transitions in the
wavefront profile located at the border between each beamlet. The SBS mirror
conjugates the overall wavefront that includes the thermally induced distortion
profile within each beamlet as well as the piston offset in phase between each
beamlet. The great power of this technique lies in the correction of the piston phase
offsets between each beam without the need to interferometrically control the
pathlengths in the amplifier arms. If there were no Brillouin–Stokes shift in the
output from the SBS phase conjugator, the phase-locking performance would be
theoretically independent of the four propagation pathlengths through the amplifier
arms, except for extreme cases in which temporal overlap of the pulses in the SBS
cell would be lost. However, because of the Stokes frequency shift, the four
pathlengths must be matched to some degree. The constant piston phase offset θ in
the output between two given beamlets is given by [50]

 

where ΔL is the pathlength difference between the beamlets, vB is the Brillouin
frequency shift, and c is the speed of light. In the case of the 90 atm of N2 used here,
the Brillouin shift is approximately 750 MHz. This means that to maintain less than
a one-tenth wave piston error between the beamlets, the pathlength in each amplifier


Figure 5.32. An illustration of the effect of pathlength differences in the amplifier beam trains using two adjacent beamlets. As shown, it is necessary to match the propagation distances to <2 cm when using high pressure nitrogen as the SBS medium. The 15 cm pathlength difference shown in Figure (a) corresponds to an 0.8pi fixed phase offset between the beamlets.

beam train must be matched to within 40 mm. The only independent adjustment of
pathlength, as shown in the optical layout of Fig. 5.27, is provided by the set of
mirrors that take the beam that emerges from each zigzag amplifier head and directs
it back into the slab for the counterpropagating path. Since each beam makes two
passes through the regenerative amplifier loop on the way to the SBS mirror (for a
total of four amplifier passes), the differences in propagation lengths for each beam
line needs to be less that 20 mm, an easily achievable goal.

Figure 5.32 shows the far-field patterns of two adjacent beamlets for different
relative pathlengths. The high-power output beams in the far field have near
“textbook” profiles as would be expected from two temporally phase-locked beams. At
a 15-cm pathlength difference, the two beamlets are out of phase by nearly one-half
wave, resulting in an irradiance null on axis. As the pathlength difference approaches
zero, a clean central lobe is achieved. In practice, this is the technique used to optmize
the relative beam paths. The center, left, and right pairs of beamlets are sequentially
examined and optical pathlength adjustments are made to achieve a symmetrical
optical distribution in the far field for each pair.

When all four amplifiers are operated simultaneously, the phase-locked beamlets
coherently sum in the far field to produce a single central lobe with one-fourth the
divergence of each individual beamlet. A progression of one, two, three, and four 25-J
beamlets at 1053 nm is shown in Fig. 5.33. Although the phase-locking performance is
good, the previously described technique of optimizing the individual propagation


Figure 5.33. Measured far-field distributions for one, two, three, and four beamlets. The coherent combination (phase-locking) of the four beamlets in the far field generates a divergence profile 4x narrower than that for an individual beamlet.

lengths had not been implemented when these data were collected, so some residual
asymmetry can be observed in the profiles. Later measurements at 527 nm show a
further reduction in the relative piston phase offset errors (Fig. 5.36).

 

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