Phase Conjugate Laser Optics

Chapter 5.4.3 - Long-pulse SBS phase conjugation

5.4.3 Long-pulse SBS phase conjugation

A challenging aspect of operating an amplifier system with SBS phase conjugation
for pulse durations of 500–1000 ns is the power threshold requirement of the phase
conjugate mirror. It was found that an SBS medium of either high-pressure nitrogen
(N2, ~ 90 atm) or xenon (Xe, ~ 50 atm) produces good results for microsecond-
duration input pulses. Ultrahigh-purity (99.999%) N2 was chosen for its low cost,
ready availability, and observed resistance to optical breakdown.

5.4.3.1   The SBS loop geometry   The measured power threshold of
>400 kW for a simple-focus N2 SBS cell and the input pulse rise times needed
for this laser system was found to be too high to generate the desired pulse durations
in the amplifier output. The SBS cell receives an incident energy of >1 J under the
operating conditions for 30-J / pulse extraction. This energy would easily exceed the
SBS threshold if delivered in a rectangular 1-μs pulse. However, the temporal


Figure 5.16. A comparison of (a) the simple single-focus SBS phase conjugate mirror with (b) the three-pass SBS loop geometry. The first and third foci in the SBS medium are overlapped, resulting in a self-pumped four-wave mixing interaction. The loop provides a lower nonlinear threshold and increased stability in the pulse shape and temporal phase.

profile at the phase conjugate mirror exhibits a large ratio in power from the end of
the pulse to the beginning due to the required exponental buildup from the oscillator.
This leaves a conventional, single-focus SBS mirror well below threshold for the
first part of the pulse.

In order to lower the power threshold of the SBS phase conjugate mirror, a three-
pass loop geometry was adopted [47]. This optical arrangement is compared
schematically to the single focus SBS cell in Fig. 5.16. In the loop configuration, the
light transmitted through the SBS cell is recollimated with a second lens of equal
focal length. A mirror then directs the beam back through the SBS cell where it
comes to a second focus. A second mirror sends the beam through the cell for a third
and final pass. In this third pass the focal waist is overlapped with that of the first
pass. These three consecutive optical foci extend the SBS nonlinear gain path for the
long pulse input, reducing the power threshold by almost a factor of three. Figure
5.17 is a plot of the output Stokes power versus incident laser power for the single
focus and the loop configurations. These were measured using input pulses with
FWHM durations of 200 ns. As can be observed by the hysteresis in this data, there
is a significant difference between the power threshold seen by the leading edge of
the pulse and the steady state threshold observed at the end of the pulse. This is due
to the transient build-up of the SBS acoustic grating and will be discussed in more
detail in the following section.

There is significant benefit of the SBS loop architecture in addition to the
reduction of the SBS threshold. As described in Ref. 47, once threshold is reached,


Figure 5.17. SBS output power versus input power measured for the SBS single-focus and loop geometries. 400 mJ pulses with a pulse duration of 200 ns FWHM were used. The single focus curve was collected by simply blocking the transmitted beam after the SBS cell, interrupting optical feedback to the loop. Both the decreased threshold and increased temporal stability for the loop geometry are readily apparent.

the overlapping first and third foci in the SBS cell generate a four-wave mixing
interaction that serves to strongly stabilize the Stokes return from the phase
conjugate mirror. The effect of this interaction is to feed a portion of the generated
Stokes signal back through the loop and into the phase conjugated wave. The
stimulated scattering system then does not rely on input light scattered from acoustic
noise at focus to sustain the Stokes return after the SBS threshold is reached. This
increased stability is readily apparent upon comparing the input/output power plots
for the single focus cell and the loop in Fig. 5.17. The power fluctuations observed in
the single-focus SBS mirror were not reproducible from shot to shot but were always
of comparable magnitude to the curve shown. This data were collected by simply
placing a block in the beam after the first pass through the SBS cell, reducing the
phase conjugator to a simple single focus. Besides the significant decrease in the
power threshold, the Stokes power fluctuations are dramatically reduced when the
loop is unblocked. The four-wave mixing interaction also plays a crucial role in
maintaining temporal phase stability in the laser amplifier output, as will be
described in the upcoming discussion on coherence length.

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