Phase Conjugate Laser Optics

Chapter 5.3.4.2 - Output beam quality

5.3.4.2   Output beam quality   In order to extract high-beam-quality output
from the phase conjugated amplifier system, a high-quality input pulse must be
provided. In ideal operation, the wavefront reversal achieved in the SBS phase
conjugator allows the spatial phase distribution of the input beam to be reproduced
in the amplified output beam. Using the previously described single-frequency self-
seeded Nd:YLF oscillator, excellent seed beam quality has been measured with less
than 1.1 times the diffraction limited divergence. The 25-mJ output of this oscillator,
however, must be further amplified and anamorphically expanded to provide the
~ 60-mJ, 8- ×120-mm input to the amplifier system. The divergence of this injected
pulse is increased to 1.25 times the diffraction limit in this process, primarily due to
optical aberrations in the Nd:YLF preamplifier.

As the pulse repetition frequency of the laser system is increased, the thermal
aberrations in the glass amplifier significantly increase output divergence when the
amplifier is operated in the unidirectional uncorrected mode without the SBS phase
conjugate mirror. The measured output divergence versus repetition rate is shown in

Figure 5.8. The measured output divergence in the narrow beam dimension versus repetition rate for 25-J output pulses. At 3 Hz, with an average flashlamp power of 7.5 kW, the divergence is increased to almost 10 times the diffraction limit.


Figure 5.9. A comparison of the far-field profiles measured at the focus of a 120-cm focal length lens for 3-Hz, 75-W operation (a) without and (b) with SBS phase conjugation. Plot (c) overlays horizontal cross sections for each case.

Fig. 5.8 for 25-J output pulses. At 3 Hz with an average output power of 75 W the
divergence in the narrow beam dimension is increased to almost 10 times the
diffraction limit. However, when the amplifier system is configured as described
previously with an SBS phase conjugator, the divergence does not measurably
increase up to the maximum achievable pulse repetition frequency. Figure 5.9
compares the corrected and uncorrected far field profiles measured at the focus of a
120-cm corrected aspherical lens for 3-Hz, 75-W operation. With the phase
conjugator, the width of the far-field pattern is dramatically reduced to a single
central peak with small side lobes characteristic of the angular distribution from a
near uniformly filled aperture.

The 8 × 120 mm output of the amplifier system is characterized by smooth
reproducible beam profiles. Figure 5.10 shows (a) a CCD image of the near-field
output imaged at the external relay plane conjugate to the amplifier aperture (Fig.
5.10a) and the far field recorded at the focus of a lens (Fig. 5.10d). In order to
quantitatively evaluate the measured divergence of the amplifier output, the
theoretically expected diffraction-limited divergence of a beam having the observed
irradiance spatial distribution must be determined. A two-dimensional super-
Gaussian distribution is first fitted to the near field profile. A comparison of this fit to
line-outs of the measured profile is shown in Figs. 5.10b and 5.10c. The results of
this numerical fit is then Fourier-transformed to generate an expected far-field
distribution given a perfectly uniform phase profile. Figures 5.10e and 5.10f plot the
predicted and experimentally measured far-field patterns for the horizontal and
vertical dimensions. It is found that if the divergence scale for the measured data is
reduced by a factor of 1.25, nearly exact overlap of the calculated and measured


Figure 5.10. (a) Profile of the near-field imaged at the external relay plane conjugate to the amplifier aperture. Figures (b) and (c) show vertical and horizontal line-outs of this profile, respectively. The smooth curve plotted with each line-out is the result of a super Gaussian fit to this near-field profile. (d) Profile of the far field measured simultaneously with the near field profile. A comparison between (e) vertical and (f) horizontal line-outs of this profile and the Fourier transform of the super Gaussian fit of the near-field profile is shown. It is found that if the divergence scale for the measured data is reduced by a factor of 1.25, nearly exact overlap of the calculated and measured profiles results.

profiles results. It is significant to note that this is the same divergence measured for
the input pulse to the amplifier as illustrated by the overlay of the far-field profiles of
the input and amplified output beams in Fig. 5.11a. It can be therefore concluded that
the beam quality of the high power output is presently limited by that of the low
power input.

The results of the analysis of the far-field images indicate that there is a far-field
output lobe whose width is 1.25 times that expected for a diffraction-limited beam.


Figure 5.11. (a) A comparison of horizontal line-outs of the far-field profiles of the low-energy input pulse (solid line) and the amplified output pulse (dashed line). The divergence is unchanged to within the uncertainty of the experimental measurement. (b) Transmission of a 0.5-mm aperture placed at the focus of a 120-cm focal length lens. The expected transmission of this “bucket” for a 1.25x diffraction-limited beam was calculated to be 96%. A transmission of ~92% was measured across the range of output energies up to 25 J.

However, it is also important to determine what fraction of the measured output
energy is contained in this narrow peak. There is the need to rule out the possibility
that high spatial frequency irradiance or phase modulation is scattering a significant
but undetected portion of the radiation into larger divergence angles. The dynamic
range of the CCD cameras is such that a very low irradiance distributed evenly
across the image background could fall below the signal-to-noise detection limit of
the camera but still account for a significant fraction of the total output power. A
straightforward measurement that can be made in this regard is the transmission of
an aperture placed at the focus of the analysis lens. In this case an aperture was
chosen that was 0.5 mm in diameter, corresponding approximately to the distance
between the first minima in the horizontal dimension of the measured far field
profile. The expected transmission of this “bucket” for a 1.25× diffraction-limited
beam is calculated to be 96%. As illustrated in Fig. 5.11b, a transmission of ~ 92%
was measured across the range of output energies up to 25 J. This 5% reduction in
the expected transmission is reasonable based on the fact that the fit between the
super-Gaussian and measured near-field profiles shown in Figs. 5.10b and 5.10c is
not perfect. The small-scale irradiance modulation on the beam profile is expected to
contribute to a small reduction in Strehl, as was observed in the measurements.

 

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