Frequency Conversion Theory in Support of the
National Ignition Facility
Peter W. Milonni


Various target simulations and experiments indicate that the most desirable laser wavelengths 
for inertial confinement fusion lie near 0.3 mm, whereas the high-energy glass laser systems 
designed for the National Ignition Facility (NIF) emit near 1.05 mm. A crucial part of NIF 
therefore centers around the frequency tripling of the 1.05 mm radiation. The NIF baseline 
design involves two KDP (potassium dihydrogen phosphate) crystals for this purpose. Laser 
radiation incident on the first crystal is doubled in frequency via the nonlinear susceptibility 
of KDP, and in the second crystal the residual fundamental mixes with the second harmonic 
via this same nonlinearity to generate the desired third harmonic (Figure 1).

This design was based on simplified theoretical analyses performed at several laboratories, 
and on experimental confirmations that third-harmonic conversion efficiencies on the order 
of 70% could in fact be realized. However, the analyses were based on highly simplied 
assumptions such as perfect plane-wave and monochromatic fields, and the experiments were 
somewhat artificial in that they were designed to meet these idealized conditions as closely as 
possible. NIF fields will have both phase and intensity variations in space and in time, and our 
work over the past three years has focused on more realistic simulations of experiments at 
Lawrence Livermore National Laboratory (LLNL), as well  as the design of more efficient 
frequency conversion schemes under conditions of practical interest for NIF.

We have developed the theory and computer codes accomodating arbitrary spatial and 
temporal variations of the fundamental and harmonic fields. Comparison of the code 
predictions with measured LLNL harmonic conversion efficiencies showed excellent 
agreement except at the highest field intensities, where the predictions for frequency tripling 
efficiencies were typically 10-20% higher than was measured. However, we found that the 
addition of small phase ripples across the incident fundamental wavefront had the effect of 
lowering the high-intensity conversion efficiencies while leaving the lower-intensity 
predictions essentially unaltered (Figure 2). Interferometric analyses of the KDP crystals 
showed that machining and polishing "grooves" on the crystal surfaces were of approximately 
the amplitude and period required to translate effectively into the sort of phase ripples we had 
postulated. Subsequent experiments at LLNL introduced deliberate phase ripples on the 
incident wavefront and corroborated the essential predictions of our code and also an 
approximate perturbation-theoretic analysis of phase ripples.

We have suggested three- and four-crystal designs in order to efficiently triple fields with the 
temporal intensity profile believed to be most propitious for NIF, as well as fields with large 
bandwidth produced by phase modulation. The latter is particularly relevant for direct-drive 
ICF. Three-crystal experiments at LLNL have produced conversion efficiencies in agreement 
with theoretical expectations, and large-bandwidth experiments are expected to be undertaken 
in the near future.


Figure 1:  Type I/type II scheme for third-harmonic generation.  o and e denote polarization 
directions for ordinary and extraordinary waves.

Figure 2:  Comparison of theory to experimental data points (D). The dashed curve is the 
theoretical prediction for the third-harmonic conversion efficiency versus input intensity to 
the doubling crystal, assuming a uniform phase profile, whereas the solid curve includes small 
phase ripples on the input field.