Electro-optical deflectors as a method of beam smoothing for Inertial Confinement Fusion Page: 4 of 9
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field in the EOD has zero value at beam center. If the EOD design does not have this optimal
arrangement then the performance when compared to SSD can be further reduced.
2. ANALYSIS OF THE ELECTRO-OPTIC DEFLECTOR
The EOD principle of operation is to imprint a time varying phase on a beam, in which the phase
also has a linear variation along the deflection direction (Fig. 1).
Peak Phase = +
Figure 1: Electric field and phase variation across the beam of width D in an EOD.
For sinusoidal modulation one has that
EEOD(x,t) = exp[i(2x / D)3 sin wt] exp[ikx(t)x] ,
where -D / 2 x < D / 2, D is the beam width, 3 is the peak phase modulation, and o is the
modulation frequency. In the far field the angular deflection is simply given by
9(t) = kx(t) / ko = ;# sin wt / 7rD ,
where k0 = 2 z / X . The peak angular excursion is given by
0max = i .
Defining the diffraction limited divergence as 2A / D, one sees that the deflector produces a beam
which is 3 / z times diffraction limit (TDL). Note that this result is independent of beam size and
In contrast, consider simple frequency modulation with the same peak phase, (i.e. modulation
EFM (t) = exp[i3 sin ot] .
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Rothenberg, J.E. Electro-optical deflectors as a method of beam smoothing for Inertial Confinement Fusion, article, January 1, 1997; California. (https://digital.library.unt.edu/ark:/67531/metadc684113/m1/4/: accessed March 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.