  Pulse walk-off in the process of sum frequency generation in a nonlinear
$\chi^{(2)}$ crystal is shown to be responsible for pulse jittering which is
reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely
moving Dirac particle. An analytical expression for the pulse center of mass
trajectory is derived in the no-pump-depletion limit, and numerical examples of
Zitterbewegung are presented for sum frequency generation in periodically-poled
lithium niobate. The proposed quantum-optical analogy indicates that frequency
conversion in nonlinear optics could provide an experimentally accessible
simulator of the Dirac equation.
