Zitterbewegung of optical pulses in nonlinear frequency conversion

Abstract

Pulse walk-off in the process of sum frequency generation in a nonlinear χ(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 centre of mass trajectory is derived in the no-pump-depletion limit, and the 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.