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Zitterbewegung of optical pulses in nonlinear frequency conversion
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abstract
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.
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