Zitterbewegung of optical pulses in nonlinear frequency conversion

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.

to be published in Journal of Physics B: Atomic, Molecular & Optical Physics

References in corpus (9)

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Cited by in corpus (4)

• Relativistic quantum mechanics with trapped ions
• Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures
• Different models of gravitating Dirac fermions in optical lattices
• Topological aspects in nonlinear optical frequency conversion