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Quantum mechanics in periodically curved optical waveguides

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Abstract

The analogy between wave optics and wave mechanics has been often used to study beam propagation in graded-index slab waveguides, fibers and photonic crystals, providing in the optical context an experimentally venhable framework to test many quantum-mechamcal eflects, such as quantum tunnelmg, quantum chaos, and of wave propagation properties m wavegmde arrays. The analogy between the dynamics of electrons m crystals and photons in periodic dielectric structures has lead to the relevant recent developments in the field of photonic crystals. In this contribution we study theoretically the properties of beam propagation in a periodically-curved optical waveguide beyond the usual perturbative approach [l] and show the existence of unusual and exotic eflects, such as dynamic beam sphttmg, dynamic directional couplmg, and reduction of radiation losses, which are fully similar to the phenomena of dynamic wave function stabilization, iomzation quenchmg and wavepacket dichotomy encountered m multiphoton radiation-matter processes with super-mtense and high-frequency laser fields [2,3]. The analogy stems from the formal equivalence of the beam propagation equation, in the scalar and paraxial approximations, with the one-electron time-dependent SchrOdinger equation in the Kramers-Henneberger reference frame [2].

© 2004 Optical Society of America

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