Abstract

Light propagation in photonic structures has provided in the past few years a conceptually and experimentally relevant model to study the optical analogue of many fundamental quantum mechanical effects. Among others, we just quote the optical analogs of Bloch oscillations, Zener dynamics, coherent destruction of tunneling and suppression of quantum diffusion, quantum billiards dynamics and quantum chaos. Photonic systems, as compared to other physical systems, offer the advantages of enabling a direct visualization of the wave packet dynamics in coordinate space, avoiding dephasing and decoherence effects, and easily engineering the system. Recently, an optical waveguide-array system has been proposed to test deviations of the Fermi golden rule in photon tunneling and to provide an optical analogue of the quantum Zeno effect [1]. Here we show that engineered waveguide-based systems can be designed to control photon tunneling decay, providing an experimentally accessible laboratory tool to test the universal features of dynamical control via parametric modulations recently proposed for quantum mechanical decay [2], By a proper design of the structure, acceleration or deceleration the tunneling decay rate, as well as suppression of fractional, can be achieved. The optical system under investigation is similar to the one considered in [1] and consists of a single-mode optical waveguide side-coupled to a semi-infinite periodic waveguide array [Fig. 1(a)]. The boundary waveguide is assumed to be weakly coupled with the array with a coupling strength which varies along the propagation distance. This is achieved by slowly modulating the distance a₀ of the waveguide from the array is a periodic fashion. Using a variational analysis, we show that photon tunneling out of the boundary waveguide is fully analogous to the decay of an unstable discrete state embedded in a tight-binding continuum with a modulated coupling strength Δ₀(z) arising from periodic bending of the boundary waveguide [Fig. 1(b)]. The mechanism of tunneling decay control by modulation of the coupling Δ₀(z) can be described by a canonical fonnulation of the tunneling process using the Hamiltonian formalism of Ref. [2], The photon decay via tunneling in the boundary waveguide can be written in the universal form exp[−Q(z)R(z)], where R(z) is the effective decay rate and Q(z) an effective interaction length. A proper design of the waveguide system can lead to either a deceleration or an acceleration of the decay rate, as shown in Fig. 2. The acceleration and deceleration of photon tunneling is clearly illustrated in the insets of Fig.2(b), where the behavior of light intensity trapped in the boundary waveguide versus the effective interaction length Q is plotted (solid curves), together with the corresponding behavior in case of a straight waveguide placed at the minimum distance reached in the oscillation period (dashed curves).

© 2007 IEEE