Abstract
Theoretical models of photon traversal through quarter-wave dielectric stack barriers that arise due to Bragg reflection predict the saturation of the propagation time with the barrier length, known as the Hartman effect. This saturation is sensitive to the addition of single dielectric layers, varying significantly from sub-luminal to apparently super-luminal and vice versa. Our research tests the suitability of photonic bandgaps as an optical model for the tunneling process. Of particular importance is our observation of subtle structural changes in dielectric stacks drastically affecting photon traversal times, allowing for apparent sub- and super-luminal effects. We also introduce a simple model to link HOM visibility to wavepacket distortion that allows us to exclude this as a possible cause of the loss of contrast in the barrier penetration process.
Highlights
The original prediction of Hartman [1] indicates that the asymptotic saturation of the transit time for an opaque barrier is smooth, it has been shown [2,3,4] that for nonevanescent barriers such as dielectric stacks this is no longer true
We study single photon traversal in stop bands of 1D Bragg gratings made of alternating quarter wave layers of higher (H) and lower (L) refractive index dielectrics
The theoretical treatments of structures via characteristic matrix approach [15] shows that different structures yield very different traversal times
Summary
The original prediction of Hartman [1] indicates that the asymptotic saturation of the transit time for an opaque barrier is smooth, it has been shown [2,3,4] that for nonevanescent barriers such as dielectric stacks this is no longer true. While there have been measurements of optical traversal times with classical optical or RF pulses, the only measurement for single photons was presented by Steinberg et al [5] They observed an apparent superluminal propagation for photons that traversed a dielectric bandgap structure. The measurements were made, on a set of similar dielectric stacks - ones that varied only by adding more high- and low-index layers in pairs It has been pointed out [8], that a model based on bandgap properties of a dielectric quarter-wave-stack is equivalent to quantum mechanical tunneling, but only if a slowly varying envelope approximation (SVEA) is applied. In our experimental work we confirm that minute changes to a dielectric stack yield dramatic changes in traversal time and put an upper bound on photon wavefunction distortion via barrier traversal
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