Goos-Hanchen effect for optical vibrational modes in a semiconductor structure

We study the tunneling of optical vibrational modes with transverse horizontal polarization that impinge, at a given angle, on a semiconductor heterostructure. We find a large influence of the Goos-Hanchen shift on tunneling times. In particular, a Goos-Hanchen shift larger than the barrier thickness is reported for the first time. The relation between Goos-Hanchen and Hartman effects is also discussed. The identity that equals the dwell time to the sum of transmission and interference times, previously derived for one-dimensional tunneling problems, is extended to the two-dimensional case. Closed-form expressions are developed for the relevant quantities. Instead of using the standard approach, the interference time is computed from the vibrational energy density. The present study could be useful for the design of semiconductor devices.