The Hartman effect describes how the delay time for a quantum tunneling particle is independent of the thickness of the opaque barrier.
The Hartman effect thus leads to predictions of anomalously large, and even superluminal tunneling velocities in the limit of thick barriers.
They also found that the measured group delay was shorter than the transit time L/c for a pulse travelling at the speed of light c over the same barrier distance L in vacuum.
[5] At optical frequencies the electromagnetic analogs to quantum tunneling involve wave propagation in photonic bandgap structures and frustrated total internal reflection at the interface between two prisms in close contact.
[8] They found that the measured group delay was independent of the number of layers, or equivalently, the thickness of the photonic barrier, thus confirming the Hartman effect for tunneling light waves.
In another optical experiment, Longhi, et al. sent 380-ps wide laser pulses through the stop band of a fiber Bragg grating (FBG).
The inferred tunneling group velocity was faster than that of a reference pulse propagating in a fiber without a barrier and also increased with FBG length, or equivalently, the reflectivity.
In a different approach to optical tunneling, Balcou and Dutriaux measured the group delay associated with light transport across a small gap between two prisms.
Yang, et al. propagated ultrasound pulses through 3d phononic crystals made of tungsten carbide beads in water.
[12] They found that inside the stop band the acoustic group delay was relatively insensitive to the length of the structure, a verification of the Hartman effect.
In 2002 Herbert Winful showed that the group delay for a photonic bandgap structure is identical to the dwell time which is proportional to the stored energy in the barrier.