Delay time measurements in a diffraction experiment: A case of optical tunneling

In an interesting paper published in 1949, Schaffner and Toraldo di Francia @1# reported experimental proof of the existence of evanescent ~surface! waves generated by diffraction. Working at the scale of microwaves, they found that the experiment was easier and the results were more accurate, compared to those that had previously been performed in the optical range @2#. Microwaves of about 3 cm wavelength were used in connection with a grating made of metal strips. The period of the grating was chosen so that all the diffracted waves except the zero-order one were surface ~evanescent! waves attenuated along the direction perpendicular to the grating. One of the first-order waves was transformed into an ordinary wave by refraction on a paraffin prism ~see Fig. 1! and then revealed by means of a receiver. The measured power of the wave, as a function of the distance of the prism from the grating, gave the value of the attenuation constant of the surface wave as predicted by the theory. We have performed a similar experiment with the aim of measuring the delay time for evanescent waves generated by diffraction. This represents a case of optical tunneling in which the duration of the process is still an open and debated question @3,4#. At the theoretical level there is complete acceptance of the idea that waves can never yield actual superluminal signals. However, increasingly imaginative experiments with evanescent waves, in tunneling processes @5–7# and in short-range propagation @8#, have been probing this idea, for example, in forcing reexamination of just what constitutes a signal. As a result there has recently been extensive discussion of these issues @9–13# including the search for an appropriate interpretational model @14–16#. In this paper we report a particularly convenient way of generating evanescent waves—as indicated, it was in this way that exponential decay of the wave amplitude for evanescent waves was first demonstrated in a diffraction experiment. The experimental setup is shown in Fig. 1 and includes, besides the grating and the prism, two horn antennas, one as a launcher and the other as a receiver. The latter is followed by a slotted waveguide where the signal picked up is combined with a reference signal derived from the generator. In this way we can make accurate phase measurements through the detection of the probe position corresponding to a minimum ~which exactly indicates the opposition of phases of the two waves! of the amplitude of the resulting signal @17#. The