Transmission of Electromagnetic Waves through a Metallic Slab. III. Effect of Boundary Scattering on Helicon Transmission near Cutoff

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Abstract
This paper, like the two in this series which precede it, is concerned with electromagnetic wave propagation under conditions where the relation between the currents in the medium and the electric field driving them is nonlocal because the electron mean free path is comparable to the length over which the fields change. For this case, both the boundary conditions on the electrons reaching the surface of the slab and the more familiar boundary conditions imposed upon the fields are important. Our concern here is the effect of the electronic boundary conditions on helicon wave propagation; in particular, on the way in which Doppler-shifted cyclotron resonance (Dscr) damps the helicon wave as the magnetic field is lowered to the Dscr threshold. Our findings may be summarized briefly as follows: At large magnetic fields, where the helicon wave is relatively undamped and exhibits standing-wave resonances, the assumption of diffuse electronic surface scattering decreases the transmission below the amount calculated assuming specular surface scattering. In addition, it leads to a softening of the resonances (decrease in the standing-wave ratio) relative to the resonances calculated assuming specular electronic surface scattering. This softening decreases as the magnetic field is raised, i.e., as the conductivity becomes local; and in fact, in the local limit, specular and diffuse transmission are identical. As the field is lowered, more of the incident energy goes into the single-particle excitations when the surface scattering is diffuse than when it is specular. Finally, when the field reaches a value close to the Dscr cutoff, the specular calculation exhibits an extra peak absent from the diffuse. The amplitude of this peak, however, is quite low because of its proximity to cutoff. Experimental data are not yet available to determine whether surface scattering is predominantly diffuse or predominantly specular, but the calculations presented here do allow one to determine the mean free path by fitting the shape of the transmission curves near Dscr.