Evanescent Intensity Of A Focused Gaussian Light Beam Undergoing Total Internal Reflection In A Prism
We calculate the evanescent electric field and intensity profile of a circular Gaussian light beam when it is focused by a lens, enters a spatially finite prism, and is totally internally reflected at a planar interface of the prism and a dielectric substance. The electric field and intensity at the interface depend on the indices of refraction of the prism, the 1 /e2 width, wavelength, and polarization of the incident beam, the focal length and exit pupil of the focusing lens, the distance from lens to prism, the shape and size of the prism, and the beam's angle of incidence. Our calculations show the evanescent intensity profile to be well approximated by a Gaussian shape for many practical realizations of the lens and prism optical apparatus. The 1 /e2 width of the profile appears to depend primarily on the beam's 1 /e2 width, the ratio of the focal length of the lens to this width, and the incidence angle. The polarization of the evanescent electric field is approximately perpendicular to the incident plane of the beam center for an incident beam polarized in this direction. It is within the incidence plane, but rotates with time and position along the interface, for an incident beam polarized in the incidence plane of the beam center. The penetration depth (into the dielectric) does not have a strong dependence on position within the illuminated area. Experimental measurement of the intensity profile in one optical geometry agrees well with our theoretical predictions.