TIR Effects at a Lossy Incident Medium Interface

Nov 12, 2014

The contour plots below compare the net 2D transverse electric field profiles for an S polarized plane wave incident from the upper left in a lossless versus a lossy medium. Plots are shown for angles less than and greater than the nominal total-internal-reflection angle (41.8° for the lossless N1=1.5 N2=1.0 interface). The pattern in N1 (upper incident medium) is caused by interference between the incident and reflected fields. A bulk plane wave (without reflection) for the 50° case is also shown to help visualize the incident electric field without the interference effect of the reflected wave. Note that when N1 is lossy and N2 lossless, the amplitude of the field in N2 GROWS in a direction normal to and away from the interface and the effect becomes stronger with increasing angle of incidence. However, if N2 is lossy, at small angles of incidence, there will always be exponential DECAY of the field in N2 in a direction normal to the interface and this complex behaviour may change to exponential GROWTH as the angle is increased.

The 2D display below maps a region of +/- four vacuum wavelengths (N2) in size with an incident field amplitude of 1.0 centered at the point x=z=0. The Ey value scale is broader for the lossy incident case to show the larger range of field values of the incident (and refracted) attenuating field amplitude:

N1 Lossless

   θ=40°    N1=1.5    N2=1.0

   θ=50°    N1=1.5    N2=1.0    TIR

   θ=50°    N1=1.5    N2=1.5

N1 Lossy

   θ=40°    N1=(1.5 - j0.05)    N2=1.0    (details)

   θ=50°    N1=(1.5 - j0.05)    N2=1.0    TIR

   θ=50°    N1=(1.5 - j0.05)    N2=(1.5 - j0.05)