Caption for Fig. 1
An exact spatio-temporal simulation of a quasi-continuous plane wave incident on an air-glass interface. The simulation contains evolution of a field distribution in accordance with the Maxwell's equations. Observe the interference structures resulting from the overlap of the incident and the reflected beams. The colors depict various field strengths, the wavelength of the field is chosen to be 3 units, with a Gaussian profile of width 3.0 in the transverse direction. The tail end of the field is continuously updated to obtain a cw field, see the reference below for details. The angle of incidence is 45 deg. The refractive index of glass is chosen to be 2.0. One obtains the angle of refraction of 20.7 deg (in agreement with the Snell's law). The velocity and wavelength of the field in glass are observed to be half of their respective values in air. The above simulation is for the TE mode. Absorbing boundary conditions are applied at the edges of the spatial integration domain.
Reference: W. Harshawardhan, Q. Su and R. Grobe in "Numerical Solution of the Time-Dependent Maxwell's Equations for Random Dielectric Media" -submitted to Physical Review A.
Caption for Fig. 2
An exact spatio-temporal simulation of a pulse incident on a collection of random dielectric ellipsoids. The simulation is undertaken by evolving a field distribution in accordance with the Maxwell's equations. One obtains both the near-field features and the far field effects in this simulation. In contrast to the traditional simulations based on Monte-Carlo technique, our simulations contain all coherent effects arising out of the interplay of phases of the field. The different colors depict various field strengths, the wavelength of the field is chosen to be 3 units, with Gaussian profiles of width 3.0 in the transverse direction and 8.0 in the longitudinal direction. The refractive indices of the ellipsoids vary randomly from 1.1 to 1.6, the radii along the axis of each ellipsoid varies from 0.5 to 1.0. The above simulation is for the TE mode. Absorbing boundary conditions are applied at the edges of the spatial integration domain.
Caption for Fig. 3
An exact spatio-temporal simulation of a quasi-continuous plane wave incident on a collection of random dielectric ellipsoids. The field parameters are identical to Fig.1 and the random medium is same as in Fig.2.