Simulation of ultrafast 2D light pulse

An analytical solution of the general boundary-value problem for a bidirectional wave equation for the propagation of the TE-wave is found. The finite difference solution of the wave equation is used to simulate the 2D light pulses in a planar waveguide with the "electric walls". The numerical and analytical solutions coincide with an unprecedented accuracy of 0.0005%. The finite difference solution of the wave equation is by an order of magnitude more accurate than the finite difference solution of Maxwell's equations obtained by the FDTD-method using the Fullwave software with the same parameters. It is numerically shown that the calculated and theoretical Fresnel coefficients coincide with the accuracy of 0.47% for the reflected and transmitted ultrashort light pulses (? 4 fs) in a glass plane-parallel plate. The transmitted pulses are found to broaden more than the reflected ones (by 3 fs, on average).