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Octave output of lossless dielectric region, and lossy layer with impedance matched to lossless dielectric

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Each of the coloured horizontal lines represent the state of the propagation of the wave in time (a snapshot of the field).  The wave starts from time 0 with frame number 0.  Each line(frame) occurs 10 time steps after the earlier line.  This means that at line (frame number) 10, the time is 100 time steps after line 0.  A Total Field/Scattered Field (TFSF) boundary is present at spatial index 50.  This allows the source (a gaussian pulse) to propagate in only one direction to the right.  The space from 0 to 100 is free space.  The space from 100 to 180 is the lossless dielectric.  Hence, there is reflection towards the left from spatial index 100.  The space from 180 to 200 is a lossy dielectric with its impedance matched to the lossless layer.  Hence, there is no reflection at spatial index 180.  The pulse is also absorbed in the lossy media.  Reference: John B. Schneider, "Understanding the Finite-Difference Time-Domain Method", April 5, 2017
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A FDTD example in Python

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This is an example of a FDTD simulation of a one dimensional light wave in Python.  The initiating waveform is a sine wave.  The electric field is in cyan colour, while the magnetic field is in magenta colour.  The perfection of this waveform is due to the boundary condition, which feeds one end of the waveform into the other end, thereby enabling the continuity in wave propagation.  Effectively, this waveform is just repeated endlessly.  Practically, this perfection does not last.  It maintains its continuity from a few seconds to about 10-15 minutes depending on the beta used. Reference: Computational Physics: Problem Solving with Python, 3rd Edition, Rubin H. Landau, Manuel J Páez, Cristian C. Bordeianu
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