OverviewThe aliasing effect of the discrete Fourier transform provides a convenient method for modeling hollow waveguides with reflective walls. Reflective walls can return light to the optical path, while aliasing causes the spillover light field to bend back into the sampled light field in the opposite direction. If the light field distribution is an even function, then the foldback acts like a reflection effect. We can convert an arbitrarily shaped light field distribution into an even function by placing the matrix corresponding to the light field in the upper left quadrant of a matrix twice the size, and then filling the matrices of the other three quadrants with the mirror image of the upper left quadrant matrix. In this way, the entire matrix represents an even function. The aliasing effect of this even function allows the reflective wall to be modeled correctly. System DescriptionThis example focuses on the use of the copy and flip commands. When the beam is eccentric and obliquely incident into the waveguide, the incident beam will be reflected sequentially on the reflection wall of the waveguide, and the distribution of the beam will gradually change with the number of reflections and diffraction effects. 
Figure 1Schematic diagram of the simulationSimulation resultsFigure 2Initial flat-top beam distribution with a tilt factor
Figure 3The beam transmission to the upper right corner meets the reflection wall on the right, Figure 4The beam is moving away from the right wall and towards the top wall
Figure 5The beam is reflected off the top reflection wall in Figure 6The beam of light bounces off the top wall and propagates to the left wall
Figure 7The beam completely leaves the top wall and travels towards the left wall
Figure 8The beam encounters the left reflective wall
Figure 9The beam is moving away from the left wall and towards the bottom wall
Figure 10The beam is moving away from the bottom reflector wall towards the initial position
Figure 11The beam has reached its initial position, but has broadened so much that it has hit the reflective wall on the right.