This BeamLab demo shows the beam propagation through a Mach-Zehnder waveguide modulator while a phase shift of π is applied through a refractive index change to one of its arms.

**BeamLab demo script: **mach_zehnder_modulator.m

The propagation structure consists of single-mode waveguides with square shaped cores and rounded corners. A single waveguide at the input is split up into two equivalent waveguides sufficiently separated from each other to act as uncoupled interferometer arms. Depending on the switching status of the modulator, the refractive index of both core and cladding can be modulated in one arm (not shown in the index contour plot). The strength of the index modulation together with the length of the interferometer arm is chosen such that the light has a phase shift of *π* at the point where the interferometer arms merge again to form the single output waveguide.

# Mach-Zehnder modulator switched off

This video shows how the intensity distribution changes along the propagation distance *z* when the modulator is switched to the state of minimum throughput. The two figures on the left depict the refractive index distribution as a two-dimensional cross section *n*(*x*,*y*) (top left) and a one-dimensional index distribution *n*(*x*) at *y* = 0 µm (bottom left). The two figures on the right show the two-dimensional intensity distribution *I*(*x*,*y*) (top right) and the one-dimensional intensity distribution *I*(*x*) at *y* = 0 µm (bottom right). All distributions are normalized to the input intensity and displayed on a logarithmic scale from -20 dB to 0 dB. The white lines in the top left figure indicate the locations of the waveguides.

After the calculation has finished, the intensity distribution as a function of propagation distance *z* is plotted. The figure above shows the intensity distribution *I*(*x*,*z*) at *y* = 0 µm when the modulator is switched to the state of destructive interference at the output arm, i.e., the state of minimum power throughput. The white lines indicate the location of the waveguide.

This figure shows a compact three-dimensional view of stacked plots, each portraying the intensity distribution *I*(*x*,*y*) at different distances *z*.

Finally, the power in each core can also be independently traced during a calculation. In this figure, the blue curve represents the power in the arm located in the positive *x* region calculated over a circular area of the same extension as the waveguide core. The red curve represents the power in the second interferometer arm. Note that in this case the red curve is only displayed over the region where the waveguides centers do not overlap.

# Mach-Zehnder modulator switched on

This video shows how the intensity distribution changes along the propagation distance *z* when the modulator is switched to the state of maximum throughput.

Here again, the figure above shows the intensity distribution *I*(*x*,*z*) at *y* = 0 µm when the modulator is switched to the state of constructive interference at the output arm, i.e., the state of maximum power throughput.

This figure shows a compact three-dimensional view of stacked plots, each portraying the intensity distribution *I*(*x*,*y*) at different distances *z*.