3.1. Mach-Zehnder interferometer

The Mach-Zehnder interferometer (MZI) we are going to design is composed of:

  1. One input fiber grating coupler
  2. Two 2x1 MMIs
  3. One output fiber grating coupler
  4. Two waveguide arms (left and right) connecting the two inputs (used as outputs) of the first MMI to the two inputs of the second.
Mach-Zehnder interferometer

IPKISS integrates the different aspects of photonic design into one framework, where you can define your component once as a parametric cell (PCell) and then use it throughout the whole design process, allowing to tightly link layout and simulations. Therefore, in order to easily create and manipulate the MZI that we need, we are going to create a PCell. This PCell inherits from CircuitCell, a custom class defined in additional_utils, that makes it is easy to place and connect components together to achieve the final circuit.

3.1.1. PCell Properties

The first step is to define the PCell properties, which will be used to design the MZI. One aspect to pay attention to is the right arm of the MZI. Depending on the length of this arm, the result of the MZI simulation will change. Therefore, we need to be able to control the shape of this arm when we instantiate the MZI PCell, without touching the code inside the PCell itself.

The PCell has the following accessible properties:

  • through_point: This is a coordinate (through point) through which the right (longest) arm of the MZI has to pass. This allows to control the shape of the right arm when we instantiate the MZI.
  • bend_radius: Here we assign the value of the bend radius to be used for the waveguide routes. In the CORNERSTONE SiN PDK, the minimum bend radius is 80 micron for the default waveguide width (1.2 micron) operating in C-band.
  • fgc_spacing_y: This the separation in the y-dimension between the two fibre grating couplers.
  • fgc: The PCell of the fiber grating coupler to be used. The default value is SiN300nm_1550nm_TE_STRIP_Grating_Coupler from the IPKISS PDK for CORNERSTONE SiN.
  • splitter: The PCell of the splitter to be used. The default value is Strip2x1MMIFixed from the library ‘pteam_library_conrerstone_sin’ which provides a circuit model for the class Strip2x1MMI in the IPKISS PDK for CORNERSTONE SiN with a given set of parameters.

Below is the code that defines the PCell properties.

Listing 3.3 luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py
class MZI(CircuitCell):

    through_point = i3.Coord2Property(doc="Point the longer arm of the MZI has to go through")
    bend_radius = i3.PositiveNumberProperty(default=80.0, doc="Bend radius of the waveguides")
    fgc_spacing_y = i3.PositiveNumberProperty(default=400.0, doc="Spacing of the fibre couplers")

    fgc = i3.ChildCellProperty(doc="PCell for the fiber grating coupler")
    splitter = i3.ChildCellProperty(doc="PCell for the splitter")

    def _default_through_point(self):
        return [(100.0, self.fgc_spacing_y/2)]

    def _default_fgc(self):
        return pdk.SiN300nm_1550nm_TE_STRIP_Grating_Coupler()

    def _default_splitter(self):
        return Strip2x1MMIFixed()

3.1.2. Child cells and connections

The next step is to define a list of child cells. We need two fiber grating couplers and two splitters.

Listing 3.4 luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py
    def _default_child_cells(self):
        child_cells = {
            "fgc_1": self.fgc,
            "fgc_2": self.fgc,
            "mmi_1": self.splitter,
            "mmi_2": self.splitter,
        return child_cells

The connections between the child cells are defined differently depending on whether we connect them end-to-end or we need a waveguide connector:

  • For end-to-end connections we use joins. This is the case for the connections between the input and output fiber grating couplers and the two splitters:

    Listing 3.5 luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py
        def _default_joins(self):
            joins = [("fgc_1:out", "mmi_1:out"), ("fgc_2:out", "mmi_2:out")]
            return joins
  • To connect components using waveguide connectors, we use connectors. Here we specify the type of connector used between the desired ports, together with other useful information, such as the bend radius of the waveguides.

    Listing 3.6 luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py
        def _default_connectors(self):
            br = self.bend_radius
            connectors = [
                ("mmi_1:in1", "mmi_2:in2", manhattan, {"adiabatic_angle": 15, "bend_radius": br}),
                ("mmi_1:in2", "mmi_2:in1", manhattan, {
                    "through_points": [self.through_point], "adiabatic_angle": 15, "bend_radius": br
            return connectors

The connections between the two splitters (between “mmi1:in1” and “mmi2:in2”, and “mmi1:in2” and “mmi2:in1”) are performed using a Manhattan-type waveguide connector. The right arm of the MMI (second connection) is forced to pass through the through point specified through the through_point coordinate when instantiating the PCell.

3.1.3. Placement of the components

Components that are placed end-to-end using joins are automatically moved by IPKISS to ensure that the connection requirement is satisfied. In the case of connections defined using connectors, this is not the case. IPKISS only knows that these two components have to be connected and the waveguide connector will be generated depending on their position, which we need to specify ourselves.

We place the input port of the bottom fiber grating coupler at the origin (0.0, 0.0). We then create an array of fiber grating couplers by placing the second grating coupler at a distance of fgc_spacing_y above the first.

Listing 3.7 luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py
    def _default_place_specs(self):
        place_specs = [
            i3.Place("fgc_1:out", (-300, 0)),
            i3.PlaceRelative("fgc_2:out", "fgc_1:out", (0.0, self.fgc_spacing_y)),
        return place_specs

3.1.4. External ports

Our circuit is almost finished. All we need to do now is to define the names of the external ports we want to access. We will use these port names to plot the transmission when we perform the circuit simulation.

Listing 3.8 luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py
    def _default_external_port_names(self):
        epn = {
            "fgc_1:vertical_in": "in",
            "fgc_2:vertical_in": "out",
        return epn

3.1.5. Run the code

Open luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py. At the bottom of the file, the MZI is instantiated and simulated:

Listing 3.9 luceda-academy/training/topical_training/cornerstone_mzi_sweep/mzi_pcell.py
    # Layout
    mzi = MZI(
        through_point=(70.0, 200.0),
    mzi_layout = mzi.Layout()

    # Circuit model
    my_circuit_cm = mzi.CircuitModel()
    wavelengths = np.linspace(1.52, 1.58, 5001)
    S_total = my_circuit_cm.get_smatrix(wavelengths=wavelengths)

    # Plotting
    plt.plot(wavelengths, 20 * np.log10(np.abs(S_total['out', 'in'])), '-', linewidth=2.2, label="TE-out1")
    plt.xlabel('Wavelength [um]', fontsize=16)
    plt.ylabel('Transmission [dB]', fontsize=16)
    plt.legend(fontsize=14, loc=4)
    axes = plt.gca()
    axes.set_ylim([-100, 0])

If you run the code, you will visualize the layout and the simulation of an MZI circuit for through_point=[(70.0, 200.0)] and bend_radius=80.0.

Mach-Zehnder interferometer
Mach-Zehnder interferometer

3.1.6. Test your knowledge

Try to change the coordinates of the through point and the bend radius to see how the simulation changes. What happens when the delay arm becomes longer? Why?