Note: The cost of running the entire notebook is higher than 1 FlexCredit.

90 degree optical hybrids (also known as quadrature optical hybrids) are essential components in coherent transmission systems. A 90 degree optical hybrid is a six-port device consisting of two inputs and four outputs. In the ideal case, the outputs are the mixed signals of the inputs with 0, $\pi$/2, $\pi$, and 3$\pi$/2 relative phase shifts.

This notebook demonstrates the simulation of a compact and low-loss 90 degree optical hybrid based on a silicon-on-insulator platform. The device consists of a Y-branch, three 2x2 MMIs, and four 90 degree waveguide bends. Building those structures natively in Tidy3D is certainly doable but time consuming. Here, we build the device structures in a separate CAD editor and import the stl file into Tidy3D for simulation. To use this functionality, remember to install Tidy3D as pip install "tidy3d[trimesh]", which will install optional dependencies needed for processing surface meshes.

The device design is adapted from Hang Guan et al., "Compact and low loss 90° optical hybrid on a silicon-on-insulator platform," Opt. Express 25, 28957-28968 (2017).

For more integrated photonic examples such as the 8-Channel mode and polarization de-multiplexer, the broadband bi-level taper polarization rotator-splitter, and the broadband directional coupler, please visit our examples page.

Simulation of the 2x2 MMI¶

To design the optical hybrid, we first design each component individually. For the Y-branch, we will use the same low-loss design demonstrated in the reference and our Y-branch notebook. The waveguide bends can be Euler bends or circular bands, which is also demonstrated in another notebook.

For the 2x2 MMIs, an optimized design is demonstrated here. The design aims to have equal power splitting and a 90 degree phase difference in the through port and cross port. To simulate the MMI, we also built the structure as a stl file and only import it here.

First, define some basic simulation parameters. We simulate at a relatively narrow wavelength band of 1530 nm to 1560 nm.

Define material properties. For simplicity, we only use non-dispersive materials in this simulation.

The structures will be imported from stl files, but it is good to define some geometric parameters to help set up the source, monitors, and simulation domains.

Import the MMI geometry from the stl file and define the MMI structure. All stl files used in this notebook can be downloaded from our documentation repo.

Define a ModeSource launching the TE0 mode at the top left waveguide. Two ModeMonitors are added to the waveguides on the right to measure the power and phase of the outputs. To visualize the field distribution within the MMI region, we also add a FieldMonitor in the xy plane. Finally, define a Simulation.

Visualize the simulation.

Submit the simulation job to the server.

The simulation is complete and the monitor data have been downloaded. First, we plot the field intensity distribution to visualize the power flow. We can observe that the two outputs have a similar intensity.

To quantitatively investigate the power in the two output waveguides, we compute the power from the mode amplitudes. Compared to the simulation results reported in the reference, the small discrepancy here is likely due to the different material properties used.

Ideally, both power levels are 3 dB. Here, we see the through port has a slightly lower power level than the cross port. However, the small difference is acceptable.

Lastly, we check the phase difference in the two outputs. Within the wavelength range, the phase difference is only about 1 degree from the ideal 90 degree.

Simulation of the Optical Hybrid -- LO Input¶

Now that we have tested individual components, we can put them together and simulate the whole device. Again, we directly import the geometry from a stl file.

In the first case, define a ModeSource at the LO input and four ModeMonitors at the outputs.

Define the simulation.

Visualize the simulation.

Submit the simulation job to the server.

Visualize the field intensity distribution.

Besides the error in the relative phase, there are three additional figures of merit (FOM) the characterize the performance of the 90 degree optical hybrid: insertion loss, common mode rejection ratio (CMRR), and imbalance. We define a function to calculate those FOMs and plot the results.

The insertion loss is calculated as $-10log_{10}(P_{tot})$, where $P_{tot}=P_{Ip}+P_{In}+P_{Qp}+P_{Qn}$ is the total power at four output ports.

The CMRR is calculated as CMRR$_I=-20log_{10}(\left|\frac{P_{Ip}-P_{In}}{P_{Ip}+P_{In}} \right|)$ and CMRR$_Q=-20log_{10}(\left|\frac{P_{Qp}-P_{Qn}}{P_{Qp}+P_{Qn}} \right|)$.

The imbalance is defined as Imbalance$_I = -10log_{10}(\frac{P_{Ip}}{P_{In}})$ and Imbalance$_Q = -10log_{10}(\frac{P_{Qp}}{P_{Qn}})$.

Calculate those FOMs and plot the results. Due to symmetry, CMRR$_I$ and CMRR$_Q$ are identical. So is Imbalance$_I$ and Imbalance$_Q$.

Overall, we see that the design has a good performance. The insertion loss is about 0.3 dB while the CMRRs are above 30 dB and the Imbalances are around 0.1 dB.

Simulation of the Optical Hybrid -- Signal Input¶

Finally, we simulate the case where the input signal is from the bottom signal port. To do so, we only need to define a ModeSource at the signal port and update the previous simulation since other settings of the simulation is identical.

Visualize the field intensity distribution.

Calculate those FOMs and plot the results. Since the signal port is the left waveguide of the bottom MMI, CMRR$_I$ and CMRR$_Q$ are expected to be slghtly different. The device performance according to the insertion loss, CMRR, and Imbalance is comparable to the case with input from the LO port. In addition, from the phase simulation, we know the phase error is going to be small too. This means the overall design of the 90 degree optical hybrid works very well.