"
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"source": [
"_ = pf.plot_s_matrix(s_matrix, y=\"dB\", input_ports=[\"P0\"])"
]
},
{
"cell_type": "markdown",
"id": "6585c506",
"metadata": {},
"source": [
"The splitter transmits close to the ideal -3 dB into each output arm with low reflection across the full band.\n",
"\n",
"## Step 4: Building an MZI with routing\n",
"\n",
"With a verified splitter in hand, we build an unbalanced Mach-Zehnder interferometer: the same Y splitter is used twice (as splitter and combiner), and the two arms are created with the [route](https://docs.flexcompute.com/projects/photonforge/en/latest/_autosummary/photonforge.parametric.route.html) function.\n",
"PhotonForge also offers fully automatic, obstacle-aware routing with crossing insertion through [route_auto](https://docs.flexcompute.com/projects/photonforge/en/latest/_autosummary/photonforge.parametric.route_auto.html) and the bundle routers [route_l](https://docs.flexcompute.com/projects/photonforge/en/latest/_autosummary/photonforge.parametric.route_l.html), [route_u](https://docs.flexcompute.com/projects/photonforge/en/latest/_autosummary/photonforge.parametric.route_u.html), and [route_z](https://docs.flexcompute.com/projects/photonforge/en/latest/_autosummary/photonforge.parametric.route_z.html) - for this simple layout, plain point-to-point routing is all we need.\n",
"\n",
"The short arm is a direct route.\n",
"For the long arm we pass waypoints that create a U-shaped detour, and we choose the detour height to hit an exact path-length imbalance: a U detour with a half-circle top adds $2 h + 2 r (\\pi - 3)$ to the direct length, where $h$ is the detour height and $r$ the bend radius."
]
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{
"data": {
"image/svg+xml": [
"08:25:56 Eastern Daylight Time Loading simulation from local cache. View cached \n",
" task using web UI at \n",
" 'https://tidy3d.simulation.cloud/workbench?taskId =mo-2144c15b-c1e8-45ac-9bfa-7e1dbe42768d' Loading simulation from local cache. View cached \n",
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" 'https://tidy3d.simulation.cloud/workbench?taskId =mo-77cb0a1d-e186-41ab-99bc-9baf2426960f' Loading simulation from local cache. View cached \n",
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" 'https://tidy3d.simulation.cloud/workbench?taskId =mo-44f8c1ab-f3dc-49ca-8e3d-9d934137120d' 08:25:57 Eastern Daylight Time Loading simulation from local cache. View cached \n",
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"source": [
"transmission = np.abs(mzi_s[(\"P0@0\", \"P1@0\")]) ** 2\n",
"\n",
"plt.figure()\n",
"plt.plot(wavelengths, 10 * np.log10(transmission))\n",
"plt.xlabel(\"Wavelength (um)\")\n",
"plt.ylabel(\"Transmission (dB)\")\n",
"plt.title(\"Unbalanced MZI transmission\")\n",
"plt.ylim(-40, 3)\n",
"plt.grid(True, alpha=0.3)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "399c80da",
"metadata": {},
"source": [
"The interference fringes are exactly what the path imbalance predicts.\n",
"The free spectral range of an unbalanced MZI is\n",
"\n",
"$$\\mathrm{FSR} = \\frac{\\lambda^2}{n_g \\, \\Delta L}$$\n",
"\n",
"where $n_g$ is the group index of the strip waveguide.\n",
"We can get $n_g$ directly from the port specification's mode solution and compare:"
]
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"Starting…\r"
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