{
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{
"cell_type": "markdown",
"id": "e86dc79c-8f50-457b-85e8-5dcb1b5c97c7",
"metadata": {},
"source": [
"# Inverse design of a GaP photon extractor for nitrogen-vacancy centers in diamond \n",
"\n",
"Designing a light extractor is crucial for enhancing photon collection efficiency in solid-state defect qubit systems, which are valuable for quantum information and metrology applications. In high refractive index materials like diamond, total internal reflection limits the ability to collect photons emitted from qubits. By optimizing light extraction through nanophotonic structures, such as waveguides or planar dielectric structures, one can significantly increase the emission directed toward detectors, improving photoluminescence detection. \n",
"\n",
"In this notebook, we use inverse design to optimize a GaP extractor structure following a similar approach discussed in `Srivatsa Chakravarthi, Pengning Chao, Christian Pederson, Sean Molesky, Andrew Ivanov, Karine Hestroffer, Fariba Hatami, Alejandro W. Rodriguez, and Kai-Mei C. Fu, \"Inverse-designed photon extractors for optically addressable defect qubits,\" Optica 7, 1805-1811 (2020)` [DOI: 10.1364/OPTICA.408611](https://doi.org/10.1364/OPTICA.408611). The optimization aims to maximize the minimum upward flux among three simulations with the dipole source oriented in the $x$, $y$, and $z$ directions. The final design achieves an order-of-magnitude enhancement in upward flux for an in-plane dipole source and over two orders of magnitude for an out-of-plane dipole source compared to the configuration without an extractor.\n",
"\n",
"\n",
"\n",
"If you are unfamiliar with inverse design, we also recommend our [intro to inverse design tutorials](https://www.flexcompute.com/tidy3d/learning-center/inverse-design/) and our [primer on automatic differentiation with tidy3d](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd1Intro/). For another example of light extractor optimization in Tidy3D, see [this example](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd12LightExtractor/)."
]
},
{
"cell_type": "code",
"id": "4ff284f4-ab91-49b7-8d83-cd0bcf37a6ce",
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"execution": {
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"source": [
"import autograd as ag\n",
"import autograd.numpy as np\n",
"import gdstk\n",
"import matplotlib.pyplot as plt\n",
"import tidy3d as td\n",
"import tidy3d.web as web"
],
"outputs": [],
"execution_count": 1
},
{
"cell_type": "markdown",
"id": "67edeae1-c26e-45ec-9b49-62392fd9433e",
"metadata": {},
"source": [
"## Static Simulation Components\n",
"\n",
"In this case, we are focusing on the photonic coupling to the negatively charged sharp zero-phonon line (ZPL) of nitrogen-vacancy centers at 637 nm. "
]
},
{
"cell_type": "code",
"id": "6fb68948-8f3d-4c3e-943f-f0c2303287ae",
"metadata": {
"execution": {
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},
"source": [
"lda0 = 0.637 # central wavelength\n",
"freq0 = td.C_0 / lda0 # central frequency\n",
"fwidth = freq0 / 10 # width of the source frequency range"
],
"outputs": [],
"execution_count": 2
},
{
"cell_type": "markdown",
"id": "03160c8a-2255-450d-8d13-9cd446644b29",
"metadata": {},
"source": [
"For the extractor structure on top of diamond, a high-index material is preferred. GaP with a refractive index of 3.31 is used in this design. "
]
},
{
"cell_type": "code",
"id": "69c0059c-99f1-4af2-9169-0ce53503abe1",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:14.988837Z",
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},
"source": [
"# define materials\n",
"n_GaP = 3.31\n",
"GaP = td.Medium(permittivity=n_GaP**2)\n",
"\n",
"n_diamond = 2.417\n",
"diamond = td.Medium(permittivity=n_diamond**2)"
],
"outputs": [],
"execution_count": 3
},
{
"cell_type": "markdown",
"id": "4873e268-ef36-4427-ae01-b1eec964a862",
"metadata": {},
"source": [
"The GaP layer thickness is 250 nm. The design region is very compact, only 1.5 μm by 1.5 μm. The design region is discretized into 10 nm grids. To ensure the FDTD grid is commensurate with the pixel, we will use the automatic nonuniform grid with `min_steps_per_wvl = lda0 / (pixel_size * n_GaP)`.\n",
"\n",
"The minimal feature size we are aiming for is 50 nm, compatible with electron beam lithography fabrication. "
]
},
{
"cell_type": "code",
"id": "71088fad-9d44-44eb-b7fe-cedc976c4933",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:14.991552Z",
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"source": [
"h = 0.25 # thickness of the extractor layer\n",
"l = 1.5 # size of the design region\n",
"pixel_size = 0.01 # pixel size in the design region\n",
"min_steps_per_wvl = lda0 / (pixel_size * n_GaP) # automatic grid size parameter\n",
"\n",
"min_feature = 0.05 # minimal feature size\n",
"\n",
"inf_eff = 1e3 # effective infinity\n",
"buffer = 0.5 # buffer spacing\n",
"run_time = 4e-13 # simulation run time"
],
"outputs": [],
"execution_count": 4
},
{
"cell_type": "markdown",
"id": "c436fb74-09a6-4f15-bca8-7e276b00bb95",
"metadata": {},
"source": [
"Now we define static components in the optimization. This includes the diamond substrate structure, the dipole sources, and the monitor that records the upward flux. The dipole source is located 100 nm below the top diamond surface.\n",
"\n",
"In this case, we will place a [FieldMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldMonitor.html) to record the upward radiation flux instead of directly using a [FluxMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FluxMonitor.html) because differentiation with respect to flux monitor data is not supported at the moment. "
]
},
{
"cell_type": "code",
"id": "e787fb24-d5d2-4ad8-8f4d-fa45216baa85",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:14.994391Z",
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"source": [
"# define the diamond substrate\n",
"substrate = td.Structure(\n",
" geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, -inf_eff), rmax=(inf_eff, inf_eff, 0)),\n",
" medium=diamond,\n",
")\n",
"\n",
"# define the dipole sources oriented in the x, y, and z directions\n",
"dipole_z = -0.1 # dipole depth\n",
"pd_x = td.PointDipole(\n",
" center=(0, 0, dipole_z),\n",
" source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
" polarization=\"Ex\",\n",
")\n",
"\n",
"pd_y = pd_x.updated_copy(polarization=\"Ey\")\n",
"pd_z = pd_x.updated_copy(polarization=\"Ez\")\n",
"\n",
"# define the field monitor above the extractor to measure the upward flux\n",
"monitor_z = h + 0.4 # monitor height\n",
"monitor_size = 1.5 # monitor size\n",
"\n",
"field_monitor = td.FieldMonitor(\n",
" center=(0, 0, monitor_z),\n",
" size=(monitor_size, monitor_size, 0),\n",
" freqs=[freq0],\n",
" name=\"field\",\n",
")"
],
"outputs": [],
"execution_count": 5
},
{
"cell_type": "markdown",
"id": "fa427716-d97d-4948-8b70-34b09858a903",
"metadata": {},
"source": [
"## Design Region\n",
"\n",
"The design region is a pixelated array of permittivity values between $\\varepsilon=1$ and $\\varepsilon=\\varepsilon_{GaP}$. To define it, we use a density array whose element values are between 0 to 1, apply a conic smoothing filter, a tanh projection function, and finally scale it linearly to $\\varepsilon=1$ and $\\varepsilon=\\varepsilon_{GaP}$."
]
},
{
"cell_type": "code",
"id": "bacc32a4-6a1a-4edc-ba35-1fa066c0d268",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:14.998374Z",
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},
"source": [
"from tidy3d.plugins.autograd import make_filter_and_project, rescale\n",
"\n",
"# define the conic filter and tanh projection\n",
"filter_project_fn = make_filter_and_project(radius=min_feature, dl=pixel_size)\n",
"\n",
"\n",
"def get_density(params: np.ndarray, beta: float) -> np.ndarray:\n",
" \"\"\"Get the density of the material in the design region as a function of optimization parameters.\"\"\"\n",
" params = (params + params.T) / 2 # impose symmetry along the diagonal\n",
" return filter_project_fn(params[..., None], beta=beta)\n",
"\n",
"\n",
"# define the design region bounding box\n",
"design_region = td.Box(\n",
" center=(0, 0, h / 2),\n",
" size=(l, l, h),\n",
")\n",
"\n",
"\n",
"def get_design_region(params: np.ndarray, beta: float) -> td.Structure:\n",
" \"\"\"Get design region structure as a function of optimization parameters.\"\"\"\n",
" density = get_density(params, beta=beta)\n",
" eps_data = rescale(density, 1, n_GaP**2)\n",
" return td.Structure.from_permittivity_array(eps_data=eps_data, geometry=design_region)"
],
"outputs": [],
"execution_count": 6
},
{
"cell_type": "markdown",
"id": "a2854c54-0a31-4b79-9be3-f702e6abd174",
"metadata": {},
"source": [
"Next we create another function that takes the design parameters and create three simulations with the dipole polarized in the $x$, $y$, and $z$ directions."
]
},
{
"cell_type": "code",
"id": "4b719ccf-dd9c-44e0-ab0d-4e174f58338e",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:15.013431Z",
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"source": [
"def make_sims(params: np.ndarray, beta: float) -> dict[str, td.Simulation]:\n",
" \"\"\"Get simulation as a function of optimization parameters.\"\"\"\n",
"\n",
" # set up the design region structure\n",
" design_region = get_design_region(params, beta=beta)\n",
"\n",
" # create a simulation with x-oriented dipole\n",
" sim_x = td.Simulation(\n",
" size=(l + buffer * 2, l + buffer * 2, monitor_z + buffer * 2),\n",
" run_time=run_time,\n",
" structures=[substrate, design_region],\n",
" sources=[pd_x],\n",
" monitors=[field_monitor],\n",
" grid_spec=td.GridSpec.auto(\n",
" min_steps_per_wvl=min_steps_per_wvl,\n",
" ),\n",
" )\n",
"\n",
" # create three simulations with different dipole orientations\n",
" sims = {\n",
" \"x\": sim_x,\n",
" \"y\": sim_x.updated_copy(sources=[pd_y]),\n",
" \"z\": sim_x.updated_copy(sources=[pd_z]),\n",
" }\n",
"\n",
" return sims"
],
"outputs": [],
"execution_count": 7
},
{
"cell_type": "markdown",
"id": "68a8312f-711d-4c4c-b650-9378109a1b14",
"metadata": {},
"source": [
"To ensure the simulation setup is correct, we can create and visualize an initial simulation. The initial condition we are going to use is a uniform design region with permittivity $\\varepsilon=\\frac{1+\\varepsilon_{GaP}}{2}$"
]
},
{
"cell_type": "code",
"id": "f1bc94ec-e1e2-4f8e-aba7-9c6000b9b817",
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"execution": {
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},
"source": [
"# number of pixels in one direction\n",
"n_pixels = int(l / pixel_size)\n",
"\n",
"# initial design parameters\n",
"params0 = np.zeros((n_pixels, n_pixels)) + 0.5\n",
"\n",
"# simulations with the initial design parameters\n",
"sims0 = make_sims(params0, beta=50.0)\n",
"\n",
"# visualize a simulation\n",
"sims0[\"x\"].plot(y=0)\n",
"plt.show()"
],
"outputs": [
{
"data": {
"text/plain": [
""
],
"image/png": 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"
},
"metadata": {},
"output_type": "display_data",
"jetTransient": {
"display_id": null
}
}
],
"execution_count": 8
},
{
"cell_type": "markdown",
"id": "cdbbe760-bcec-4fad-a80c-9dd776f21972",
"metadata": {},
"source": [
"## Baseline Simulations\n",
"\n",
"As a baseline, we will first simulate the scenario with no extractor. This result will be compared to that with the optimized extractor later on."
]
},
{
"cell_type": "code",
"id": "72b5baa3-91c1-4bfc-8c44-ee456c0551cf",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:15.128825Z",
"iopub.status.busy": "2025-05-15T10:49:15.128736Z",
"iopub.status.idle": "2025-05-15T10:49:26.993540Z",
"shell.execute_reply": "2025-05-15T10:49:26.992459Z"
},
"ExecuteTime": {
"end_time": "2026-03-18T10:43:47.042543Z",
"start_time": "2026-03-18T10:43:01.346842Z"
}
},
"source": [
"# create simulations without the extractor structure\n",
"sims_ref = {axis: sims0[axis].updated_copy(structures=[substrate]) for axis in [\"x\", \"y\", \"z\"]}\n",
"\n",
"# run the simulations\n",
"ref_results = web.run(sims_ref, path=\"data\")"
],
"outputs": [
{
"data": {
"text/plain": [
"Output()"
],
"application/vnd.jupyter.widget-view+json": {
"version_major": 2,
"version_minor": 0,
"model_id": "9c8143a16dec40829bba5f5fad4bbdde"
}
},
"metadata": {},
"output_type": "display_data",
"jetTransient": {
"display_id": null
}
},
{
"data": {
"text/plain": [],
"text/html": [
"\n"
]
},
"metadata": {},
"output_type": "display_data",
"jetTransient": {
"display_id": null
}
},
{
"data": {
"text/plain": [
"\u001B[2;36m11:43:16 CET\u001B[0m\u001B[2;36m \u001B[0mStarted working on Batch containing \u001B[1;36m3\u001B[0m tasks. \n"
],
"text/html": [
"
11:43:16 CET Started working on Batch containing 3 tasks. \n",
"
\n"
]
},
"metadata": {},
"output_type": "display_data",
"jetTransient": {
"display_id": null
}
},
{
"data": {
"text/plain": [],
"text/html": [
"\n"
]
},
"metadata": {},
"output_type": "display_data",
"jetTransient": {
"display_id": null
}
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ex dipole flux is 739.103.\n",
"Ey dipole flux is 734.065.\n",
"Ez dipole flux is 850.759.\n",
"Relative Ex dipole flux enhancement is 9.879.\n",
"Relative Ey dipole flux enhancement is 9.811.\n",
"Relative Ez dipole flux enhancement is 186.343.\n"
]
}
],
"execution_count": 23
},
{
"cell_type": "markdown",
"id": "913bbdc3-425a-4d52-95e3-244bfdb81523",
"metadata": {},
"source": [
"Lastly we can plot the simulation in 3D to better visualize the optimized extractor geometry."
]
},
{
"cell_type": "code",
"id": "15ea1829-2ef0-4cdb-a48c-982823af9b71",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T12:11:30.899424Z",
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"source": [
"sims_loaded[\"x\"].plot_3d()"
],
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""
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"\n",
" \n",
" \n",
" "
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"execution_count": 24
},
{
"cell_type": "markdown",
"id": "9c70e188-33d9-4fcd-a1d2-69ecd1d8aaa9",
"metadata": {},
"source": [
"## Final Remarks\n",
"\n",
"In this notebook, we focus exclusively on a single frequency. In the referenced [paper](https://doi.org/10.1364/OPTICA.408611), optimization is also conducted at a single frequency, while the extractor's performance is evaluated across a broad wavelength range. This can be achieved by specifying frequency sampling points in the [FieldMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldMonitor.html).\n",
"\n",
"The enhancement of upward radiation flux in the optimized design can arise from two mechanisms: (1) the structure redirects the dipole radiation toward the upward direction, and (2) the total radiation from the dipole is increased due to the Purcell effect. Although we do not examine the Purcell factor in this notebook, it can be analyzed as demonstrated in the tutorial provided [here](https://www.flexcompute.com/tidy3d/examples/notebooks/CavityFOM/). Based on the findings of the paper, the Purcell effect is not very significant in our case since the dipole is deeply buried (100 nm) under the surface.\n",
"\n",
"In this example, we only used the filter to enforce the fabrication constraint. For better fabrication constraint compliance, one can also consider adding a fabrication penalty term in the objective function such as the one demonstrated in this [example](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd6GratingCoupler/). Before fabrication, we should also closely examine the small features in the design to ensure fabricability. "
]
}
],
"metadata": {
"applications": [
"Nanophotonics",
"Quantum emitters"
],
"description": "This notebook demonstrates how to perform inverse design optimization of a light extractor for NV centers in diamond in Tidy3D FDTD.",
"feature_image": "./img/adjoint_21.png",
"features": [
"Adjoint inverse design",
"GDS component"
],
"kernelspec": {
"display_name": ".venv",
"language": "python",
"name": "python3"
},
"keywords": "inverse design, quantum emitter, light extractor, single-photon source, nanocavity, adjoint optimization, Tidy3D, FDTD",
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.10"
},
"title": "Inverse Design of a Photon Extractor for NV Centers in Diamond",
"widgets": {
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{
"data": {
"text/html": "
Uploading data for 3 tasks ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━ 33%0:00:02\n
![\"Schematic](\"img/adjoint_21.png\")
\n",
"\n",
"If you are unfamiliar with inverse design, we also recommend our [intro to inverse design tutorials](https://www.flexcompute.com/tidy3d/learning-center/inverse-design/) and our [primer on automatic differentiation with tidy3d](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd1Intro/). For another example of light extractor optimization in Tidy3D, see [this example](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd12LightExtractor/)."
]
},
{
"cell_type": "code",
"id": "4ff284f4-ab91-49b7-8d83-cd0bcf37a6ce",
"metadata": {
"execution": {
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},
"source": [
"import autograd as ag\n",
"import autograd.numpy as np\n",
"import gdstk\n",
"import matplotlib.pyplot as plt\n",
"import tidy3d as td\n",
"import tidy3d.web as web"
],
"outputs": [],
"execution_count": 1
},
{
"cell_type": "markdown",
"id": "67edeae1-c26e-45ec-9b49-62392fd9433e",
"metadata": {},
"source": [
"## Static Simulation Components\n",
"\n",
"In this case, we are focusing on the photonic coupling to the negatively charged sharp zero-phonon line (ZPL) of nitrogen-vacancy centers at 637 nm. "
]
},
{
"cell_type": "code",
"id": "6fb68948-8f3d-4c3e-943f-f0c2303287ae",
"metadata": {
"execution": {
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},
"source": [
"lda0 = 0.637 # central wavelength\n",
"freq0 = td.C_0 / lda0 # central frequency\n",
"fwidth = freq0 / 10 # width of the source frequency range"
],
"outputs": [],
"execution_count": 2
},
{
"cell_type": "markdown",
"id": "03160c8a-2255-450d-8d13-9cd446644b29",
"metadata": {},
"source": [
"For the extractor structure on top of diamond, a high-index material is preferred. GaP with a refractive index of 3.31 is used in this design. "
]
},
{
"cell_type": "code",
"id": "69c0059c-99f1-4af2-9169-0ce53503abe1",
"metadata": {
"execution": {
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},
"source": [
"# define materials\n",
"n_GaP = 3.31\n",
"GaP = td.Medium(permittivity=n_GaP**2)\n",
"\n",
"n_diamond = 2.417\n",
"diamond = td.Medium(permittivity=n_diamond**2)"
],
"outputs": [],
"execution_count": 3
},
{
"cell_type": "markdown",
"id": "4873e268-ef36-4427-ae01-b1eec964a862",
"metadata": {},
"source": [
"The GaP layer thickness is 250 nm. The design region is very compact, only 1.5 μm by 1.5 μm. The design region is discretized into 10 nm grids. To ensure the FDTD grid is commensurate with the pixel, we will use the automatic nonuniform grid with `min_steps_per_wvl = lda0 / (pixel_size * n_GaP)`.\n",
"\n",
"The minimal feature size we are aiming for is 50 nm, compatible with electron beam lithography fabrication. "
]
},
{
"cell_type": "code",
"id": "71088fad-9d44-44eb-b7fe-cedc976c4933",
"metadata": {
"execution": {
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"source": [
"h = 0.25 # thickness of the extractor layer\n",
"l = 1.5 # size of the design region\n",
"pixel_size = 0.01 # pixel size in the design region\n",
"min_steps_per_wvl = lda0 / (pixel_size * n_GaP) # automatic grid size parameter\n",
"\n",
"min_feature = 0.05 # minimal feature size\n",
"\n",
"inf_eff = 1e3 # effective infinity\n",
"buffer = 0.5 # buffer spacing\n",
"run_time = 4e-13 # simulation run time"
],
"outputs": [],
"execution_count": 4
},
{
"cell_type": "markdown",
"id": "c436fb74-09a6-4f15-bca8-7e276b00bb95",
"metadata": {},
"source": [
"Now we define static components in the optimization. This includes the diamond substrate structure, the dipole sources, and the monitor that records the upward flux. The dipole source is located 100 nm below the top diamond surface.\n",
"\n",
"In this case, we will place a [FieldMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldMonitor.html) to record the upward radiation flux instead of directly using a [FluxMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FluxMonitor.html) because differentiation with respect to flux monitor data is not supported at the moment. "
]
},
{
"cell_type": "code",
"id": "e787fb24-d5d2-4ad8-8f4d-fa45216baa85",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:14.994391Z",
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},
"source": [
"# define the diamond substrate\n",
"substrate = td.Structure(\n",
" geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, -inf_eff), rmax=(inf_eff, inf_eff, 0)),\n",
" medium=diamond,\n",
")\n",
"\n",
"# define the dipole sources oriented in the x, y, and z directions\n",
"dipole_z = -0.1 # dipole depth\n",
"pd_x = td.PointDipole(\n",
" center=(0, 0, dipole_z),\n",
" source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
" polarization=\"Ex\",\n",
")\n",
"\n",
"pd_y = pd_x.updated_copy(polarization=\"Ey\")\n",
"pd_z = pd_x.updated_copy(polarization=\"Ez\")\n",
"\n",
"# define the field monitor above the extractor to measure the upward flux\n",
"monitor_z = h + 0.4 # monitor height\n",
"monitor_size = 1.5 # monitor size\n",
"\n",
"field_monitor = td.FieldMonitor(\n",
" center=(0, 0, monitor_z),\n",
" size=(monitor_size, monitor_size, 0),\n",
" freqs=[freq0],\n",
" name=\"field\",\n",
")"
],
"outputs": [],
"execution_count": 5
},
{
"cell_type": "markdown",
"id": "fa427716-d97d-4948-8b70-34b09858a903",
"metadata": {},
"source": [
"## Design Region\n",
"\n",
"The design region is a pixelated array of permittivity values between $\\varepsilon=1$ and $\\varepsilon=\\varepsilon_{GaP}$. To define it, we use a density array whose element values are between 0 to 1, apply a conic smoothing filter, a tanh projection function, and finally scale it linearly to $\\varepsilon=1$ and $\\varepsilon=\\varepsilon_{GaP}$."
]
},
{
"cell_type": "code",
"id": "bacc32a4-6a1a-4edc-ba35-1fa066c0d268",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:14.998374Z",
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},
"source": [
"from tidy3d.plugins.autograd import make_filter_and_project, rescale\n",
"\n",
"# define the conic filter and tanh projection\n",
"filter_project_fn = make_filter_and_project(radius=min_feature, dl=pixel_size)\n",
"\n",
"\n",
"def get_density(params: np.ndarray, beta: float) -> np.ndarray:\n",
" \"\"\"Get the density of the material in the design region as a function of optimization parameters.\"\"\"\n",
" params = (params + params.T) / 2 # impose symmetry along the diagonal\n",
" return filter_project_fn(params[..., None], beta=beta)\n",
"\n",
"\n",
"# define the design region bounding box\n",
"design_region = td.Box(\n",
" center=(0, 0, h / 2),\n",
" size=(l, l, h),\n",
")\n",
"\n",
"\n",
"def get_design_region(params: np.ndarray, beta: float) -> td.Structure:\n",
" \"\"\"Get design region structure as a function of optimization parameters.\"\"\"\n",
" density = get_density(params, beta=beta)\n",
" eps_data = rescale(density, 1, n_GaP**2)\n",
" return td.Structure.from_permittivity_array(eps_data=eps_data, geometry=design_region)"
],
"outputs": [],
"execution_count": 6
},
{
"cell_type": "markdown",
"id": "a2854c54-0a31-4b79-9be3-f702e6abd174",
"metadata": {},
"source": [
"Next we create another function that takes the design parameters and create three simulations with the dipole polarized in the $x$, $y$, and $z$ directions."
]
},
{
"cell_type": "code",
"id": "4b719ccf-dd9c-44e0-ab0d-4e174f58338e",
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:49:15.013431Z",
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"source": [
"def make_sims(params: np.ndarray, beta: float) -> dict[str, td.Simulation]:\n",
" \"\"\"Get simulation as a function of optimization parameters.\"\"\"\n",
"\n",
" # set up the design region structure\n",
" design_region = get_design_region(params, beta=beta)\n",
"\n",
" # create a simulation with x-oriented dipole\n",
" sim_x = td.Simulation(\n",
" size=(l + buffer * 2, l + buffer * 2, monitor_z + buffer * 2),\n",
" run_time=run_time,\n",
" structures=[substrate, design_region],\n",
" sources=[pd_x],\n",
" monitors=[field_monitor],\n",
" grid_spec=td.GridSpec.auto(\n",
" min_steps_per_wvl=min_steps_per_wvl,\n",
" ),\n",
" )\n",
"\n",
" # create three simulations with different dipole orientations\n",
" sims = {\n",
" \"x\": sim_x,\n",
" \"y\": sim_x.updated_copy(sources=[pd_y]),\n",
" \"z\": sim_x.updated_copy(sources=[pd_z]),\n",
" }\n",
"\n",
" return sims"
],
"outputs": [],
"execution_count": 7
},
{
"cell_type": "markdown",
"id": "68a8312f-711d-4c4c-b650-9378109a1b14",
"metadata": {},
"source": [
"To ensure the simulation setup is correct, we can create and visualize an initial simulation. The initial condition we are going to use is a uniform design region with permittivity $\\varepsilon=\\frac{1+\\varepsilon_{GaP}}{2}$"
]
},
{
"cell_type": "code",
"id": "f1bc94ec-e1e2-4f8e-aba7-9c6000b9b817",
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"execution": {
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"source": [
"# number of pixels in one direction\n",
"n_pixels = int(l / pixel_size)\n",
"\n",
"# initial design parameters\n",
"params0 = np.zeros((n_pixels, n_pixels)) + 0.5\n",
"\n",
"# simulations with the initial design parameters\n",
"sims0 = make_sims(params0, beta=50.0)\n",
"\n",
"# visualize a simulation\n",
"sims0[\"x\"].plot(y=0)\n",
"plt.show()"
],
"outputs": [
{
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"