"
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"source": [
"sim_after_mnt_xy = td.FieldMonitor(\n",
" center=(*monitor_near.center[:2], H / 2 + focal_length),\n",
" size=monitor_near.size,\n",
" freqs=monitor_near.freqs,\n",
" fields=(\"Ex\", \"Ey\", \"Ez\"),\n",
" name=\"focal_fields_xy\",\n",
")\n",
"sim_after_mnt_xz = td.FieldMonitor(\n",
" size=(0, td.inf, td.inf),\n",
" freqs=monitor_near.freqs,\n",
" fields=(\"Ex\", \"Ey\", \"Ez\"),\n",
" name=\"focal_fields_yz\",\n",
")\n",
"sim_after_mnt = sim_after.updated_copy(\n",
" center=(0, 0, focal_length / 2),\n",
" size=(length_xy, length_xy, focal_length + 4 * buffer_z),\n",
" monitors=[sim_after_mnt_xy, sim_after_mnt_xz],\n",
")\n",
"sim_after_mnt.plot(y=0)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"13:56:14 CEST Created task 'meta_near_field_after' with task_id \n",
" 'fdve-1e8606f2-3390-410c-9234-5a45d5a59a91' and task_type 'FDTD' . \n",
" View task using web UI at \n",
" 'https://tidy3d.simulation.cloud/workbench?taskId=fdve-1e8606f2-33 90-410c-9234-5a45d5a59a91' Task folder: 'default' 13:56:16 CEST Maximum FlexCredit cost: 0.504 . Minimum cost depends on task \n",
" execution details. Use 'web.real_cost(task_id)' to get the billed \n",
" FlexCredit cost after a simulation run. \n",
"13:56:17 CEST status = queued \n",
" To cancel the simulation, use 'web.abort(task_id)' or \n",
" 'web.delete(task_id)' or abort/delete the task in the web UI. \n",
" Terminating the Python script will not stop the job running on the\n",
" cloud. \n",
"13:56:29 CEST status = preprocess \n",
"13:56:33 CEST starting up solver \n",
" running solver \n",
"13:57:13 CEST early shutoff detected at 12 %, exiting. \n",
" status = postprocess \n",
"13:57:14 CEST status = success \n",
"13:57:16 CEST View simulation result at \n",
" 'https://tidy3d.simulation.cloud/workbench?taskId=fdve-1e8606f2-33 90-410c-9234-5a45d5a59a91' . \n",
"13:57:18 CEST loading simulation from simulation_data.hdf5 \n",
""
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},
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],
"source": [
"fig, (ax1, ax2) = plt.subplots(1, 2, tight_layout=True, figsize=(10, 4))\n",
"sim_data_after_mnt.plot_field(\"focal_fields_xy\", field_name=\"E\", val=\"abs^2\", vmax=105, ax=ax1)\n",
"sim_data_after_mnt.plot_field(\"focal_fields_yz\", field_name=\"E\", val=\"abs^2\", vmax=180, ax=ax2)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conclusions\n",
"\n",
"We notice that our metalens does quite well at focusing at this high NA! For the purposes of demonstration, this is quite a small device, but the same the same principle can be applied to optimize a much larger metalens.\n",
"\n",
"For more case studies using `autograd` support in `tidy3d`, see the\n",
"\n",
"* [Gradient Checking Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd2GradientChecking/).\n",
"\n",
"* [Inverse Design Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd3InverseDesign/).\n",
"\n",
"* [Multi-Objective Gradient Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd4MultiObjective/).\n",
"\n",
"* [Boundary Gradients Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd5BoundaryGradients/).\n",
"\n",
"* [Grating Coupler Notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd6GratingCoupler/).\n"
]
}
],
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"text/html": "↑ simulation.json ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 629.0/629.0 kB • 2.1 MB/s • 0:00:00 \n↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 2.7/2.7 MB • 20.9 MB/s • 0:00:00 \n🚶 Starting 'metalens'... \n↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 23.5/23.5 MB • 20.3 MB/s • 0:00:00 \n🏃 Starting 'metalens'... \n🏃 Finishing 'metalens'... \nsolver progress (field decay = 5.96e-06) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% 0:00:00 \n \n",
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"source": [
"\n",
"\n",
"## Setup\n",
"\n",
"We first perform basic imports of the packages needed."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": []
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"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import optax\n",
"import tidy3d as td\n",
"from autograd import value_and_grad\n",
"from tidy3d import web"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The metalens design consists of a rectangular array of Si rectangular prisms sitting on an SiO2 substrate.\n",
"\n",
"Here we define all of the basic parameters of the setup, including the wavelength, NA, geometrical dimensions, and material properties.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": []
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"source": [
"# 1 nanometer in units of microns (for conversion)\n",
"nm = 1e-3\n",
"\n",
"# free space central wavelength\n",
"wavelength = 850 * nm\n",
"f0 = td.C_0 / wavelength\n",
"fwidth = f0 / 20\n",
"\n",
"# desired numerical aperture\n",
"NA = 0.78\n",
"\n",
"# shape parameters of metalens unit cell (um) (refer to image above and see paper for details)\n",
"H = 430 * nm\n",
"S = 320 * nm\n",
"\n",
"# minimum and maximum radius of cylinder in unit cell\n",
"rmin = 50 * nm\n",
"rmax = S / 2 - 10 * nm # to avoid touching cylinders\n",
"\n",
"# space above and below metalens (in substrate and air, respectively)\n",
"buffer_z = wavelength / 2\n",
"\n",
"# buffer region in x and y\n",
"buffer_xy = wavelength\n",
"\n",
"# diameter of entire metalens (um)\n",
"diameter = 10\n",
"\n",
"# Define material properties at 850 nm\n",
"n_Si = 3.84 # aSi\n",
"n_SiO2 = 1.45\n",
"air = td.Medium(permittivity=1.0)\n",
"SiO2 = td.Medium(permittivity=n_SiO2**2)\n",
"Si = td.Medium(permittivity=n_Si**2)\n",
"\n",
"# define symmetry\n",
"symmetry = (-1, 1, 0)\n",
"\n",
"# simulation run time\n",
"run_time = 100 / fwidth\n",
"min_steps_per_wvl = 10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we will also define some derived parameters:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Compute the domain size in x, y\n",
"length_xy = diameter + 2 * buffer_xy\n",
"\n",
"# focal length given diameter and numerical aperture\n",
"focal_length = length_xy / 2 / NA * np.sqrt(1 - NA**2)\n",
"\n",
"# total domain size in z: unit cells + buffer in z\n",
"length_z = H + 2 * buffer_z\n",
"\n",
"# construct simulation size array\n",
"sim_size = (length_xy, length_xy, length_z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create Metalens Geometry\n",
"\n",
"Now we will define the structures in our simulation. We will first write a function to get the coordinates of the centers of the cylinders in the metalens."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def get_cylinder_centers(diameter, spacing, full_circle: bool = False):\n",
" r_eff = diameter / 2 - spacing / 2 # max radius of centers\n",
" coords = np.arange(0, r_eff, spacing)\n",
"\n",
" if full_circle:\n",
" coords = np.concatenate([-coords[::-1], coords])\n",
"\n",
" x, y = np.meshgrid(coords, coords)\n",
" points = np.vstack((x.flat, y.flat)).T\n",
"\n",
" # Create a boolean mask for points within the circle\n",
" mask = x**2 + y**2 <= r_eff**2\n",
"\n",
" # Apply the mask to get the final points\n",
" return points[mask.flat]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For a diameter of 10.0 µm, there are 780 cylinders.\n",
"The metalens has an area of 78.5 µm² and a focal length of 4.7 µm.\n"
]
}
],
"source": [
"centers_quarter = get_cylinder_centers(diameter, S, full_circle=False)\n",
"centers_full = get_cylinder_centers(diameter, S, full_circle=True)\n",
"N = len(centers_full)\n",
"\n",
"print(f\"For a diameter of {diameter:.1f} µm, there are {N} cylinders.\")\n",
"print(\n",
" f\"The metalens has an area of {np.pi * (diameter / 2) ** 2:.1f} µm² and a focal length of {focal_length:.1f} µm.\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's visualize the cell centers."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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",
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