{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Metal oxide sunscreen\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note: the cost of running the entire notebook is larger than 1 FlexCredits.\n",
"\n",
"Sunscreen technology, developed in the 1940s to mitigate sunburn, has advanced significantly with the integration of metal oxide particles, primarily zinc oxide and titanium dioxide. These formulations provide robust protection against UV rays, ensuring effective defense against varying intensities of sun exposure. A common misconception is that the protective action mainly arises from the reflection and scattering of these active metal oxide particles, rather than their absorption.\n",
"\n",
"In this notebook, we will reproduce the results presented in the paper titled: `Cole, C., Shyr, T., & Ou‐Yang, H. (2015). Metal oxide sunscreens protect skin by absorption, not by reflection or scattering` [https://doi.org/10.1111/phpp.12214](https://onlinelibrary.wiley.com/doi/10.1111/phpp.12214), where the authors confirmed, through absorption and reflectance measurements, that the main mechanism underlying UV block in metal oxide particle-based sunscreen relies on absorption of the particles, rather than reflection or scattering.\n",
"\n",
"\n",
"The simulation model consists of an agglomerate of TiO₂ nanoparticles excited by a plane wave at normal incidence. Flux monitors are positioned on the top and bottom of the simulation domain to compute transmitted and forward scattered fields (which would penetrate the skin) and reflected and back-scattered fields (which do not penetrate the skin due to the nanoparticles action). The material properties of the TiO₂ particles are obtained directly from [refractiveindex.info](https://refractiveindex.info/), and fitted using `Tidy3D`'s dispersion fitting tool.\n",
"\n",
"\n",
"\n",
"\n",
"For more examples involving scattering of nanoparticles and structured surfaces, please refer to our [example library](https://www.flexcompute.com/tidy3d/learning-center/example-library/), where you can find interesting case studies such as [scattering cross-section calculation of a dielectric sphere](https://www.flexcompute.com/tidy3d/examples/notebooks/Near2FarSphereRCS/), [the scattering of a plasmonic nanoparticle ](https://www.flexcompute.com/tidy3d/examples/notebooks/PlasmonicNanoparticle/), [the gradient metasurface reflector](https://www.flexcompute.com/tidy3d/examples/notebooks/GradientMetasurfaceReflector/), and [the dielectric metasurface absorber](https://www.flexcompute.com/tidy3d/examples/notebooks/DielectricMetasurfaceAbsorber/).\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation Setup\n",
"\n",
"First, we will import the necessary libraries."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:35:32.894454Z",
"iopub.status.busy": "2025-05-15T10:35:32.894352Z",
"iopub.status.idle": "2025-05-15T10:35:34.270560Z",
"shell.execute_reply": "2025-05-15T10:35:34.270009Z"
}
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import tidy3d as td\n",
"from tidy3d import web\n",
"\n",
"# defining a random seed for reproducibility\n",
"np.random.seed(12)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Retrieving refractive index data and creating the medium.\n",
"\n",
"We will retrieve material property data from [refractiveindex.info](https://refractiveindex.info/) using the `from_url` method of the [`FastDispersionFitter`](https://docs.flexcompute.com/projects/tidy3d/en/v2.5.2/_autosummary/tidy3d.plugins.dispersion.FastDispersionFitter.html) class, and fit a pole residue medium. \n",
"\n",
"For more information about fitting dispersive material, please refer to this example [notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Fitting/)."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:35:34.272356Z",
"iopub.status.busy": "2025-05-15T10:35:34.272148Z",
"iopub.status.idle": "2025-05-15T10:36:00.388046Z",
"shell.execute_reply": "2025-05-15T10:36:00.387812Z"
}
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "15a4b288db3549c0bd377ad7636772f4",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Output()"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n"
],
"text/plain": []
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"
12:36:00 CEST WARNING: Unable to fit with weighted RMS error under \n",
"'tolerance_rms' of 1e-05\n",
"
\n"
],
"text/plain": [
"\u001b[2;36m12:36:00 CEST\u001b[0m\u001b[2;36m \u001b[0m\u001b[31mWARNING: Unable to fit with weighted RMS error under \u001b[0m\n",
"\u001b[2;36m \u001b[0m\u001b[32m'tolerance_rms'\u001b[0m\u001b[31m of \u001b[0m\u001b[1;36m1e-05\u001b[0m\u001b[31m \u001b[0m\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from tidy3d.plugins.dispersion import FastDispersionFitter\n",
"\n",
"url = \"https://refractiveindex.info/tmp/database/data-nk/main/TiO2/Zhukovsky.txt\"\n",
"\n",
"# creating the fitter object loading that from the url\n",
"fitter = FastDispersionFitter.from_url(url, delimiter=\"\\t\")\n",
"\n",
"# fitting the data\n",
"medium, error = fitter.fit(max_num_poles=5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although the RMS error cannot be below $10^{-5}$, we can see that the material properties are well described by the fit."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:36:00.561811Z",
"iopub.status.busy": "2025-05-15T10:36:00.561744Z",
"iopub.status.idle": "2025-05-15T10:36:00.656413Z",
"shell.execute_reply": "2025-05-15T10:36:00.656061Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plotting for comparison\n",
"fig, ax = plt.subplots()\n",
"\n",
"# original dataset\n",
"freq = td.C_0 / fitter.wvl_um * 10**-12\n",
"ax.plot(freq, fitter.n_data, \"o\", alpha=0.2, color=\"black\", label=\"n\")\n",
"ax.plot(freq, fitter.k_data, \"o\", alpha=0.2, color=\"black\", label=\"k\")\n",
"\n",
"\n",
"medium.plot(np.linspace(td.C_0 / 0.215, td.C_0 / 1.5, 1000), ax=ax)\n",
"ax.lines[-1].set_ls(\"--\")\n",
"ax.lines[-1].set_label(\"Fitted n\")\n",
"ax.lines[-2].set_ls(\"--\")\n",
"ax.lines[-2].set_label(\"Fitted k\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Define parameters for building the simulation\n",
"\n",
"We are now defining the parameters that will be used to build the simulation."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
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"source": [
"# for simplicity, the nanoparticles are modeled as spheres\n",
"size = 0.025\n",
"\n",
"# volume to place the nanoparticles\n",
"lx = 1.2\n",
"ly = 1.2\n",
"lz = 10 * size\n",
"\n",
"# target spectrum\n",
"wl1 = 0.22\n",
"wl2 = 0.800\n",
"\n",
"central_wl = (wl2 - wl1) / 2 + wl1\n",
"freq1 = td.C_0 / wl1\n",
"freq2 = td.C_0 / wl2\n",
"freq0 = (freq1 - freq2) / 2 + freq2\n",
"fwidth = (freq1 - freq2) / 2\n",
"\n",
"# frequencies to be analyzed in the monitors\n",
"freqs = np.linspace(freq0 - fwidth, freq0 + fwidth, 1000)\n",
"\n",
"# size of the simulation domain\n",
"Lz = 2 * wl2 + lz\n",
"Lx = lx\n",
"Ly = ly\n",
"\n",
"# source and monitor position\n",
"monitor_z = (Lz / 2 - lz / 2) / 3\n",
"source_z = -Lz / 2 + 2 * (Lz / 2 - lz / 2) / 3\n",
"\n",
"structures_center = (0, 0, 0)\n",
"\n",
"# simulation runtime\n",
"run_time = 5e-12\n",
"\n",
"# boundary specifications. We will define PML at the z-boundaries and periodic conditions on the remaining ones.\"\n",
"boundary_spec = td.BoundarySpec(\n",
" x=td.Boundary.periodic(), y=td.Boundary.periodic(), z=td.Boundary.pml()\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we will create an auxiliary function to randomly place the nanoparticles as a function of the concentration. The number of particles is calculated with parameters given in the paper."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:36:00.662091Z",
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"outputs": [],
"source": [
"def get_particles(proportion=0.2):\n",
" # concentration of petrolatum matrix\n",
" petrolatum_concentration = 1.3e-8 # mg/um^3\n",
" active_proportion = proportion\n",
" particle_volume = (4 / 3) * np.pi * size**3\n",
" Ti02_density = 4.23e-9 # mg/um^3\n",
" particle_weight = Ti02_density * particle_volume\n",
"\n",
" # calculate the total mass of Ti02 nanoparticles\n",
" volume = lx * ly * lz\n",
" Ti02_mass = active_proportion * volume * petrolatum_concentration # mg\n",
"\n",
" # defining the number of particles\n",
" N_particles = int(Ti02_mass / particle_weight)\n",
"\n",
" # create arrays of random positions for each particle\n",
" positions_x = np.random.uniform(-lx / 2, lx / 2, N_particles)\n",
" position_y = np.random.uniform(-ly / 2, ly / 2, N_particles)\n",
" positions_z = np.random.uniform(\n",
" structures_center[2] - lz / 2, structures_center[2] + lz / 2, N_particles\n",
" )\n",
"\n",
" # create a first geometry object and sum the others to form the agglomerate\n",
" particles = td.Sphere(center=(positions_x[0], position_y[0], positions_z[0]), radius=size)\n",
"\n",
" for pos in zip(positions_x[1:], position_y[1:], positions_z[1:]):\n",
" particles += td.Sphere(center=pos, radius=size)\n",
"\n",
" particles = td.Structure(geometry=particles, medium=medium)\n",
"\n",
" return [particles]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define source and monitors:\n",
"\n",
"The source spectrum is chosen to cover the most intense part of the solar emission and the UV region, which is the main concern for skin health.\n",
"\n",
"Since the size of the nanoparticles is much smaller than the target wavelengths, \n",
"we will add a [mesh override structure](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.MeshOverrideStructure.html) \n",
"to properly resolve the nanoparticles agglomerate.\n",
"\n",
"We will simulate for two active particle concentration, 10% and 20%.\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:36:00.665918Z",
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"text/html": [
"\n",
" \n",
" \n",
" "
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""
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"source": [
"source = td.PlaneWave(\n",
" center=(0, 0, source_z),\n",
" size=(td.inf, td.inf, 0),\n",
" source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
" direction=\"+\",\n",
")\n",
"\n",
"monitor_bottom = td.FluxMonitor(\n",
" center=(0, 0, -Lz / 2 + monitor_z),\n",
" size=(td.inf, td.inf, 0),\n",
" freqs=freqs,\n",
" name=\"z-\",\n",
")\n",
"\n",
"monitor_top = td.FluxMonitor(\n",
" center=(0, 0, Lz / 2 - monitor_z),\n",
" size=(td.inf, td.inf, 0),\n",
" freqs=freqs,\n",
" name=\"z\",\n",
")\n",
"\n",
"\n",
"mesh_override = td.MeshOverrideStructure(\n",
" geometry=td.Box(center=structures_center, size=(lx, ly, lz + 2 * size)),\n",
" dl=(size / 6,) * 3,\n",
")\n",
"grid_spec = td.GridSpec.auto(min_steps_per_wvl=10, override_structures=[mesh_override])\n",
"\n",
"sim = td.Simulation(\n",
" size=(Lx, Ly, Lz),\n",
" structures=[],\n",
" sources=[source],\n",
" monitors=[monitor_bottom, monitor_top],\n",
" run_time=run_time,\n",
" boundary_spec=boundary_spec,\n",
" grid_spec=grid_spec,\n",
")\n",
"\n",
"Simulations = {\n",
" \"proportion 10%\": sim.updated_copy(structures=get_particles(0.1)),\n",
" \"proportion 20%\": sim.updated_copy(structures=get_particles(0.2)),\n",
"}\n",
"\n",
"# visualizing\n",
"Simulations[\"proportion 10%\"].plot_3d()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will run both simulations in parallel using the [`web.Batch`](https://docs.flexcompute.com/projects/tidy3d/en/v1.5.0/_autosummary/tidy3d.web.container.Batch.html) function."
]
},
{
"cell_type": "code",
"execution_count": 7,
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"execution": {
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"shell.execute_reply": "2025-05-15T10:39:49.178415Z"
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"Output()"
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"data": {
"text/html": [
"\n"
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"
12:36:15 CEST Started working on Batch containing 2 tasks. \n",
"
![\"Schematic](\"img/MetalOxideSunscreen_1.png\")
\n",
"\n",
"For more examples involving scattering of nanoparticles and structured surfaces, please refer to our [example library](https://www.flexcompute.com/tidy3d/learning-center/example-library/), where you can find interesting case studies such as [scattering cross-section calculation of a dielectric sphere](https://www.flexcompute.com/tidy3d/examples/notebooks/Near2FarSphereRCS/), [the scattering of a plasmonic nanoparticle ](https://www.flexcompute.com/tidy3d/examples/notebooks/PlasmonicNanoparticle/), [the gradient metasurface reflector](https://www.flexcompute.com/tidy3d/examples/notebooks/GradientMetasurfaceReflector/), and [the dielectric metasurface absorber](https://www.flexcompute.com/tidy3d/examples/notebooks/DielectricMetasurfaceAbsorber/).\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation Setup\n",
"\n",
"First, we will import the necessary libraries."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:35:32.894454Z",
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"shell.execute_reply": "2025-05-15T10:35:34.270009Z"
}
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"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import tidy3d as td\n",
"from tidy3d import web\n",
"\n",
"# defining a random seed for reproducibility\n",
"np.random.seed(12)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Retrieving refractive index data and creating the medium.\n",
"\n",
"We will retrieve material property data from [refractiveindex.info](https://refractiveindex.info/) using the `from_url` method of the [`FastDispersionFitter`](https://docs.flexcompute.com/projects/tidy3d/en/v2.5.2/_autosummary/tidy3d.plugins.dispersion.FastDispersionFitter.html) class, and fit a pole residue medium. \n",
"\n",
"For more information about fitting dispersive material, please refer to this example [notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/Fitting/)."
]
},
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"cell_type": "code",
"execution_count": 2,
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"Output()"
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