{ "cells": [ { "cell_type": "markdown", "id": "a65a6737", "metadata": {}, "source": [ "# Session 3 Challenge: Designing Filters and Reflectors" ] }, { "cell_type": "markdown", "id": "47e433db", "metadata": {}, "source": [ "An [anti-reflection coating](https://en.wikipedia.org/wiki/Anti-reflective_coating) (ARC) is usually a thin film applied to photovoltaic solar cells, lenses, or other optical devices to reduce reflection. In its simplest form, an ARC is made of a dielectric material with a specific thickness and refractive index.\n", "\n", "For instance, when dealing with silicon solar cells (refractive index $n_2=3.5$) exposed to normal light incidence from the air ($n_0=1.0$), a good choice for an ARC would be a thin film made of $Si_{3}N_{4}$ ($n_1=2.0$) with a thickness of $t_1=\\lambda_{0}/(4n_{1})$, where $\\lambda_{0}$ refers to the central light wavelength. However, if $n_1>n_2$, a half-wavelength thin film may be used instead.\n", "\n", "The reflectance of the device ($R_{ARC}$) can be calculated using the formula [1]\n", "\n", "$$\n", "R_{ARC} = \\frac{r_{1}^{2} + r_{2}^{2} + 2r_{1}r_{2}cos(2\\beta)}{1 + r_{1}^{2}r_{2}^{2} + 2r_{1}r_{2}cos(2\\beta)},\n", "$$\n", "\n", "where\n", "\n", "$\n", "r_{1} = \\frac{n_{0} - n_{1}}{n_{0} + n_{1}},\n", "$\n", "\n", "$\n", "r_{2} = \\frac{n_{1} - n_{2}}{n_{1} + n_{2}},\n", "$\n", "\n", "and\n", "\n", "$\n", "\\beta = \\frac{2\\pi n_{1}t_{1}}{\\lambda _{0}}.\n", "$" ] }, { "cell_type": "markdown", "id": "f333a270", "metadata": {}, "source": [ "## Challenge description\n", "\n", "1. Firstly, calculate the thickness of a $Si_{3}N_{4}$ film to create an ARC that will lower the reflectance of a silicon solar cell, assuming the central light wavelength is 0.6 $\\mu m$. Next, create an FDTD model to determine the reflectance of the device when illuminated with normal light incidence within a wavelength range of 0.3 $\\mu m$. You can perform this task using either the Tidy3D [Python notebook](https://tidy3d.simulation.cloud/notebook) or the [Graphical User Interface (GUI)](https://tidy3d.simulation.cloud/folders) web-based environments.\n", "\n", "2. (Optional) - Compare the reflectance values obtained from the simulation with the analytical values." ] }, { "cell_type": "markdown", "id": "3f10dcc4", "metadata": {}, "source": [ "## References\n", "[1] Born M, Wolf E, Bhatia AB, et al. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7th ed. Cambridge: Cambridge University Press; 1999. doi:10.1017/CBO9781139644181" ] } ], "metadata": { "description": "This notebook demonstrates how to model distributed Bragg reflector and cavity in Tidy3D FDTD.", "feature_image": "./img/dbr_schematic.png", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "keywords": "distributed bragg reflector, DBR, cavity, 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": "3.12.1" }, "title": "Distributed Bragg Reflector and Cavity | Flexcompute", "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "09a6392e66064180940d99f350a67ac9": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "0f58e3a1357c42c3b22815068f47a6e4": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_58602acbc14b44f5840f3ed061c0dabd", "msg_id": "", "outputs": [ { "data": { "text/html": "
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🚶  Starting 'dbr_cavity'...\n
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↑ simulation.hdf5.gz ━━━━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 9.1/9.1 kB • ? • 0:00:00\n
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null, "visibility": null, "width": null } }, "7919953542774e61a0b79f60b0379c61": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "813e4900cc5d411e814689a78d905317": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_3f62f8cc5d9d4abfbc97bb52020b45fe", "msg_id": "", "outputs": [ { "data": { "text/html": "
↑ simulation.hdf5.gz ━━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 17.0/17.0 kB • ? • 0:00:00\n
\n", "text/plain": "\u001b[1;31m↑\u001b[0m \u001b[1;34msimulation.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m17.0/17.0 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n" }, "metadata": {}, "output_type": "display_data" } ], "tabbable": null, "tooltip": null } }, "8345c8ec24f84508b704a28be435e2e2": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "8dd1213dae46438e807b9b818ba315ee": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_c1506714dabd47e1b1b744d308235342", "msg_id": "", "outputs": [ { "data": { "text/html": "
↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 110.2/110.2 kB • ? • 0:00:00\n
\n", "text/plain": "\u001b[1;32m↓\u001b[0m \u001b[1;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m110.2/110.2 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n" }, "metadata": {}, "output_type": "display_data" } ], "tabbable": null, "tooltip": null } }, "8e42d3d1684b49b6941ce6577767a2a7": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_7919953542774e61a0b79f60b0379c61", "msg_id": "", "outputs": [ { "data": { "text/html": "
N=2.00: status = success  ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% 0:00:00\nN=3.00: status = success  ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% 0:00:00\nN=4.00: status = success  ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% 0:00:00\nN=5.00: status = success  ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% 0:00:00\nN=10.00: status = success ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% 0:00:00\n
\n", "text/plain": "N=2.00: status = success \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\nN=3.00: status = success \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\nN=4.00: status = success \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\nN=5.00: status = success \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\nN=10.00: status = success \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n" }, "metadata": {}, "output_type": "display_data" } ], "tabbable": null, "tooltip": null } }, "8fdd2cf4d9c1471f943af89a8a4e0bc6": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "8fde6f97af6a4a078403e84e43e3e21a": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_2edd86b37cab403a81740fceb08aff35", "msg_id": "", "outputs": [ { "data": { "text/html": "
↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━ 100.0% • 29.0/29.0 MB • 17.5 MB/s • 0:00:00\n
\n", "text/plain": "\u001b[1;32m↓\u001b[0m \u001b[1;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m29.0/29.0 MB\u001b[0m • \u001b[31m17.5 MB/s\u001b[0m • \u001b[36m0:00:00\u001b[0m\n" }, "metadata": {}, "output_type": "display_data" } ], "tabbable": null, "tooltip": null } }, "9287cc892b6d4466ab4912c230d5e684": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_779ae4e2a850442e8006445b59567e66", "msg_id": "", "outputs": [ { "data": { "text/html": "
↓ monitor_data.hdf5 ━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 122.7/122.7 kB • ? • 0:00:00\n
\n", "text/plain": "\u001b[1;32m↓\u001b[0m \u001b[1;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m122.7/122.7 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n" }, "metadata": {}, "output_type": "display_data" } ], "tabbable": null, "tooltip": null } }, "9fd252d935e14dcbb1686a1a64c0186c": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_10a4452f1a1648e3b1852bb0dd223173", "msg_id": "", "outputs": [ { "data": { "text/html": "
↑ simulation.hdf5.gz ━━━━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 9.0/9.0 kB • ? • 0:00:00\n
\n", "text/plain": "\u001b[1;31m↑\u001b[0m \u001b[1;34msimulation.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m9.0/9.0 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n" }, "metadata": {}, "output_type": "display_data" } ], "tabbable": null, "tooltip": null } }, "c1506714dabd47e1b1b744d308235342": { "model_module": "@jupyter-widgets/base", "model_module_version": "2.0.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "2.0.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "2.0.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border_bottom": null, "border_left": null, "border_right": null, "border_top": null, "bottom": null, "display": null, "flex": null, "flex_flow": null, "grid_area": null, "grid_auto_columns": null, "grid_auto_flow": null, "grid_auto_rows": null, "grid_column": null, "grid_gap": null, "grid_row": null, "grid_template_areas": null, "grid_template_columns": null, "grid_template_rows": null, "height": null, "justify_content": null, "justify_items": null, "left": null, "margin": null, "max_height": null, "max_width": null, "min_height": null, "min_width": null, "object_fit": null, "object_position": null, "order": null, "overflow": null, "padding": null, "right": null, "top": null, "visibility": null, "width": null } }, "c7a79a946ade4b0587df8af104fe9846": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/output", "_model_module_version": "1.0.0", "_model_name": "OutputModel", "_view_count": null, "_view_module": "@jupyter-widgets/output", "_view_module_version": "1.0.0", "_view_name": "OutputView", "layout": "IPY_MODEL_8fdd2cf4d9c1471f943af89a8a4e0bc6", "msg_id": "", "outputs": [ { "data": { "text/html": "
↑ simulation.hdf5.gz ━━━━━━━━━━━━━━━━━━━━━━━━━ 100.0% • 9.1/9.1 kB • ? • 0:00:00\n
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