{ "cells": [ { "cell_type": "markdown", "id": "a65a6737", "metadata": {}, "source": [ "# Session 4 Challenge: Photonic Crystal Slabs" ] }, { "cell_type": "markdown", "id": "47e433db", "metadata": {}, "source": [ "Photonic crystal (PhC) slab waveguides are built by removing one line of holes from the bulk periodic slab lattice. Light is confined by the photonic bandgap effect [1, 2] in the in-plane direction, and by index guiding in the vertical direction. Their ability to confine and guide light with low loss while simultaneously providing the flexibility to engineer dispersion properties makes them highly desirable for realizing compact and efficient optical components within integrated circuits. This includes on-chip light sources, modulators, detectors, and other passive and active devices essential for information processing and communication systems." ] }, { "cell_type": "markdown", "id": "a0c8e122", "metadata": {}, "source": [ "## Challenge Description\n", "\n", "1. Create a photonic crystal slab waveguide by removing the central row of holes in a hexagonal array of holes. The photonic crystal lattice should have 15 holes in the y-direction and 13 in the x-direction. Use a lattice constant ($a$) of 0.440 $\\mu m$, a hole radius ($r$) of 0.154 $\\mu m$, a slab thickness ($t$) of 0.26 $\\mu m$. Then, connect two 1 $\\mu m$ long and 0.45 $\\mu m$ wide input and output waveguides. Use the [Crystalline Silicon (\"cSi\") 'Palik_Lossless'](https://docs.flexcompute.com/projects/tidy3d/en/v2.6.0rc1/api/material_library.html) from the Tidy3D material library to create the core material. You can see this [example](https://www.flexcompute.com/tidy3d/examples/notebooks/PhotonicCrystalWaveguidePolarizationFilter/) for getting help on how to create this photonic crystal structure. \n", "\n", "2. Create a mode source and inject the transverse electric (TE) fundamental waveguide mode at the input waveguide.\n", "\n", "3. Measure the coupling efficiency into the same mode at the output waveguide. Set the mode monitor to wavelengths between 1.4 $\\mu m$ and 1.7 $\\mu m$ using 151 wavelength points.\n", "\n", "4. Plot the coupling efficiency x wavelength graph and identify the cutoff wavelength.\n", "\n", "### Notes\n", "\n", "a) This simulation presents long-lived resonances potentially caused by band-edge states. So, the fields can take longer to decay fully. However, a simulation `runtime` of **4 ps** is good enough to identify the waveguide cutoff wavelength clearly.\n", "\n", "b) Include symmetry about `y` and `z`-axis to reduce the computational cost. See details [here](https://www.flexcompute.com/tidy3d/examples/notebooks/Symmetry/).\n", "\n", "c) You can develop this example using the Tidy3D [Python notebook](https://tidy3d.simulation.cloud/notebook) or the [Graphical User Interface (GUI)](https://tidy3d.simulation.cloud/folders) web-based environments." ] }, { "cell_type": "markdown", "id": "a585286d", "metadata": {}, "source": [ "## References\n", "\n", "[1] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).\n", "\n", "[2] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062." ] } ], "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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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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