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April 5, 2025 13:29
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "7a0fcecb", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import matplotlib.pyplot as plt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 30, | |
| "id": "1e431629", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Define parameters\n", | |
| "w = 55 / 2 # 1/e^2 radius (half of 55 µm)\n", | |
| "x = np.linspace(0, 105, 1000) # µm" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 31, | |
| "id": "805e04cb", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Gaussian beam profile: I(x) = I0 * exp(-2 * (x/w)^2)\n", | |
| "I0 = 1 # peak intensity\n", | |
| "I = I0 * np.exp(-2 * (x / w)**2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 34, | |
| "id": "7febc60a", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 800x400 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(8, 4))\n", | |
| "plt.plot(x, I, label=r'$I(x) = I_0 e^{-2(x/w)^2}$')\n", | |
| "plt.axhline(y=np.exp(-2), color='red', linestyle='--', label=r'$1/e^2$ level')\n", | |
| "plt.axvline(x=w, color='gray', linestyle='--')\n", | |
| "\n", | |
| "probe_spacing = 20.0 # um\n", | |
| "for probe_x_index in np.arange(0, 5):\n", | |
| " probe_x = probe_x_index * probe_spacing\n", | |
| " plt.axvline(x=probe_x, color='black', linestyle='-')\n", | |
| "\n", | |
| "y_text_pos = 30\n", | |
| "plt.text(w + 2, y_text_pos, f'w = {w:.1f} µm', verticalalignment='center')\n", | |
| "\n", | |
| "plt.xlabel('x (µm)')\n", | |
| "plt.ylabel('Intensity (a.u.)')\n", | |
| "plt.legend()\n", | |
| "\n", | |
| "plt.grid(True)\n", | |
| "plt.yscale(\"log\")\n", | |
| "\n", | |
| "plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 42, | |
| "id": "d8b58880", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "0\t232.00000\n", | |
| "1\t80.55065\n", | |
| "2\t3.37141\n", | |
| "3\t0.01701\n", | |
| "4\t0.00001\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "probe_spacing = 20.0 # um\n", | |
| "for probe_x_index in np.arange(0, 5):\n", | |
| " probe_x = probe_x_index * probe_spacing\n", | |
| " intensity = I0 * np.exp(-2 * (probe_x / w)**2)\n", | |
| " print(f\"{probe_x_index}\\t{232 * intensity:.5f}\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "141cccfe", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "base", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.10.0" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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