Updating Definition of Hermite-Gaussian Modes (#319)

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxence Thévenet <[email protected]>

docs/source/api/profiles/transverse/hermite_gaussian_profile.rst

@@ -2,10 +2,8 @@ Hermite Gaussian Transverse Profile
 ===================================
 
 Used to define a Hermite-Gaussian transverse laser profile.
-Hermite-Gaussian modes are a family of solutions to the paraxial wave equation written in cartesian coordinates. The modes are characterised by two transverse indices :math:`n_x` and :math:`n_y`.
+Hermite-Gaussian modes are a family of solutions to the paraxial wave equation written in cartesian coordinates. The modes are characterised by two transverse indices :math:`m` and :math:`n`.
 
-.. image:: https://user-images.githubusercontent.com/27694869/211018259-15d925bb-f123-42c6-b5ba-86488356ae70.png
-    :alt: Hermite-Gauss-Modes
 
 ------------
 

docs/source/tutorials/denoised_laser.ipynb

@@ -309,19 +309,19 @@
    "outputs": [],
    "source": [
     "# Maximum Hermite-Gauss mode index in x and y\n",
-    "n_modes_x = 2\n",
-    "n_modes_y = 2\n",
+    "m_max = 10\n",
+    "n_max = 10\n",
     "\n",
     "# Calculate the decomposition and waist of the laser pulse\n",
     "modeCoeffs, waist = hermite_gauss_decomposition(\n",
-    "    transverse_profile, n_x_max=n_modes_x, n_y_max=n_modes_y, res=cal\n",
+    "    transverse_profile, longitudinal_profile.lambda0, m_max=m_max, n_max=n_max, res=cal\n",
     ")\n",
     "\n",
     "# Create a num profile, summing over the first few modes\n",
     "energy_frac = 0\n",
     "for i, mode_key in enumerate(list(modeCoeffs)):\n",
     "    tmp_transverse_profile = HermiteGaussianTransverseProfile(\n",
-    "        waist, mode_key[0], mode_key[1]\n",
+    "        waist, waist, mode_key[0], mode_key[1], longitudinal_profile.lambda0\n",
     "    )\n",
     "    energy_frac += modeCoeffs[mode_key] ** 2  # Energy fraction of the mode\n",
     "    if i == 0:  # First mode (0,0)\n",
@@ -365,13 +365,14 @@
     "# Determine the figure parameters\n",
     "fig, ax = plt.subplots(1, 3, figsize=(12, 4), tight_layout=True)\n",
     "fig.suptitle(\n",
-    "    \"Hermite-Gauss Reconstruction using n_x_max = %i, n_y_max = %i\"\n",
-    "    % (n_modes_x, n_modes_y)\n",
+    "    \"Hermite-Gauss Reconstruction using m_max = %i, n_max = %i\" % (m_max, n_max)\n",
     ")\n",
     "\n",
     "# Plot the original profile\n",
     "pltextent = np.array([np.min(x), np.max(x), np.min(x), np.max(x)]) * 1e6  # in microns\n",
     "prof1 = np.abs(laser_profile_raw.evaluate(X, Y, 0)) ** 2\n",
+    "maxInten = np.max(prof1)\n",
+    "prof1 /= maxInten\n",
     "divider0 = make_axes_locatable(ax[0])\n",
     "ax0_cb = divider0.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
     "pl0 = ax[0].imshow(prof1, cmap=\"magma\", extent=pltextent, vmin=0, vmax=np.max(prof1))\n",
@@ -383,6 +384,7 @@
     "\n",
     "# Plot the reconstructed profile\n",
     "prof2 = np.abs(laser_profile_cleaned.evaluate(X, Y, 0)) ** 2\n",
+    "prof2 /= maxInten\n",
     "divider1 = make_axes_locatable(ax[1])\n",
     "ax1_cb = divider1.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
     "pl1 = ax[1].imshow(prof2, cmap=\"magma\", extent=pltextent, vmin=0, vmax=np.max(prof1))\n",
@@ -403,6 +405,51 @@
     "ax[2].set_ylabel(\"y ($ \\\\mu m $)\")\n",
     "ax[2].set_title(\"Error\")\n",
     "\n",
+    "plt.show()\n",
+    "\n",
+    "fig2, ax2 = plt.subplots(2, 1, figsize=(8, 6), tight_layout=True)\n",
+    "fig2.suptitle(\n",
+    "    \"Hermite-Gauss Reconstruction using m_max = %i, n_max = %i\" % (m_max, n_max)\n",
+    ")\n",
+    "ax2[0].plot(\n",
+    "    x * 1e6,\n",
+    "    prof2[int(len(x) / 2), :],\n",
+    "    label=\"Reconstructed Profile\",\n",
+    "    color=(1, 0.5, 0.5),\n",
+    "    lw=2.5,\n",
+    ")\n",
+    "ax2[0].plot(\n",
+    "    x * 1e6,\n",
+    "    prof1[int(len(x) / 2), :],\n",
+    "    label=\"Original Profile\",\n",
+    "    color=(0.3, 0.3, 0.3),\n",
+    "    lw=1.0,\n",
+    ")\n",
+    "ax2[0].legend()\n",
+    "ax2[0].set_xlim(pltextent[0], pltextent[1])\n",
+    "ax2[0].set_xlabel(\"x ($ \\\\mu m $)\")\n",
+    "ax2[0].set_ylabel(\"Intensity (norm.)\")\n",
+    "\n",
+    "ax2[1].plot(\n",
+    "    x * 1e6,\n",
+    "    prof2[int(len(x) / 2), :],\n",
+    "    label=\"Reconstructed Profile\",\n",
+    "    color=(1, 0.5, 0.5),\n",
+    "    lw=2.5,\n",
+    ")\n",
+    "ax2[1].plot(\n",
+    "    x * 1e6,\n",
+    "    prof1[int(len(x) / 2), :],\n",
+    "    label=\"Original Profile\",\n",
+    "    color=(0.3, 0.3, 0.3),\n",
+    "    lw=1.0,\n",
+    ")\n",
+    "ax2[1].legend()\n",
+    "ax2[1].set_xlim(pltextent[0], pltextent[1])\n",
+    "ax2[1].set_yscale(\"log\")\n",
+    "ax2[1].set_xlabel(\"x ($ \\\\mu m $)\")\n",
+    "ax2[1].set_ylabel(\"Intensity (norm.)\")\n",
+    "\n",
     "plt.show()"
    ]
   },
@@ -473,7 +520,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": ".venv",
+   "display_name": "base",
    "language": "python",
    "name": "python3"
   },
@@ -487,7 +534,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.0"
+   "version": "3.12.7"
   }
  },
  "nbformat": 4,