{ "cells": [ { "cell_type": "markdown", "id": "bd45434d", "metadata": { "papermill": { "duration": 0.001346, "end_time": "2026-05-27T19:59:02.510210+00:00", "exception": false, "start_time": "2026-05-27T19:59:02.508864+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Rectangular Dielectric Waveguide Modes\n", "\n", "This notebook solves a dielectric core inside cladding, classifies guided modes, and plots transverse and longitudinal fields." ] }, { "cell_type": "code", "execution_count": 1, "id": "c33a4d96", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T19:59:02.516568Z", "iopub.status.busy": "2026-05-27T19:59:02.516386Z", "iopub.status.idle": "2026-05-27T19:59:03.251287Z", "shell.execute_reply": "2026-05-27T19:59:03.250599Z" }, "papermill": { "duration": 0.737451, "end_time": "2026-05-27T19:59:03.251854+00:00", "exception": false, "start_time": "2026-05-27T19:59:02.514403+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from palacetoolkit.mode_solver import WaveguideModeSolver\n", "from palacetoolkit.utils import write_and_finalize_gmsh\n", "from palacetoolkit.viz import view_mesh\n", "\n", "import gmsh\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "216a1ceb", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T19:59:03.258093Z", "iopub.status.busy": "2026-05-27T19:59:03.257842Z", "iopub.status.idle": "2026-05-27T19:59:03.264005Z", "shell.execute_reply": "2026-05-27T19:59:03.263462Z" }, "papermill": { "duration": 0.011741, "end_time": "2026-05-27T19:59:03.264843+00:00", "exception": false, "start_time": "2026-05-27T19:59:03.253102+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "def _set_lc_for_dielectric(a_core, b_core, lc_core, lc_clad):\n", " pts = gmsh.model.getEntities(0)\n", " for _, ptag in pts:\n", " coord = gmsh.model.getValue(0, ptag, [])\n", " in_core = (abs(coord[0]) <= a_core / 2 + 1e-10 and abs(coord[1]) <= b_core / 2 + 1e-10)\n", " gmsh.model.mesh.setSize([(0, ptag)], lc_core if in_core else lc_clad)\n", "\n", "\n", "def make_dielectric_waveguide_mesh(a_core, b_core, a_clad, b_clad, nx_core=16, ny_core=8, nx_clad=8, ny_clad=8, filename=None):\n", " gmsh.initialize()\n", " gmsh.option.setNumber(\"General.Verbosity\", 0)\n", " gmsh.model.add(\"dielectric_waveguide\")\n", "\n", " clad = gmsh.model.occ.addRectangle(-a_clad / 2, -b_clad / 2, 0, a_clad, b_clad)\n", " core = gmsh.model.occ.addRectangle(-a_core / 2, -b_core / 2, 0, a_core, b_core)\n", " _, outmap = gmsh.model.occ.fragment([(2, clad)], [(2, core)])\n", " gmsh.model.occ.synchronize()\n", "\n", " core_surfs = [tag for _, tag in outmap[1]]\n", " clad_surfs = [tag for _, tag in outmap[0] if tag not in core_surfs]\n", "\n", " gmsh.model.addPhysicalGroup(2, core_surfs, tag=1, name=\"core\")\n", " gmsh.model.addPhysicalGroup(2, clad_surfs, tag=2, name=\"cladding\")\n", "\n", " all_surfs = [(2, t) for t in core_surfs + clad_surfs]\n", " outer_bnd = gmsh.model.getBoundary(all_surfs, oriented=False, combined=True)\n", " pec_tags = [abs(tag) for _, tag in outer_bnd]\n", " gmsh.model.addPhysicalGroup(1, pec_tags, tag=1, name=\"PEC\")\n", "\n", " lc_core = min(a_core / nx_core, b_core / ny_core)\n", " lc_clad = max(lc_core * max(nx_core / nx_clad, ny_core / ny_clad), 1.5 * lc_core)\n", " _set_lc_for_dielectric(a_core, b_core, lc_core, lc_clad)\n", "\n", " gmsh.model.mesh.generate(2)\n", " return write_and_finalize_gmsh(filename, prefix=\"wg_diel_\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "b05177fc", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T19:59:03.267746Z", "iopub.status.busy": "2026-05-27T19:59:03.267612Z", "iopub.status.idle": "2026-05-27T19:59:03.270540Z", "shell.execute_reply": "2026-05-27T19:59:03.270115Z" }, "papermill": { "duration": 0.004997, "end_time": "2026-05-27T19:59:03.270922+00:00", "exception": false, "start_time": "2026-05-27T19:59:03.265925+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Guided-mode window: 5.4414 < kn < 10.8828\n" ] } ], "source": [ "a_core, b_core = 1.0, 0.5\n", "a_clad, b_clad = 4.0, 3.0\n", "eps_core, eps_clad = 4.0, 1.0\n", "mu = 1.0\n", "\n", "k0_cutoff_approx = np.pi / a_core / np.sqrt(eps_core - eps_clad)\n", "omega = 3.0 * k0_cutoff_approx\n", "\n", "kn_min = omega * np.sqrt(mu * eps_clad)\n", "kn_max = omega * np.sqrt(mu * eps_core)\n", "print(f\"Guided-mode window: {kn_min:.4f} < kn < {kn_max:.4f}\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "ce38bb09", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T19:59:03.273263Z", "iopub.status.busy": "2026-05-27T19:59:03.273150Z", "iopub.status.idle": "2026-05-27T19:59:14.003479Z", "shell.execute_reply": "2026-05-27T19:59:14.003062Z" }, "papermill": { "duration": 10.732601, "end_time": "2026-05-27T19:59:14.004469+00:00", "exception": false, "start_time": "2026-05-27T19:59:03.271868+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading mesh file: /tmp/wg_diel_7ttrgedl.msh\n", "Groups to render transparent: ['air_none', 'air_plastic_enclosure']\n", "\n", "Mesh loaded successfully with 2 cell blocks\n", "Found 3122 triangles total\n", "Physical group tags in mesh: {1: 'core', 2: 'cladding'}\n" ] }, { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " FE spaces: ND dofs = 15722, H1 dofs = 6357, total = 22079\n", " Essential DOFs: ND = 224, H1 = 224, total = 448\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.4414, sigma = -130.279, size = 22079)...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Found 10 modes:\n", " Mode 1: kn = +9.51611978e+00 -0.00000000e+00j <-- selected\n", " Mode 2: kn = +8.98886548e+00 -0.00000000e+00j\n", " Mode 3: kn = +8.06679983e+00 -0.00000000e+00j\n", " Mode 4: kn = +7.86873770e+00 -0.00000000e+00j\n", " Mode 5: kn = +6.41320112e+00 -0.00000000e+00j\n", " Mode 6: kn = +6.00582037e+00 -0.00000000e+00j\n", " Mode 7: kn = +5.85640924e+00 -0.00000000e+00j\n", " Mode 8: kn = +5.54115884e+00 -0.00000000e+00j\n", " Mode 9: kn = +5.31151432e+00 -0.00000000e+00j\n", " Mode 10: kn = +5.27932424e+00 -0.00000000e+00j\n", "Computed modes:\n", " Mode 1: kn= +9.516120 -0.000000j [guided]\n", " Mode 2: kn= +8.988865 -0.000000j [guided]\n", " Mode 3: kn= +8.066800 -0.000000j [guided]\n", " Mode 4: kn= +7.868738 -0.000000j [guided]\n", " Mode 5: kn= +6.413201 -0.000000j [guided]\n", " Mode 6: kn= +6.005820 -0.000000j [guided]\n", " Mode 7: kn= +5.856409 -0.000000j [guided]\n", " Mode 8: kn= +5.541159 -0.000000j [guided]\n", " Mode 9: kn= +5.311514 -0.000000j [radiation/substrate]\n", " Mode 10: kn= +5.279324 -0.000000j [radiation/substrate]\n" ] } ], "source": [ "mesh_file = make_dielectric_waveguide_mesh(\n", " a_core,\n", " b_core,\n", " a_clad,\n", " b_clad,\n", " nx_core=16,\n", " ny_core=8,\n", " nx_clad=8,\n", " ny_clad=8,\n", ")\n", "view_mesh(mesh_file)\n", "mu_inv_dict = {1: 1.0 / mu, 2: 1.0 / mu}\n", "eps_dict = {1: eps_core, 2: eps_clad}\n", "\n", "solver = WaveguideModeSolver(mesh_file, order=2, mu_inv=mu_inv_dict, eps=eps_dict, pec_bdr=\"all\")\n", "results = solver.solve(omega, num_modes=10, mode_idx=1)\n", "\n", "print(\"Computed modes:\")\n", "for i, kn in enumerate(results[\"kn\"], start=1):\n", " if kn_min < kn.real < kn_max:\n", " mode_type = \"guided\"\n", " elif abs(kn.imag) > 0.1 * abs(kn.real):\n", " mode_type = \"evanescent\"\n", " else:\n", " mode_type = \"radiation/substrate\"\n", " print(f\" Mode {i:2d}: kn={kn.real:+10.6f}{kn.imag:+10.6f}j [{mode_type}]\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "f3f8e9c8", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T19:59:14.074156Z", "iopub.status.busy": "2026-05-27T19:59:14.073124Z", "iopub.status.idle": "2026-05-27T19:59:51.926492Z", "shell.execute_reply": "2026-05-27T19:59:51.925969Z" }, "papermill": { "duration": 37.884199, "end_time": "2026-05-27T19:59:51.927262+00:00", "exception": false, "start_time": "2026-05-27T19:59:14.043063+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.4414, sigma = -130.279, size = 22079)...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Found 10 modes:\n", " Mode 1: kn = +9.51611978e+00 -0.00000000e+00j <-- selected\n", " Mode 2: kn = +8.98886548e+00 -0.00000000e+00j\n", " Mode 3: kn = +8.06679983e+00 -0.00000000e+00j\n", " Mode 4: kn = +7.86873770e+00 -0.00000000e+00j\n", " Mode 5: kn = +6.41320112e+00 -0.00000000e+00j\n", " Mode 6: kn = +6.00582037e+00 -0.00000000e+00j\n", " Mode 7: kn = +5.85640924e+00 -0.00000000e+00j\n", " Mode 8: kn = +5.54115884e+00 -0.00000000e+00j\n", " Mode 9: kn = +5.31151432e+00 -0.00000000e+00j\n", " Mode 10: kn = +5.27932424e+00 -0.00000000e+00j\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.4414, sigma = -130.279, size = 22079)...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Found 10 modes:\n", " Mode 1: kn = +9.51611978e+00 -0.00000000e+00j\n", " Mode 2: kn = +8.98886548e+00 -0.00000000e+00j <-- selected\n", " Mode 3: kn = +8.06679983e+00 -0.00000000e+00j\n", " Mode 4: kn = +7.86873770e+00 -0.00000000e+00j\n", " Mode 5: kn = +6.41320112e+00 -0.00000000e+00j\n", " Mode 6: kn = +6.00582037e+00 -0.00000000e+00j\n", " Mode 7: kn = +5.85640924e+00 -0.00000000e+00j\n", " Mode 8: kn = +5.54115884e+00 -0.00000000e+00j\n", " Mode 9: kn = +5.31151432e+00 -0.00000000e+00j\n", " Mode 10: kn = +5.27932424e+00 -0.00000000e+00j\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.4414, sigma = -130.279, size = 22079)...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Found 10 modes:\n", " Mode 1: kn = +9.51611978e+00 -0.00000000e+00j\n", " Mode 2: kn = +8.98886548e+00 -0.00000000e+00j\n", " Mode 3: kn = +8.06679983e+00 -0.00000000e+00j <-- selected\n", " Mode 4: kn = +7.86873770e+00 -0.00000000e+00j\n", " Mode 5: kn = +6.41320112e+00 -0.00000000e+00j\n", " Mode 6: kn = +6.00582037e+00 -0.00000000e+00j\n", " Mode 7: kn = +5.85640924e+00 -0.00000000e+00j\n", " Mode 8: kn = +5.54115884e+00 -0.00000000e+00j\n", " Mode 9: kn = +5.31151432e+00 -0.00000000e+00j\n", " Mode 10: kn = +5.27932424e+00 -0.00000000e+00j\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.4414, sigma = -130.279, size = 22079)...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Found 10 modes:\n", " Mode 1: kn = +9.51611978e+00 -0.00000000e+00j\n", " Mode 2: kn = +8.98886548e+00 -0.00000000e+00j\n", " Mode 3: kn = +8.06679983e+00 -0.00000000e+00j\n", " Mode 4: kn = +7.86873770e+00 -0.00000000e+00j <-- selected\n", " Mode 5: kn = +6.41320112e+00 -0.00000000e+00j\n", " Mode 6: kn = +6.00582037e+00 -0.00000000e+00j\n", " Mode 7: kn = +5.85640924e+00 -0.00000000e+00j\n", " Mode 8: kn = +5.54115884e+00 -0.00000000e+00j\n", " Mode 9: kn = +5.31151432e+00 -0.00000000e+00j\n", " Mode 10: kn = +5.27932424e+00 -0.00000000e+00j\n" ] }, { "data": { "image/png": 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rdevWKSEhoUl1C+jF8bq7+pYsWeKofF5ensaOHavRo0crNzdXM2fO1J133qm33norkNUEAIS98OsSJpSR3wCA4KBbdX8jwwEAgee//E5OTlZcXJzrlZWV5deaDhkyRN26ddM111yjv/71r675FRUV2rFjh9LS0lzzWrVqpbS0NG3bts2vdXCC/AYABEdw29+jRo1SdXW1x6vuhq6cnBxt2rTJVX7WrFnau3evjh8/rqNHj+rdd9/V6NGjPdY7Y8YMff755yovL9cHH3yg1NTUJtVLCnC36hkZGcrIyHBcPjs7W71799bChQslSf3799fWrVv15JNPKj093bpMeXm5212FJSUlvlUaABB+qqt861WVHlndBCO/JTIcAFo8X/NbIsMNtMEBAAHnx/zOz8936/Y8JibGxxXX6Natm7KzszVs2DCVl5frueee06hRo/TBBx/okksu0ZdffqnKykqPp8wSEhK0a9cuv9ShKchvNLeAPkFpqArie/kL+wcRg3PoLsH8u27Utm3b3O7Yk6T09PQz3rGXlZXldodhcnJyoKsJAADq8Sa/JTIcAIDmRhscANCcYmNj3V7+ujjet29f/fCHP9TQoUM1cuRILVu2TCNHjtSTTz7pl/U3N/IbAADfhNTF8cLCQusdeyUlJTp+/Lh1mdmzZ6u4uNj1ys/PD0ZVAQChpMoPL3jNm/yWyHAAaPH8kd9kuE9ogwMAmixM83v48OHau3evJKlz586Kjo5WUVGRW5mioiIlJiYGv3JNRH4DALwShvkdKAHtVj0YYmJi/HZXIQAgTFXWvnxZHkFHhgNAC+drftetA0FFfgNACxem+Z2bm6tu3bpJktq0aaOhQ4dq48aNGj9+vCSpqqpKGzdu1IwZM4JfuSAgvwEAnEM/LaQujicmJlrv2IuNjVW7du2aqVYAAOBMyG8AAMITGQ4ACAelpaWup74lKS8vT7m5uerUqZN69Oih2bNn69ChQ1q+fLkkadGiRerdu7cGDBigEydO6LnnntM777yjt99+27WOzMxMTZ48WcOGDdPw4cO1aNEilZWVaerUqUHfvqYivwEA8E1IXRwfMWKE3nzzTbd569ev14gRI5qpRgCAsMBdb82K/EakC+Q4RBHUIxXQdGH65FkkIcMBAE3WDPm9fft2jR492jWdmZkpSZo8ebJycnJUUFCgAwcOuH5eUVGh+++/X4cOHVL79u01ePBgbdiwwW0dt9xyi44cOaI5c+aosLBQQ4YM0bp16zy6Kw9F5DcaElJj6DbAmzp6224Oh/1h8rbOnFuAI5xDdwnoxfGm3tV3zz336Omnn9asWbN0xx136J133tGqVau0du3aQFYTABDufB3zhCNIN+Q3ACAo/DFmGRnuhgwHAARcM+T3qFGjVF1d3eDPc3Jy3KZnzZqlWbNmNbreGTNmhEQ36uQ3ACAoOIfuEtCL4029q693795au3at7rvvPi1evFjdu3fXc889p/T09EBWEwAQ7rjrza/IbwBAUPDkuN+R4QCAgCO//Y78BgAEBefQXaKqz3TbXRgqKSlRXFyc2kuKau7KAADcVEv6VlJxcbFiY2N9Xl/dd35xvuTL6kpKpLhk/9UL3iHDEaroVh0tXajmd826yPDmRn4DQGgiv3Em5HdkCsduxJ1oSd2qe4tzC5ElVDM8kvI7pMYcBwDAK3QJA0Dh2fANZp35qkPIoVt1IGSFY6aG2tcB+xARi/wGmkUwcyU6gOv25sHT5s7UQO4Pk7cP5jrZR3z1gnPop3FxHAAQ/qrkW7cuERTsAACEDV/zu24dAAAgeMhvAADCE+fQXZr7phsAAAAAAIJiy5YtGjdunJKSkhQVFaU1a9acsfymTZsUFRXl8SosLHQrt2TJEvXq1Utt27ZVamqqPvzwwwBuBQAAAAAA8BYXxwEA4a/SDy8AABBc/sjvJmZ4WVmZUlJStGTJkiYtt3v3bhUUFLheXbt2df3s5ZdfVmZmpubOnauPPvpIKSkpSk9P1xdffNG0ygEAEA6aIb8BAIAfkN8udKsOAAh/jJcCAED4aYYxSzMyMpSRkdHkt+natavi4+OtP3viiSd01113aerUqZKk7OxsrV27VsuWLdODDz7Y5PcCACCkMeY4AADhiXPoLlwcBwAAQEhp7q6NopvxvQN5E66T/RpB7Ry0MCUlJW7TMTExiomJ8dv6hwwZovLycg0cOFDz5s3TZZddJkmqqKjQjh07NHv2bFfZVq1aKS0tTdu2bfPb+wP+1Nw5GyjBzDn2IQDAn/yVK4Fsy3pTR1tmeFNHf7WT/bV/vP28nGSokzp6uz/IeeC0SD2eBwC0JHQJAwBA+PFjt6zJycmKi4tzvbKysvxSxW7duik7O1uvvvqqXn31VSUnJ2vUqFH66KOPJElffvmlKisrlZCQ4LZcQkKCx7jkAABEBLpVBwAgPJHfLjw5DgAIf76GcwQFOwAAYcMfjeva5fPz8xUbG+ua7a+nxvv27au+ffu6pkeOHKl9+/bpySef1O9//3u/vAcAAGHFj/kNAACCiHPoLlwcBwCEP8ZLAQAg/PhxzNLY2Fi3i+OBNHz4cG3dulWS1LlzZ0VHR6uoqMitTFFRkRITE4NSHwAAgooxxwEACE+cQ3fh4jjgpUgdkyCCvt8AAGEi1MZXi9SMd3KDL2OQAY3Lzc1Vt27dJElt2rTR0KFDtXHjRo0fP16SVFVVpY0bN2rGjBnNWEu0VIHMsECOY+oP3uack1zzZr+G+v6SvHv4h2MFAPBdMNvAzZlhtvU054On3u73QO2PQO4Lf41LTqYjUnFxHAAQ/ugSBgCA8NMM3bKWlpZq7969rum8vDzl5uaqU6dO6tGjh2bPnq1Dhw5p+fLlkqRFixapd+/eGjBggE6cOKHnnntO77zzjt5++23XOjIzMzV58mQNGzZMw4cP16JFi1RWVqapU6f6uHEAAIQgulUHACA8cQ7dhYvjAIDwVy3fbmWs9ldFAACAY77md906mmD79u0aPXq0azozM1OSNHnyZOXk5KigoEAHDhxw/byiokL333+/Dh06pPbt22vw4MHasGGD2zpuueUWHTlyRHPmzFFhYaGGDBmidevWKSEhwbdtAwAgFDVDfgMAAD/gHLpLpPYaCQBAQG3ZskXjxo1TUlKSoqKitGbNmjOW37Rpk6KiojxehYWFbuWWLFmiXr16qW3btkpNTdWHH34YwK0AAKBlGTVqlKqrqz1eOTk5kqScnBxt2rTJVX7WrFnau3evjh8/rqNHj+rdd991uzBeZ8aMGfr8889VXl6uDz74QKmpqUHaIgAAAAAA0BRcHAcAhL9KP7yaqKysTCkpKVqyZEmTltu9e7cKCgpcr65du7p+9vLLLyszM1Nz587VRx99pJSUFKWnp+uLL75oegUBAAh1/sjvCOrWDQCAsEB+AwAQnshvF7pVR4sXzDtEogO4bn99L3mzP3ztTQvwWTOMl5KRkaGMjIwmL9e1a1fFx8dbf/bEE0/orrvuco1Rmp2drbVr12rZsmV68MEHm15JIAR4kyve5mUw3ytQnNQn2G0R8/2c7GeODeAIY5YCPvNXe9abPAzHpy389ZXhZH+F2v6xZXOgjjts286xQQQhv4Em8TYP/JXNTtYTqOOAYGaPE7b3Dmamm/vD9t7ebruTdXvzXmR6hGHMcZdQO1YHAKDZlJSUuL3Ky8v9/h5DhgxRt27ddM011+ivf/2ra35FRYV27NihtLQ017xWrVopLS1N27Zt83s9AAAAAAAAAABoabg4DgAIf1V+eElKTk5WXFyc65WVleW3Knbr1k3Z2dl69dVX9eqrryo5OVmjRo3SRx99JEn68ssvVVlZqYSEBLflEhISPMYlBwAgIvgjv3lsAQCA4CK/AQAIT+S3C92qAwDCn5+6hMnPz1dsbKxrdkxMjE/Vqq9v377q27eva3rkyJHat2+fnnzySf3+97/32/sAABA26JYVAIDwQ34DABCe6FbdhYvjiCiB6grBX+ORBrKrBnPd/rqJx9uxR5yIoBuN0Nz8FOyxsbFuF8cDbfjw4dq6daskqXPnzoqOjlZRUZFbmaKiIiUmJgatToAvAjmWmpN1m+sJ5tjlgRTIcckaey/b+zEuGfyGk+tAk4RazvrrvZ0I5vibNt7sw0CN8WrjZP8E8vjBm2MDjgvCGPkNnJE3eR3IrDbnBXNcchtvMsPbDHOy7Y0t09A8bzR3W9pf5xbI9DDGxXGXUDv3BwBAi5Gbm6tu3bpJktq0aaOhQ4dq48aNrp9XVVVp48aNGjFiRHNVEQAAAAAAAACAiMGT4wCA8OfrmCdeLFtaWqq9e/e6pvPy8pSbm6tOnTqpR48emj17tg4dOqTly5dLkhYtWqTevXtrwIABOnHihJ577jm98847evvtt13ryMzM1OTJkzVs2DANHz5cixYtUllZmaZOnerDxgEAEKL8MWYZjykAABBc5DcAAOGpGc6hhyoujgMAwl+VfOvWxYtg3759u0aPHu2azszMlCRNnjxZOTk5Kigo0IEDB1w/r6io0P33369Dhw6pffv2Gjx4sDZs2OC2jltuuUVHjhzRnDlzVFhYqCFDhmjdunVKSEjwftsAAAhVvuZ33ToAAEDwkN8AAISnZjiHHqq4OA4AgBdGjRql6urqBn+ek5PjNj1r1izNmjWr0fXOmDFDM2bM8LV6AAAAAAAAAADAwMVxhK1WXi4XHaD38ma9geSkPr7e6Ovrus39GkE3HiHY6BIGaBb+ykdzPU6WsZVxsh5v6uP0/Rvjbe46+Yoy1217L7POTso0VK6p9ZHIfVjQLSvQoEC2d23r9iZ7g9lOPssyz8waJxl20j/VsdbHyf4J1HkDJ5+Fv74ubetxcoxhstWZr/QwQX4DPvNXO9mb7PG2Le1Nu93GzAjb14GZ17ZcMbPYSfvWVmdzPf46vrHVx9xWb9vkTj5nJ1nsr0xHGOEcugsXxwEA4a9Svh2tcaQHAEDw+ZrfdesAAADBQ34DABCeOIfu4u3NyAAAAAAAAAAAAAAAhA2eHAcAhD/uegMAIPzw5BkAAOGH/AYAIDxxDt2Fi+MIScEeX82b9Xgz3pq37+WEN99LTsYw8dfYozZOxksxRdCwFvAnxksBAi5Q44vblnMyvlkbB2X8NS65vzLe2zG/nIwn7mTsMidlvB2L1Vy3t+Ok8XXcwjBmKeDir6zxNq+DOWapvwRqPHEbczxSJ2OOOynjL97mvvl5BfIr1ZtxyPmKD1HkN+Dir255g9lOtuWTuZyTDPN2280//wpLGSdjjptlvM1mc56TfeiEk7a97djFyf6w/S7YlvOGN1/PtO3DSJDPoW/ZskULFizQjh07VFBQoNWrV2v8+PENln/ttdf0zDPPKDc3V+Xl5RowYIDmzZun9PR0V5l58+Zp/vz5bsv17dtXu3btalLd6FYdABD+Kv3wAgAAweWP/CbDAQAILvIbAIDwFOT8LisrU0pKipYsWeKo/JYtW3TNNdfozTff1I4dOzR69GiNGzdOH3/8sVu5AQMGqKCgwPXaunVr0yomnhwHAAAAAAAAAAAAAPhJRkaGMjIyHJdftGiR2/Rjjz2m119/XX/605908cUXu+a3bt1aiYmJPtWNi+MAgPDHeCkAAIQfxiwFACD8kN8AAIQnP51DLykpcZsdExOjmJgYH1ZsV1VVpW+++UadOnVym79nzx4lJSWpbdu2GjFihLKystSjR48mrZtu1QEA4a9ap8dM8eZVHfwqAwDQ4vma32Q4AADBR34DABCe/HQOPTk5WXFxca5XVlZWQKr7+OOPq7S0VDfffLNrXmpqqnJycrRu3To988wzysvL0xVXXKFvvvmmSevmyXGEBCd3aUQHaD229ZrrsZUx53m7Df66Q6XKmHZyA5C5jG0523rM7fDXDb9O1mPbX7btAAD4JlDZbFvmLGO6jYMy5rRt3bYy5jx/HQd4y0nuOsn4k41MS1JFI+uV7NtlLuekjJN127bD3PdkPIBI5G0b0NvscZKPgSpj21ZvtsNJPppZJEnlxvQJB+t2kmG2YxXzWRlbGSfHGE44qbNZxnZsYM7ztm3vZDlvziPQ/kedLVu2aMGCBdqxY4cKCgq0evVqjR8/vsHyr732mp555hnl5uaqvLxcAwYM0Lx585Senu4qM2/ePM2fP99tub59+2rXrl2B2gxEAG8y3NvzwU4y1cwaJ23gtpYy5jxbGW/a0k7yyZbNZj45KWPjZNudlHHyWXjTbrdtl5N5TrbddlxkctImd7pcY+shvyNLfn6+YmNjXdOBeGp8xYoVmj9/vl5//XV17drVNb9+N+2DBw9WamqqevbsqVWrVmnatGmO1x+UJ8eXLFmiXr16qW3btkpNTdWHH37YYNmcnBxFRUW5vdq2tX0lAQBQq9IPL3ggvwEAAeWP/CbDPZDfAICAaob8LisrU0pKipYsWeKo/JYtW3TNNdfozTff1I4dOzR69GiNGzdOH3/8sVu5AQMGqKCgwPXaunVr0yrmR+Q3ACDg/JTfsbGxbi9/XxxfuXKl7rzzTq1atUppaWlnLBsfH68LL7xQe/fubdJ7BPzJ8ZdfflmZmZnKzs5WamqqFi1apPT0dO3evdvtan99sbGx2r17t2s6Kioq0NUEAISzuq5dfFkebshvAEDA+ZrfdeuAC/kNAAi4ZsjvjIwMtyfFGrNo0SK36ccee0yvv/66/vSnP+niiy92zW/durUSExObVpkAIL8BAEERBufQX3rpJd1xxx1auXKlxo4d22j50tJS7du3TxMnTmzS+wT8yfEnnnhCd911l6ZOnaqLLrpI2dnZat++vZYtW9bgMlFRUUpMTHS9EhISAl1NAABQD/kNAED4Ib8BAOGkpKTE7VVebg6G4B9VVVX65ptv1KlTJ7f5e/bsUVJSkvr06aPbbrtNBw4cCMj7N4b8BgBEotLSUuXm5io3N1eSlJeXp9zcXFfezp49W5MmTXKVX7FihSZNmqSFCxcqNTVVhYWFKiwsVHFxsavMAw88oM2bN2v//v167733dMMNNyg6OloTJkxoUt0C+uR4RUWFduzYodmzZ7vmtWrVSmlpadq2bVuDy5WWlqpnz56qqqrSJZdcoscee0wDBgywli0vL3c7cCopKfHfBiAgAjm+uL/GE3cyhoq/ypic7B8nN+jYxhXxZuwTb8d2C+a45IxhAp+7VaVLVjfByG+JDI9ETrLZNgaaOU6arTMmb8ZAczKWmr/GVLVxkoVOxgw1c9Y2vpg5BpltnDLzVKMtv23LNVYfyfMzdHIcAvilW3Qy3IX8jixOx6IOVPvWSc7axtQ2y3iboSYnGWq7pFbmYN1mZtmOZ8z90d5SpoMxbTuecXLOwglvxhO3ZbOTsU9N3j5lYx4H2Ladr/Qw4cf8Tk5Odps9d+5czZs3z8eVe3r88cdVWlqqm2++2TUvNTVVOTk56tu3rwoKCjR//nxdccUV2rlzpzp27Oj3OjSE/I483ny3OzmH7SR3nbSBbRlm/sabmWZbj5Pxzb0dd/sbB2WcZJZZZyfbZds/tm01mTnnpM7fWsrYjl3M3w8n225jHgt4m8WBOu+PIAjyOfTt27dr9OjRrunMzExJ0uTJk5WTk6OCggK3G9OeffZZnTp1StOnT9f06dNd8+vKS9LBgwc1YcIEHT16VF26dNHll1+u999/X126dGlS3QJ6cfzLL79UZWWlx51rCQkJ2rVrl3WZvn37atmyZRo8eLCKi4v1+OOPa+TIkfrHP/6h7t27e5TPysrS/PnzA1J/AECY4OK4XwUjvyUyHABaPC6O+xX5DQAICj/md35+vmJjY12z/T1mqVTzFNr8+fP1+uuvu3VRXr+b9sGDBys1NVU9e/bUqlWrNG3aNL/XoyHkNwAgaIJ8Dn3UqFGqrq5u8Od1F7zrbNq0qdF1rly5smmVaEDAu1VvqhEjRmjSpEkaMmSIrrzySr322mvq0qWLfvvb31rLz549W8XFxa5Xfn5+kGsMAACamt8SGQ4AQHMjvwEAzSk2Ntbt5e+L4ytXrtSdd96pVatWKS0t7Yxl4+PjdeGFF2rv3r1+rUMgkN8AAPgmoE+Od+7cWdHR0SoqKnKbX1RUpMTEREfrOOuss3TxxRc3eGASExMTkLsKAQBhpEq+9ddLX79ugpHfEhkOAC2er/ldtw5IIr8BAEESJvn90ksv6Y477tDKlSs1duzYRsuXlpZq3759mjhxYuArVw/5DQAIGs6huwT0yfE2bdpo6NCh2rhxo2teVVWVNm7cqBEjRjhaR2VlpT799FN169YtUNUEAIS7Sj+84EJ+AwCCwh/5TYa7kN8AgKBohvwuLS1Vbm6ucnNzJUl5eXnKzc11jVM6e/ZsTZo0yVV+xYoVmjRpkhYuXKjU1FQVFhaqsLBQxcXFrjIPPPCANm/erP379+u9997TDTfcoOjoaE2YMKGpe8Qn5DcAIGhof7sE9MlxqWaA9cmTJ2vYsGEaPny4Fi1apLKyMk2dOlWSNGnSJJ177rnKysqSJD3yyCP67ne/q/PPP1/Hjh3TggUL9Pnnn+vOO+8MdFURIE7uwIj2Yj1t/FTmLEsZc7m2ljLmcrb1mPOc1MfJvrB9B5k37VRYypxsZNo274SljLlu22fspD7mttrKmOux7R9zfzipDyJMlXwLZ35BPJDfLYu3We0kw5xkYXtjuoOljPmMQ6yljJP1mGW8zXhzO7zNHjP7nGRzmaVMuYMy3zoo841lnpNjE3M7nCxjQ6a3ML7md9064EJ+hyZ/PZVgW4/5fWv7/jXnOck+J1lsK2Ou20k72VtmPtoyzMl72dq8JvP4Id5SpmMj007r44STtr25XU6ODWzM3x/b/vLmq9jbr2/z74AYaAbNkN/bt2/X6NGjXdOZmZmSpMmTJysnJ0cFBQWuC+WS9Oyzz+rUqVOaPn26pk+f7ppfV16SDh48qAkTJujo0aPq0qWLLr/8cr3//vvq0qWL99vlJfI7NIVaftvWY+aKLePNPIqzlDmnkWUkz+wzs1HyrLPtq8LMEVsWmZluy/gSyzyTeawSbyljbqttu2zHPCZzW215WWxMH7WUOWaZ5831Atu+N9fjbYZ6sxxt+xDBOXSXgF8cv+WWW3TkyBHNmTNHhYWFGjJkiNatW6eEhARJ0oEDB9Sq1ek/ja+//lp33XWXCgsLdfbZZ2vo0KF67733dNFFFwW6qgAAoBb5DQBA+CG/AQCRaNSoUaqurm7w53UXvOts2rSp0XWuXLnSx1r5D/kNAEBwRVWf6cgiDJWUlCguLk7tJUU1d2UgiSfHm1qfcHxy3LYeJ/XxpoyNk5udIuimprBWrZo7QouLixUba3vus2nqvvOLn5Fi2/mwnuNS3L3+qxe8Q4Y3H54cd8eT4+6c3NnvZDvMvLbtHzI9NIVqfktkeCggvxvnzZNnTnLXVs5JFrekJ8fNeccsZb5y8F6djOl4S5lIeHLc1v53co7ALGPLc38dB5g4LmgY+Y0zIb8b5+2T406e+PYmv20ZYuauLZt5cvy0eEuZcHhy3FzOtj/MnHeS107a7U6uQ3j7IDIZ3rBQzfBIyu+APzkOAEDA+TrmSQSNlwIAQNjwx5hlZDgAAMFFfgMAEJ44h+7CxXGEJNsddeYTWk7uQHdyR7yTJ9icjNdiK2POc1Ifb58cd3I3tznPVsbJU2VmGSdPqds+U9vdaSZzW50sAwBoHrYMM3PWfOpM8rwL28md7E7KxFvKOHmqy5uny52MEeckL51ks7dPxpl3pZt3n0v24yuznLdPd0dQGwphbMuWLVqwYIF27NihgoICrV69WuPHj2+w/GuvvaZnnnlGubm5Ki8v14ABAzRv3jylp6e7ysybN0/z5893W65v377atWtXoDYDEchJO9BJ1jhpJ9vKmFlsy0dzXryDMk4y1MkTdU7awLZ8LHSwHttyJnO7EixlEhtZRnJ2/ODkCWsnxw9mW972hLx5nObkSTR/5bltu5x87gAQSpzktxNOstDJk+O2p57NPDLzSpKSjOlkS5kuxrTZ/pY862j7Hjfbt7anp48Y00WWMseMadtn4SS/nWyXuV9t72Vm8TFLGXO78i1lDlvmmZz00OLtE9/eZK+T4xkg1HjbOwgAAKGjyg8vAAAQXP7I7yZmeFlZmVJSUrRkyRJH5bds2aJrrrlGb775pnbs2KHRo0dr3Lhx+vjjj93KDRgwQAUFBa7X1q1bm1YxAADCRTPkNwAA8APy24UnxwEA4Y8uYQAACD/N0C1rRkaGMjIyHJdftGiR2/Rjjz2m119/XX/605908cUXu+a3bt1aiYm253AAAIgwdKsOAEB44hy6C0+OAwAAAADCWklJidurvLw8IO9TVVWlb775Rp06dXKbv2fPHiUlJalPnz667bbbdODAgYC8PwAAAAAA8A0XxwEA4a/SDy8AABBc/sjv2gxPTk5WXFyc65WVlRWQKj/++OMqLS3VzTff7JqXmpqqnJwcrVu3Ts8884zy8vJ0xRVX6JtvnIxkDABAmPFjfgMAgCAiv13oVh1+5eRui2gHy7WxlDnLmG5rKdPemO7gYD22Mh2N6ThLmXhj+hwH67HVOcaYtu0fc16FpYz5bMwJSxnz9NxRS5ljxnSxg/XY3sucV2Yp861lXmOcfP/aypi/YxE0PAYk38c84RcCLYw3eW1bxkkZc54tC828tHVMnGxMJ1nKmMslOCjTyVIm3piONg8wJM8NMQ8wbE5a5hmBWWkJx2PG9BHLasx5RZYyhcb0YUsZ22dofkXajkPMTXPy++IEmR7h/DFmWe3y+fn5io2Ndc2OiTGPsn23YsUKzZ8/X6+//rq6du3qml+/m/bBgwcrNTVVPXv21KpVqzRt2jS/1wOhzV9PIDhdj1nO9l3rTVva1gY2M9SW12b22t7LrKMtQm3Lmcw251eWMuYxho2ZobZ9aG7rBZYyvYxp2zGGN9tlO3ww89HWJjePBWzvbR4b2HLXnGcrY36VO1mPk2MOJ/y1HjSBH/MbiEROstmc5+35cvO73Xae28wjW34PMqZTLGV6mRWyrcgMXtvf+jH3yQpLA/ffjUxLnjlny4MuxnQfSxlzXhtzIcnzJIHtzcwT5pbt2m+E+nbLamy7zMx5Wx9Z5vGC7fjBSV578/XMV3oY4Ry6CxfHAQDhr0q+3bkWQcEOAEDY8DW/69YhKTY21u3iuL+tXLlSd955p1555RWlpaWdsWx8fLwuvPBC7d27N2D1AQCg2fgxvwEAQBBxDt2FbtUBAAAAAGjASy+9pKlTp+qll17S2LFjGy1fWlqqffv2qVu3bkGoHQAAAAAAaAqeHAcAhD+6hAEAIPw0Q7espaWlbk905+XlKTc3V506dVKPHj00e/ZsHTp0SMuXL5dU05X65MmTtXjxYqWmpqqwsKYT4nbt2ikurqbj6QceeEDjxo1Tz549dfjwYc2dO1fR0dGaMGGCjxsHAEAIolt1AADCE+fQXbg4jpDgZMxScxwy2/Cf8ca0bTxS8+/XNu6WuZw5zqmtjG2YFXOIEtu4beZQLLbxY5yM8WUOa2IbK9wc6sQcX0zyHH8030EZ29ij5mdqW4/JybhktjF4zM/UVsbXHr8Q4irl24fsxbJbtmzRggULtGPHDhUUFGj16tUaP358g+Vfe+01PfPMM8rNzVV5ebkGDBigefPmKT093VVm3rx5mj9/vttyffv21a5du5peQSAInIyT5s04p7ZxwC4xpntaypjjf3awHQj0Mqa7W8o4GZjc7L3ZNryxGVC2Qb/K3CejLeOSnWME9jkHPcv022+s1jKg+B5j+nNLdWzjvprDoJdZyjgZH9XJ+GZoYXzN77p1NMH27ds1evRo13RmZqYkafLkycrJyVFBQYEOHDjg+vmzzz6rU6dOafr06Zo+fbprfl15STp48KAmTJigo0ePqkuXLrr88sv1/vvvq0sX24CFgD0vvV3OyfjdZhvTlsVmu/QcSxmzXdzXUuYaY/qYpYzZdrW1k82/njaWkwQnjGCxRJ9yjWlbPtnGMTWZxyapljJDjGnbYUhbYzsqLCcYzUMB21jq5qGJbVCJzcb0p5YyTsYnDdQYpk6+vmnbh6hmyG8gGILZxa6TccnNTLdlvDnP1iw1M952hDrSLGMbRcgciLyXpYwZULa/9S/dJ9tYTnn1++jM05K038FFOo9x0s0TC7Z5/SxlOhvTtg/smDFtOcDo9Yn79FkbPMtYTgnoaCNvJTn7fTHP4TvJ2UB+XZsfTwRddw1dzXAOPVRxcRwAAC+UlZUpJSVFd9xxh2688cZGy2/ZskXXXHONHnvsMcXHx+v555/XuHHj9MEHH+jiiy92lRswYIA2bDh9dNy6NVENAIC/jBo1StXV1Q3+vO6Cd51NmzY1us6VK1f6WCsAAAAAABAsnHEHAIQ/P931VlJS4jY7JiZGMTG2+26ljIwMZWRkOH6LRYsWuU0/9thjev311/WnP/3J7eJ469atlZho64sCAIAIw5NnAACEH/IbAIDwxJPjLsHsLQQAgMCo8sNLUnJysuLi4lyvrKyswFW5qkrffPONOnVy73Nqz549SkpKUp8+fXTbbbe5de0KAEBE8Ud+0/ceAADBRX4DABCeyG8XnhxHi5J79906cOWVkqQrf/pTdTx4UCfbtdMfn3vOrVzdH8ZV2dnq+5e/SJIWLVyoo/We5qwrM/qtt3Tr8uWSpCdmzNDWESNcZerG7Rj4r3/p6dpxhJePHavFP/iBq0xU7b9tTp3Sp5MnS5Le799fP3j4Yes2vPHggzo/P19lbdvqkqVLXfPrdw4597e/1ZVbtkiSbl+4UAdr613/xp6M9es1rrbbyOemT9ffRtaMLnOqXpnkvXuVMXeuJOmT667Te7fd5lGmVWWlxk6aJEk62q+f/vqzn6nH5s0a+uyz1voDoSw/P1+xsadH7GvoqXF/ePzxx1VaWqqbb77ZNS81NVU5OTnq27evCgoKNH/+fF1xxRXauXOnOnY0R4kCWo4Nd9+t39bmd53f/vSn6nnwoMratdMttTlujqm18OVs3bi9Jsevemih9ndJ9Dj6nbzvLc3dXpPjP75shv7Ua4THwFtDv/2XXvlnTY7/LnGssnr8wOMW0zY6pV37anO8XX/94FxLjldLf973oPqW56usVVsN6rfUPcAlqVL61c7f6r8O1+T41ZctVF5bozeJU9LE3PWavzFHkjTzuun64wXuo8RVn5IG792rFbU5/sJ11+mx2hyvtxpFV1bqN7U5/q9+/bThP/5DaWQ4AMBPHrv7bq2tzfDf//Sn6lOb3TfWa4PXj9SHs7N1XW0bPH3hQu2vbctG1Ssz+e23NPf3Ndl9/4wZerO2DV6/vVu/Db5+7Fi9VtsGP1GvTPSpU5pS2wYv699fBxpog/d+8EEpP18n27bV8to2+ItGmUm//a2GGG1wcxzPH6xfr/9dniNJmvmj6frjiJEehwFD9u7V07XZ/dJ11+mp227zeECndWWl/lqb3R/366fpP/uZbty8WY+Q3wAAP/np6Lv1Sv+a/F638qe68KuD+ia6nVL+o9459HoN8McLs3VjSW3b+5yF2h/t2SPi5LK3NLektu197gz9Ka72HPoFp8sM/epfeuWvtW3v4WOVdVXtOfTy02XanDqlXVNr8vvj/v314wby+/kHH1SvQzXn0Af9rvYcunGa71drf6v/Um3be/RC5X0n0ePEwsSv1mv+qRxJ0sz46fpjO3OEdunik3v16rGa/F4af53+t/NtUk/3Mq2rK/WvT2ry+8Okfrp1/M80ps9m/T/yG2gWXByHT5x0PWA2CG3LmGXMacnzhHcHS5kuxvQFxvSfr7xS3yYkqF1Rkcpr13mePP8Q2tT+20tSSu3rBUnfWurTL0r6XitJ/aTETlJMm3qFalfcIVHqkyEpUfrOBVKr+te4andIVJXU5j5JbSXFSYq3bKCk6LulNl9JJ6OlqLjT86Pq3bXTcbTUp3YHtTtHat2+tjr1rmqf26W23pLejZL+UTv/ZL336lK77ZJ0VKf3S31ROr1fTkj6NiFBn195pW4ygv2EuaBlnq2MeTOS7eYk82SBkxuYbL+HEXTjU8vjpy5hYmNj3S6OB8qKFSs0f/58vf766+ratatrfv1u2gcPHqzU1FT17NlTq1at0rRp0wJeL8BXtvz2JuNPGtP/vPJKFSck6DtFRa55f5TUSVKFpNLaeeZ3+9tfS0cO1/z/cLn0zSmp1Sn3Mnt3Sm+tqvn/512l453dT8BL0lf/kv5W0z7X/rFS+Q88y1Sfkj6dXrvO/lKFvX2uz34hHc+XjreVKizXxqslffam9Jea9rmO9ZSOG+cVqiT9M1/6v/dqpvdcLH3T271MpaR9kn5dO71dp/dT/fW0kvRW7fSbkyapuGdPXWlkuLlfvf2czc8VoFtW4DQn37VO2tK2Mm0bmZY829edLGWSjelLLWU6prtPr77ySh1JSFCXoiLtkvSNpGFyb4NH1TtRfc550rnHJQ2SorpJUd+p/UH9Db1MUoLUtkxqPViKqj18b10vaDp0lfqMlvq8W9OWfUueWktKlfSRavZbQ+c3YmvLnZC0qm79RplU1byfJLU7W2rdTh4HOK0vlVR36N9fUrwUZXyHteopnTus5v9n95SiY6RW5e5loiV9XPv/f0k6mJCg1zOu1JOfu+d3irHRRy3bdsyYLrOU+daYtrXbK4xp2++v+XVtK2OijR6iyG/A7wJ5vtyc195S5pAxvbzXlfoiNkFdi4r0l/ekvIPSib9Kx1NOl6lfn38/J330l5rT2ccXSqdq27D1281lb0lHlte8/8kZUvUIzzLV/5Yqn5WiW0lK1OmL4vULRUlqI/VqJRW2lVo3EODd29aU01n1ljcyVXlS5aba9+5b855mG71ivXQkp+b/x6dLlSM9y5TtlT6quTauz6+TKm6z5F6l9NaGmv/v7id9PilBf7zySt1ttL9tn4/5GdqO5czfBSftdrqVboHoVt0lqrq62vxbDmslJSWKi4tTe3metIT/+eviuHnR1fwylzyD4RxLmSRj+iJj+tcvvqgKSdfUe3LKLCOdviDc0LQk9TM3pJ+lkHGHmGzDCMcb07Z0M9lao8eM6UJLmc+N6V2eRXYZrc9PLKsx5/2z3v/Xv1hzD/0DxtNp/5SnfGP6mKWMeczipCHu5AK6DQ3vwKtWzcmV4uJiv1yErvvOL35QinXyt9PQek5Icb/wvl5RUVFavXq1xo8f32jZlStX6o477tArr7yisWPHNlr+0ksvVVpaWkC7eA8VZHjwBCq/bX+GZn7HW8okGNNmpD7z4ouqlHR7vWyxNfrNE/m2E/vm8YOtTwazzt42PE22LDIvGNtyzjwp/Y2ljHnC+ytLGXOeeQL8Dy++qGhJ9xoZbh4uFMnTMWParLPkuW1mfkueWUx+h4ZQzW/J9wyH78hvd95krG05JyfAJc8stvV7ZP5l2LLPvNHcbMpK0iBj+kpLmWTj4njipJr24XP1smW0sUyHYQ7ezKyg5Blktkbnu+6TL1uKPGOZZ7rXmL7FVsjcMNvJBvMA5oilzKfuk99s9yyyud7/73zxRbVvL/072z2/842L4+9Y3srcZWYbXfLM/WOWMuZHYbbjJc/ct9005+TGd44NnCO/cSbktydvLhT6K9Ntf1LmPFsbOM6Ytp16Nm9u62spY577zqg9v5tTL7/N7bKdm483pr1tb0ebb2Z7YsvJB2YGgqURWmmU8bZNfsyYtt2UVv+tptS2v98w2t+2c/G7jen9ljLmIUWxpYyZ104eZgtkXpvI79NCNcMjKb95chwAEP6q5dsRVJBuE3vppZd0xx13aOXKlY4ujJeWlmrfvn2aOHFiEGoHhK5xjz3m8dQzgAjga37XrQMAAAQP+Q0AQHgKk3PowcDFcQAAvFBaWqq9e/e6pvPy8pSbm6tOnTqpR48emj17tg4dOqTly2vGU1qxYoUmT56sxYsXKzU1VYWFNd07tGvXTnFxNff6PvDAAxo3bpx69uypw4cPa+7cuYqOjtaECROCv4FACOn+j39Yn1ICAAAAAAAAgKbg4jiCzkl3M7bu4pyMk2Z21WL2vDb1scf0d2NZW3dxlxjTF5j9tUvSSGPa1ve62Y2a7c3MSjrpjaLEMs/sO8XsQl3y7DPN0k9Lv/fcp6MPe5Y5Zkz/u97/67piMjfL1o2O2R2QrSsXs+sWJ2Pw0AVLC9QM46Vs375do0ef7jsxMzNTkjR58mTl5OSooKBABw4ccP382Wef1alTpzR9+nRNnz7dNb+uvCQdPHhQEyZM0NGjR9WlSxddfvnlev/999Wli60fSSC4nI592thyTr7HbXnQy5i29VRqzutjO6DoY0ybfcxJnn3R2fpnN0PM1o+tydbHqJnptr7PzKFSLNmsPe6T+y19n+00ps3DgrMknZLn/vfmM7Rx0r0gGd7CMGYp4DNvxip3MgyKk2HMkm2DYg50n/x/jz3msf4OZtv5B5b1pJlvZilj9ldq6X7czOuUNzyLxFsWM5m9vOs/LYVuN6ZTLWXMN9tvKbPZfbKjJdPb12vLt5JqQtzY98l/MaYtY56YXabbhmUxf19sh1eMYdrCkN9owZy0e5ws42Q9Zhknw6s4Oadu657dfK9XH6/J75H1Fx5hFPIIR3m2pW0VOmZM28b0MBurez2LfGOux6JjvDFjoGeZaGNctw6W8/cdjAOjLraTFma7/VNLmQ9O/7ddK+lklednaPt8nFwXcfK74M3vnbddppvr4Ws/RDDmuAsXx9Gi9PnHP6znk+E///Hgg81dBbREVfLtiooXy44aNUrV1Q33JVN3wbvOpk2bGl3nypUrm14RoAV4ISdH0ZIemDKluasCwJ98ze+6dQAIWQP+8Y/mrkLEe+zBB/Xdqc1dC7Qo5DcQ8UZ+Rn4H2ptzH9Te481dC7Q4zXAOPVRxcRyAX8Xm2273AwDAe6fOst3zDH+b+uCD+rK5KwEAAJqkR36++pU1dy0AAEBT9DuYrypLry4AgoOL42hRHs3J0beSruPJs4A5FVPbr2y5re9YIEDoEgYAfNY1Pz+SbgJGOKBbViDiTa3tTel52uABcyImRt+2ktpX0QZHkJDfQMTr/9scSdJnP5zSrPWIZN/GxOh4pdSOc+gIJs6hu3BxHC3KqbPO4qRvgK1btkySNOq225q5JmhRCHYA8FlFTIxOSjqLxjmChZPrQMQ7Se8vAXfnsmVqGyf9+13a4AgS8huIeOXkd8AN/M0ynayS3uIcOoKJc+guXBxHSIq2zGtjTLe1lOloTHcypltJijKWPdeyngvM/L/UUuhKY3qEpcwQYzp6uKXQ+cb0OZYyhvhiz3k9drlPX/KhZ5me5nos6z7pPnnBm55Fdhtl6u/PqNp/zX1vfjbmcpL9c7fNAwCEplYOyjj5rm9vWW9ruSfm5Zb1xF9kzEi1FEoxpvtaypxnTCdZynSIMd/dUshU6jmrxOgH9SvLYkbEa6+lzN/cJ3t95Fmk40736Qrj5/cuW6YKSdONxrn5+TjJZie/C07Y3iuC2mIAIoC/vu9M3raNbGXM5q2ZYJLUwZi2td+6mDNsjWkji+v2T3z9mZcYy2RY1tNvpDFjqGeZ+EPu04mveZYxRv3q94ZlNZa3N11kftBXWQr9lzEdfbOlkLHThuzwLNJhi/v0J55F4uvNayXVnDDpd+a36rLHcz3m52w7z2L+vtgul3jTbg9kxpsfFw9JAAgmf30nmt9ltmMO8zvZ9j1utq/jLGXMprTrwOCGevNuN8qY58YlqYPt4MBwzMjv9yxlXjemLW1gs5ls43FK3zwGkdy3UZK+aykTb55UP+VZ5rixXRss63mp3v/bS2eVep6SMNZSV9SN7XM2fxdsvy/mPNvv3UnLPJO5HDmLcMTFcQBA+KuSb0diHMUBABB8vuZ33ToAAEDwkN8AAIQnzqG7cHEcABD+6BIGiGgjXnpJPZq7EgD8j25ZAQAIP+Q3AADhiXPoLlwcBwCEvyr5Fs4RdNcbEIkueeMNa+9nAMKcr/ldtw4AABA85DcAAOGJc+guXBxHwHk7/mhj67GNc2WOtxFrTN/80kv6u9zHzDLHxpbkObaoOSy45DkYi+2sfdSNxozLLIUGGNOJthoZCi3zdhvv3d2zyCXGGGyWocu135i2jLPa6XP36fr7s27McXPfOxkLxfaZejMWiu13LoJuagIAv3Myvpm3nHyPm9//ZoZIUrIxHZ9gKWSOMT7aUsYcwvQ824rMwdPMrJYkc8yxeEsZ0zHPWbFGqMZaBhbttdl9et9RzzLmwHGWHX2OMZ558mH36daqyVRz3Fnz8wnm70sEtbsAICDM72Tb97FZxvY9brbXzLEtJcs45B6DkMsjsH/465c8l+1jLNPPNvrpbca0GfKSdNB9ssMxzyID33GftrRvYw57zvNgDqE60FIm+npjxh2WQmZ733Ky4QLjWKCnZ8O9/v6MkmpC3Dw0MT6fDpYxx52MYerk98fJ8R7jkwKIRP5qBznh5PvXdm7VbN+dY1u3kc0PltYOjn15vZnXmTXItKzJPPdtGZs7fqP79OhnPMsYp7ltJ3Y/sry76VJzuQsshczmf7t7HRSyJGa7D9ynxz3hWSa/3H0VJ6RoI7/PMU4RSI230SVnWRwotr8Dch6hjovjaFHGvPGGx4VU+Ffqs882dxXQEjFeChDR/jB3rt6WlDV/fnNXBYA/MWYpEPFufeON5q5CxPvJs8+q28PNXQu0KOQ3EPHuPkZ+B9ovi56V/tjctUCLwzl0l2De3ASgBeizebP6bN7ceEHAnyr98AIQsg5deKE+u/DC5q5GxJvx7LMaw01uCCZ/5DcZDqCFy9i8WTdV0wZHEJHfAOCzm77ZrJv+Rn4jyIKc31u2bNG4ceOUlJSkqKgorVmzptFlNm3apEsuuUQxMTE6//zzlZOT41FmyZIl6tWrl9q2bavU1FR9+OGHTauYuDiOFuYXc+dqw9y5zV0NAACAkJO2ebMGcYMbAMCPfjx3rn5MGxwAgLBy87lzdfO55DcA35SVlSklJUVLlixxVD4vL09jx47V6NGjlZubq5kzZ+rOO+/UW2+95Srz8ssvKzMzU3PnztVHH32klJQUpaen64svvmhS3ehWHS3K3gsv1LfNXYkIt3bBAknSuJ/8pJlrghaFLmEAAAg/dMsKRLxP6fkl4KYsWKD20dL6StrgCBLyG4h429uR34F2TY8F0gPS+sfJbwSRn86hl5SUuM2OiYlRTEyMR/GMjAxlZGQ4Xn12drZ69+6thQsXSpL69++vrVu36sknn1R6erok6YknntBdd92lqVOnupZZu3atli1bpgcffNDxe3FxHCHJSZcGtjJnGdPmn2NU7b/R9ea1ta28ozEdbynTxVy57aChrzGdYikzwJhOtNXIkGCZZ27Jl55FonYaq/mXZ5lzjGlzX1jeqf7+LElKkuS5783PRgpu1xXRxjQ9eEUYX7tl4xcCCBpv87uVjDi2xWWSMX2epcx5ZiJcaSl0tTE91LYiY/o7ljLmobYlm3XImO5sKWMk73kvexY5YnyR7basxjh2iT/sPj1lwQJ9KelHxg1utgwH/MIf3aqS4QgDZvI09/vb6mPms+2736PtbGkrqpP7ZNQRy/qMMvbANtvJtra02Xg1l5HU5R336XjPIm0Oe87zYG6reT5AkrP2v3kAU2opY+yPcz7yKFF/f+YnJal1tKQ4o1D7M056rEeyH6c5+f0JJtr2IYD8BoLCyfetk+9oM79t8e2RzXVN2V71Z5rt5HTLisz29Qnbu7lrt9FzXpxxztrynfFJ42uWThrTtvxu18eY4WS74i1lzHMCOzyL9Hrb9d99bZOkbp51av+552JmXts+Z29+X9AC+ekcenJystvsuXPnat68eT6suMa2bduUlpbmNi89PV0zZ86UJFVUVGjHjh2aPXu26+etWrVSWlqatm3b1qT3Csq1qab2//7KK6+oX79+atu2rQYNGqQ333wzGNUEAAD1kN9Ay3IgKUlHk8w7DACEG/IbABBpQnnMUn8hvwEA4SI/P1/FxcWuV/2L1b4oLCxUQoL7g6EJCQkqKSnR8ePH9eWXX6qystJaprCwsEnvFfCL403t//29997ThAkTNG3aNH388ccaP368xo8fr507d1rLAwDguuvNlxfckN8IJRe9/75Gvf9+c1cDgL/5I7/JcDfkNwAg4Johv0N5zFJ/IL8BAEHhp/yOjY11e9m6VA91Ab84Xr//94suukjZ2dlq3769li1bZi2/ePFijRkzRj/5yU/Uv39//fznP9cll1yip59+OtBVBQCEqyo/vOCG/EYo+f5TT2nOU081dzUA+Js/8psMd0N+AwACrhnyOyMjQ48++qhuuOEGR+Xrj1nav39/zZgxQ//1X/+lJ5980lWmqZkZSOQ3ACAoQrz9nZiYqKKiIrd5RUVFio2NVbt27dS5c2dFR0dbyyQmOhmu+LSAXhyv6/+9fh/xjfX/3lCf8g2VLy8vV0lJidsLaEjq+++rJ0+eAcAZBSO/JTIcAAB/Ir8Rika//75G0wYH0AAzT8rLy/2y3sbyzZvMDBTyG6FobOX7GltJfgMIrhEjRmjjxo1u89avX68RI0ZIktq0aaOhQ4e6lamqqtLGjRtdZZxq7Xt1G3am/t937dplXaahPuUb6i8+KytL8+fP90+FEfGmP/WUVnuzYLS/axK5LtywobmrgJaoSr51q8pTZ26Ckd8SGY6GmX+Sb0+cqDxJ03//++aoTotSrca/EgPe9RRaDl/zu24dkER+oxk4+Pudb+v5xdHfbUBPV0WU8Rs2KH6avPo+9OYrlNEs4M/8Tk5Odps9d+5czZs3z8eVNz5m6ddff93kzAwU8huBZv65OvnzfeokPbcF2u2VG6SPPOfbLkNwaQJ+E+Rz6KWlpdq7d69rOi8vT7m5uerUqZN69Oih2bNn69ChQ1q+fLkk6Z577tHTTz+tWbNm6Y477tA777yjVatWae3ata51ZGZmavLkyRo2bJiGDx+uRYsWqaysTFOnTm1S3cK+tTF79mxlZma6pktKSjwOrAAEz/Dnn2/uKqAlqpRvV2s4w9MsyHA49eGYMdopLo4H2vc2bNC/mrsSaFl8ze+6dSCoyG8gtGQ+/7x63dvctUCL4sf8zs/PV2xsrGt2OI5ZGi7IbyC0PHLyeent5q4FWpwgn0Pfvn27Ro8e7Zquy6HJkycrJydHBQUFOnDggOvnvXv31tq1a3Xfffdp8eLF6t69u5577jmlp6e7ytxyyy06cuSI5syZo8LCQg0ZMkTr1q3zuGmsMQG9OO5N/+8N9SnfUPmYmBgOnODYHyZO1GeShnFyHYgsvo55wlNnboKR3xIZDoSaHz//vN5o7kqgZfHHmGVkuAv5jVD064kTJUn/QxsciBx+zO/Y2Fi3i+P+0tiYpdHR0X4bs9RX5DdC0c9b1+T3z06R30BECfI59FGjRqm6urrBn+fk5FiX+fjjj8+43hkzZmjGjBlNq4whoL0ietP/e2N9ygO+eHvMGO0aM6a5qxHR/vqjH+mvP/pRc1cDgA/IbwAAwg/5jVD0f2PG6P9ogwfUz3/0I91XThscqC+YY5b6ivxGKHq+9Rg935r8DqT7zvqR7htHfgPNJeDdqjfW//ukSZN07rnnKisrS5L04x//WFdeeaUWLlyosWPHauXKldq+fbueffbZQFcVIcTJDSi2MieN6XJjuu4elfq9P5ywrfwbY/qopcwRc+WWjkijdhszOltWdMqYLrKUMdnGEDLf6x+eRcw62t7K3C5zX8hzn9Xfn3mXXSZJKv/Nb9zKmJ9NQ/MChR43Ixzdqvsd+Y1AcZLftnyoknSs/gwzryQp35jeYymTYPzBn7fZUshky92exnS8g/Ucs8z73Jj+xFLGqOM+y5eWua2HLasx9plZmyd+9CMdlDTOyHDzM+NBXfgN3ar7Hfkdmsxf02CPG+lkrFHzu92WxR5t528thb5yn6xrg7utz6N9vc+yIjMP21rKHDSmLW1g83jhmGeRCsuaPZjtYttxiEeb3JbpZiPcVsbYH5bzEfX359uXXaazTkpPVrjnt/n5WJr2Hr8LtowPta/ZUKtPi9QM+R3KY5b6A/kNGyd/Jk4y3sx0W3yb+e06Xb2//kyz7ZxiWdEx29oN7jd26LjlnLpZH8vBk+3dPZxlTNvy+/i/3afbrbUUMo+CbJfVdhjTlnMN+0//9/XzL5P6S0/+wT2/yxy8u7dZSIaCc+inBfzieGP9vx84cECtWp3+NEaOHKkVK1bo4Ycf1kMPPaQLLrhAa9as0cCBAwNdVQBAuKJbdb8jv4GWZ8tll+mEPC+OAwFDt+p+R34DAAKuGfI7lMcs9QfyGwAQFJxDdwn4xXHpzP2/b9q0yWPeTTfdpJtuuinAtQIAAGdCfiNUxBcV6ezmrgSAiLBlyxYtWLBAO3bsUEFBgVavXq3x48efcZlNmzYpMzNT//jHP5ScnKyHH35YU6ZMcSuzZMkSLViwQIWFhUpJSdFTTz2l4cOHB25DzoD8BgBEmlAes9RfyG8AAIInoGOOAwAQFJV+eAEIWT/MzNQztU+HAIgg/sjvJmZ4WVmZUlJStGTJEkfl8/LyNHbsWI0ePVq5ubmaOXOm7rzzTr311luuMi+//LIyMzM1d+5cffTRR0pJSVF6erq++OKLplUOAIBw0Az5DQAA/ID8dgnKk+NAqOhaVKQvm7sSAPyP8VIAAAg/zTBmaUZGhjIyMhyXz87OVu/evbVw4UJJUv/+/bV161Y9+eSTrq5Zn3jiCd11112ucUGzs7O1du1aLVu2TA8++GDTKghEmHOLzDG2AYS9ZshvAMHV8yT5DUQkzqG7cHEcAWcOQxBtKePkb+pkI9OSdMKYLjGmH8zM1NuSyuvN+8r2ZvnG9F5LmU+N6ThLmSGvuU9HH7QUOt+YPsdWI0OxZd4u98nqDz2LfGRM/9Oymn8b0+a+kOc+q78/4/ftk+S5783PRvL83bB9pmYZJ78rETT0BQAEhZPvVlt+O+Hke9z8/jczZPdll+mopNS//tU174LDnuuJ3+6gQseM6Yssjf5eq9ynkyzr6RBjvruDNy/1nFVW5j5daFlsjzG921LGzHjLvjhq7DMz4k+p5vNqLMNtn6G/steb3AckqaTE/Tc3JiZGMTHm32nTbdu2TWlpaW7z0tPTNXPmTElSRUWFduzYodmzZ7t+3qpVK6WlpWnbtm0+vz/QGPN70vZ9bJZx0pb+1lLmG3PGUUshI1x+U9vzi9uynxvL7LK0b/u9aMzYaXkzI8OPv+NZxFzMcvxQ7jnL0yEH1bnqj+7T0d+xFDLHMt7hWcTcH+b+kvv+PH/fPsXHyWN36Ij7pK1Nbn7OFZYy5u+Pk+MA8htAS2HLXW/bzo1x8v1ry3ijxWmN70rjfPC7L1p6butlJOblCzzLxJ5rWbuhxAjVrZYyZhvYslMvabyI50xzvZK02Zj+7u88y8S/bcywpGqZEcSWw5L625rSbp+qD0qVRp2M+K5ZtTFt+5zNecHMYs7FIxxxcRyAX101Z05zVwEtUbV8OxJreOgyACFgw49+pDZyvzgO/+u1b5/HvQNAQPma33XrkJScnOw2e+7cuZo3b56PK5cKCwuVkOB+MSshIUElJSU6fvy4vv76a1VWVlrL7Npl3LwKAAGwcM4cXbK0uWuBFsWP+Q0ALdXq9XNU+VJz1wItDufQXbg4jhZl+2WX6YCkHpxcByJLpaQoH5cHgBbup3PmeDyADgSUr/ldtw5J+fn5io2Ndc32x1PjAHz37mWXSZJG0wYHIocf8xtAaFrTsya/x39OfgMRhXPoLlwcR4vyhx/9SMfFxfFA2lM7huO1f/5zM9cELQrBDgBA+PHjyfXY2Fi3i+P+kpiYqCJjzOSioiLFxsaqXbt2io6OVnR0tLVMYmKi3+sDhJsnf/QjSVwcD6TXMzKU21G64xva4AgSLo4DES9zRE1+c3E8cJb1zVBVhjSVc+gIJs6hu3BxHCHByfhU5jzbeFnmGGjm2NhVqun5of6y5tBhkvRvo0J9bI9RndXIm0ueY4P1tIwD3sWY5+ScnjkYqOQ5IIllXDKPMcZt2/U390lzX0ie+6z+/vzk9tslSV8ZwW7bPU7GMI2g71tEmC1btmjBggXasWOHCgoKtHr1ao0fP/6My2zatEmZmZn6xz/+oeTkZD388MOaMmWKW5klS5ZowYIFKiwsVEpKip566ikNHz48cBsC+JGTnpmcfNeb419WqWY87L315rWxrGegkXO9bOOJfWBMJ1vKmNezOlnKdDDGW4uxjF1usg1qag4eZh68SJ7jkJuDhUuSMUZcvmUQsk+M6b3G9N8yMlQsaaCR4U7GGjUx5hgixYgRI/Tmm2+6zVu/fr1GjBghSWrTpo2GDh2qjRs3uo4DqqqqtHHjRs2YMSPY1UUzML/vWvlpvbbvWtu6zWapbTkzEpyMOW5rv3mMgWnLIyOLq2oHBD1Wf6bZDn3Lsp6T77lPJ73nWcaspJnxksc4orbBDo5Z5pn+aXzQF9nGEU0yplNXeJaJN6Zt+9Bct6Xdfqze/393++1q21664wPj5LrRcLeNYWruQttY8+bhi+33x8mxgTfHE97iOARAczK/35yMQe5kPHHbd5v5nWw7X25+txdbypinjF3t1NX15pntUlt+JxrhYx6oSJ7B6+B4wqZf40U82c6FmzvNNgZ6vHGi3RaG5mDutveqd6zy6NLbVXGBlGq0v22fj/kZ2j5ns0q23xcn12Cc4Hw9IoG/2m0AADSfKj+8mqisrEwpKSlasmSJo/J5eXkaO3asRo8erdzcXM2cOVN33nmn3nrrdGvi5ZdfVmZmpubOnauPPvpIKSkpSk9P1xdffNH0CgJAE71z++36oPYmNyAo/JHfTczw0tJS5ebmKjc3V1JNPufm5urAgQOSpNmzZ2vSpEmu8vfcc4/+/e9/a9asWdq1a5d+85vfaNWqVbrvvvtcZTIzM/W73/1OL7zwgj777DPde++9Kisr09SpU5u6RwAACH3NkN8AAMAPyG8XnhwHAIS/ZugSJiMjQxm1wwg4kZ2drd69e2vhwoWSpP79+2vr1q168sknlZ6eLkl64okndNddd7lOpmdnZ2vt2rVatmyZHnzwwaZXEgCAUNYM3bJu375do0ePdk1nZmZKkiZPnqycnBwVFBS4LpRLUu/evbV27Vrdd999Wrx4sbp3767nnnvOld2SdMstt+jIkSOaM2eOCgsLNWTIEK1bt04JCQm+bRsAAKGIbtUBAAhPdKvuwsVxAABqlZS4j1kQExOjmJgYv6x727ZtSktLc5uXnp6umTNnSpIqKiq0Y8cOzZ492/XzVq1aKS0tTdu2bfNLHYBwdftdd4lLTAD8YdSoUaqurm7w5zk5OdZlPv744zOud8aMGXSjDgAAAABAGKBbdQBA+PNTlzDJycmKi4tzvbKysvxWxcLCQo8nyBISElRSUqLjx4/ryy+/VGVlpbVMYaE5sBPQssR8+63afmsbBRNAWKNbVgAAwg/5DQBAeCK/XXhyHEFn63kh2pg+aSlzopFpSfrGmD5iTN9511361Fj2c8t6/mZMV+R7lul3yJjxT8uKehrTiZYy8cZ0W0sZk23jjxnTtmtp5sbu8iyyy/iC+8TBatyqU1WzAnPfm5+Nx3KWacnzd8H2/RtBvXnAW37qEiY/P1+xsbGu2f56ahyIBE7y28lyTr7HzSj8KilJn0iKO3zYNc/MGckziuMsBxTn7Haf7rjbs0z7RuojSWcZ097sC8kz52xZaN4WcMxSxpxXbClj7rMyS12i5bm93nyGNuZy5DfolhXwnZPvVidZY2bCUUuZw8Z0vuW+tWQjjBc9c5ck9yz7xmhkdvyD5c3MhmgXSxmz0rY2+btnXq1kz1XTp8b0RW84qM9fLGU6GNNfWcrkuk+a+0syjg2qqhRdLmmnexnz8zE/P8nzczY3QfL8fbGdr3FyrIAIQn6jBTN/db1tB5pPLJrtS9tytu/fCgdlzO9x23e9+V6P31mT32/VW7iVkannGNOS52nujpb3ctLejjZ3UBvPMh3NFdmYG/+RZ5HK7WdeRPJsk9vOcx8zpm3HUvXzsfxUlaLlue+9zWInvwtOvnrNMt5+XfM1H6LoVt2Fi+NoUWK+/dZ6sAH/SZs4sbmrAHgtNjbW7eK4PyUmJqqoqMhtXlFRkWJjY9WuXTtFR0crOjraWiYx0XZnDdByvLxggSol3X7bbc1dlYjWqqrK5/OcAADU156eXwLu2YkT9Z/pzV0LAEAk6UB+B9yyiRMZPg5oRlwcR4vyVVKSSiV957DtnmkAYatKvt25FoRHG0aMGKE333zTbd769es1YsQISVKbNm00dOhQbdy4UePHj6+pVlWVNm7cyBimAILiBxMnetzpDwSUr/ldtw4AIetwUpIkKYk2OBA5yG8g4pHfQIQKg3PowcLFcbQof1iwQMeSktS+XrBvrv338hde0KC335YkLXj0UeX37u0qU9dzy7Vbtugnv/2tJOn/3TFNL42+SmahC784qHVLfipJWtlvtB76jztPl6nX185nr09RTNVJ7ezYS9cP/9/TP6j3yNaqv8/XsJJ/SZLOu/wPqq77YfXpMnP+tVxT8t+SJH1v9KP6NL623vW+5G7Ys1UL331GkvSz/5yqFy9Nq/lBvf5WLjh0SG89OEuS9Obo0XryzjvNIpKkx6dMkU6e1Jc9e+qVxx7zKBObl6cLf/97abeln1ogUKrkW5cwXgR7aWmp9u7d65rOy8tTbm6uOnXqpB49emj27Nk6dOiQli9fLkm655579PTTT2vWrFm644479M4772jVqlVau3atax2ZmZmaPHmyhg0bpuHDh2vRokUqKyvT1KlTfdg4IDJ8k5SkP7z4omu6rpe1kS+8oAG1+f3Co4+qsF5+15W5eMsWfb82v1dMm6a/XnWVR5lzDx7U//60Jr83jh6tZ+88nd/1v15WTZmiNidPam+vXpr5v/Xyu57H58/XgH/V5Pd1f/iDqqM8v6DuXr5c179Vk98PPPqo9tbWu17E64qtWzXjmZr8fmHqVL2bVpPf9b+yEg8d0kOzavJ7++jRWlNbb/NrLbNefq+uzW+zzLWPPKJ48hvB5Gt+160DQMias2CBipKSlFCvDd6u9t8HX3hBP6jN8O9NeVSfJp7O8Lr29fcPbNGCHbVt8Aum6aWkem3w2r//C0sPat3W2jb4gNF66Kp6bfB6//2sNgvze/XSgnoZXlKvvhfNn6+OtRn+wR/+INVm+Gf1yty4fLluqc3w7z36qD6tO/Zod7rMDbu2auGh2jb4gKl6Mbm2DV6vm9gLyg7prbdrMvzlnqM1O6W2smPk5oMJU9T25Ent6tlTN9dm+PF6P++Zl6eEPb/XpYVkOIKE/AYi3kMLFqgwKUmJlovjE194QdfU5ndmvbasdDrm0rds0ezaNvhj06bpNUsb/PyDB7Wmtg3+8ujRerheG7y+z+6Yohid1M6evXT93AbOoWfN17C9tefQn6vXBq9/Dn3Fck15sza/H6mX3/V8b+tWPVrbBn9k6lStsrTB+xw6pKW1bfA3Ro/W4w20wX9be+7g85499bPa/K6vZ16e/vv3v9cA2uAIpmY4hx6quDgOn5h/C+ZwIJJ3Y1nY1mOOk2Ebf8McS3OPMZ1x2236U70T65J0qvbfYp0eprtE7hd86+p3QKeHLPtXtft4I9G1CxSXSh/UjnVWlCCdGna6TP3tOrpcijkpnewlVfc9Pd/tu+l5Sf+q/f8fTv+w/onzU29JFW/VjHVScZ5UVXsBvv5nU5wn/fvPNfvnUKpUXuG+XZL0haTXq2rGIfuHTje2zc/m09qyx3R639Wv8ze9e+uLK6/UP41gt40Naxvr1ORknBNvvpMj6Hscku93rXux/Pbt2zV69GjXdGZmpiRp8uTJysnJUUFBgQ4cOOD6ee/evbV27Vrdd999Wrx4sbp3767nnntO6emn+0C85ZZbdOTIEc2ZM0eFhYUaMmSI1q1bp4QEOlpCeLD9KTn5Hje//80hUP7nttv0WyO/6w5iR0gaV/v/z+SezVG1hVK+I/2w5sZ3Hegu5dYf1Ky2TOdEKf3mmv9/PVRqG1evTL0AH/awFFMttesqtTmn/pud/u/5P5UG1Q4K1qZLvdyuF+A9JkhD0iWVSPF9pZi6MUjrBVT3i6Ur/kfSYWlrf+n9ujL1dmJivHTLSEn7pfizpY2121N9Sm7ukZQvaZ+k9bXzjCL6rux57WQ8W3+NS4YWxh+/KPyyIUI4aZ/YxjV1MtazkzHHzbEzbUNh5xvTlmE71fHP7tP7/nybBjbQBv+qdp1x26UT46XKs0+XiS6v+bfqU6ny+dqxR++QdPrw2xWrVQelE0tq2rJFkk6NOF2mvN77rpH0gaQv5b4P6u/D4nrT9fdl/fL/lvRa7f8LdLpdG1PvinVxvnTimdrtnSpV1x5XuLX3D0kVz9WWGS1V9/F8X0n6XFJMTXHXZ1l/6NWC3r217MCVSnzLvQ1ufj7m5yd5fs62MVSdjHPq5FjBmzIIUeQ3IpST89zBem/Ju7a07Xy5Oc/WYbo5mF/B87epz49edLvxqy58BqZL1wyQ1EeK6yG1qd++rt1p8f8p9fmPmkq3j5Oi648PXrsh0R2kDgsk7ZFa9ZBUf5TD+gE+RNLfVLOx9drUp+r9//AJaX/thp2qkqprA9ft4lelpEtq/x+vmnBVvX8ltRosdXiidnO7SVG1xybR9Q7C2pwt9ak9tEloK7Wuq7fxIV49U2pbJf3zO1K7uvML9S44fHFRb22+8koNN86h2z4f8zO0fc7m74KTdntz525zv3+L1Azn0ENVVHV1dXXjxcJHSUmJ4uLi1F6+38SIpnNy0GBr0JsnwW3jgrc1pjtaysQb00mWMm2MaVudzQOCZEsZc922EYG7GNNxljLmdpj1szGf5pY8G7HFljLmCe9CSxnzfkBbA9osYzu5Yn5P2k62HzOmvW2I2+Y1Vh/Ct3lUq+Ygr7i42C9je9d95xcPlGJtXy5O11Mpxe30X73gHTI8eLzJa9syZmbZ8ru9MR1vKWPm5SWWMpca090tZS4wpjvYDgR6OViRGeqdLGXMr4oYSxlTuWVeiTFtuxphBq+tZ7v97pNlljLmTYOfW1bznmWeeR+77fjhmDFta9CbeW07nnFy4ryxZeB/oZrfEhkeCshvd962iZ2sx9ZWNLPXbDfb5tna0mbU2dq3fYzpiyxlrjSmbccGZv7Y2snm+0dbdsgJIwBs8ZhrTG+1lNlgTNv2/VXG9OWWMkOMadthSFtj5RWWEDPbzrZDg3jLPJN5cfyfljL/NqZtGe/NBXTbOQJvjgNsODZwjvzGmZDfjfM2083lnJwLt2W82cTsYCljZrqt6Wqe1+5nKXODMZ2YZik0yJg2DwxsFbB9aRcZ02ZDVfIMMcsdefsdfNn3Mj8M28kGc55tB3U2pm0fqhmY+y1lPnGf3GMehMjzuESSdhnT3t7wZl5Ut52iMPPZycNsTm7usCGvGxaqGR5J+c2T4wCA8MddbwAAhB+ePAMAIPyQ3wAAhCfOobtwcRwAEP4YLwUAgPDDmKUAAIQf8hsAgPDEOXSXYA6dAQAAAAAAAAAAAABAs+DJcYQEszcG27AH5vgWtrEsG1tG8hxvzTYmm7nuo5Yy5tgetnHbzHm2Mk7GmDH3j633CnOMEHMMEclzrBHb2CPmttrGLjeXs40nZs6z1cfcz7bPy5uxRyOodw84RZcwQLMw/3Rsd12a3+22zDDzwBz/0raeBEuZvWYZy+CjXYx55njnkuc4ntHmwOmS5wGEbVBVky3ojI2vtOwgc+ww23GJOT6pOYyb5DmOqG1sVts8J7lvbprta5WvWnigW1a0ULZfWydD/9mWM7PXFjVmGdv3uPldb4s1c57tvcyssY2P2th6Jc+YjbY8pWK2Mc0slDzb7bZjDNv+MO03pm11NrPXNu5rWwdP25j1se1nk62Mue228cTNYwon44nbxgoP1HEAX/EhivwGfObkfKf53Wr7rjfn2caQNr/bbXn5gTGdYhn4utc7xoxEy4rM4Ldt2DH3yRNmg1eeuWvLb3M7bBGbYMzss92zjDmvjS3A441p24GAgx293/jAPrWsxvb5mKu2fc7e/L7YPp4IejAYNpxDd+HiOAAg/NElDAAA4YduWQEACD/kNwAA4Ylz6C50qw4AAAAAAAAAAAAAiHg8OQ4ACH++3rUWQXe9AQAQNvyRv2Q4AADBRX4DABCeOIfuwsVx+JXtb8PsnsDJsAS2MaycMNdtG1vDyRjf5thlxyxlzOFQbGOXOxnf3MkQpU44GdPVyTjgTsYuN8eGdTLmmJPxSW2fl7lu2++Yk9+pCPrehk2lpGoflucXBC2M+Stv60rIm2GEbOOlmu/lZJxT25iY5nK2cbfNsT7jLWXijGnbWKjmEONtzeCzzLPtL/MYw1bGybii5v6xjQdqzjtmKWPus2IHZWzrtn2G5ufsJK/JdPic3xK/EAg5TtrEgXw/J2OW2r7HzQx3kumWePQYJ9NJG9i2f5yMwW6+f4mljNlud3KMYXPYQRkzLztaypjbbttOJ3np5DN1cmxglrF9pk6OVZzU2eSvr29ioBmQ38AZefPr7SQLbedfnZzrNbPQdi7afH/LMOAe43fHW8LRlvsmJ2Ogm+1SWxmzjrZM3W9M51vK/NOYjrdsfEdjnu29zM/imKWMuR22+tiOVcwq2T5n8/1tvy9OjhvNeYxLHmE4h+5Ct+oAAAAAAAAAAAAAgIjHk+MAgPBHlzAAAIQfumUFACD8kN8AAIQnzqG7cHEcABD+6BIGAIDwQ7esAACEH/IbAIDwxDl0Fy6OAwDCH8EOAED44eQ6AADhh/wGACA8cQ7dhYvjCEm2v7EKB8tVOlhPK2P6LEuZE8Z0W0uZbxyUMd+rjYMy0ZYyJnM7Jc9tte0vs4y5nZJ00kEZc93mMt7Wx0kZAEDosuWTk/wuc1DGzJpvLWW+MqY7WsqYed3BUsY8NrAdK5jzbPlt2x8mb7LZtr/M/WFbj3ns4mQ9tnLlljLm5+xk2wEApwXze9OWWeZ3vZNMt2XNMWPaSYZ6y8mxwTFj2sxC23pszPXY9qGZj+0tZQK17bZtMD8fW+6bdbaVcfJe5jzb74+T33GOHwCEG9v3lpNzuybb+U9z3U6+623vbc4zz0Xb3r/YUuaQMW07F+4k58zsKbGUMd/flt9Ojl3M9r55zkCS4ozpWEsZc7uc7ENbnc15xyxljjpYznbMY/4u2H5fnFw78Qb5jXDExXEAQPhjvBQAAMIPY5YCABB+yG8AAMIT59BduDgOAAh/VfKtSxhfu4QDAABN52t+yw/LAwCApiG/AQAIT5xDd7H1AAEAAAAAAAAAAAAAgNeWLFmiXr16qW3btkpNTdWHH37YYNlRo0YpKirK4zV27FhXmSlTpnj8fMyYMU2qE0+OI+DMnhZsd2SY41LYxkdxMj61uZyTMcedjJdlG0vNyVijTsqYnNyx4qT3CttYH07GAXNSxpuxwp2MOebtdjX23mgBqiRF+bB8BN31BnjDSV56O4aUmX22zHDyXk7GOTXHHDtmKdPGmI5xUMaWzeZ2eTvmuJMsNLfdyVhzTsYut5WxzTPHhLN9ht4cP5Dp8Dm/JTIcYcFJm9ib9Thlvp/tu96bzDLzQfJsA9vGHvVmLFYn7UlbfcxjA9sYnWauORlP/JiljJmFtmMMJ8cPTjgZh9ac5yS/nRw/OPksnBwHeItjgxBAfqOFcNJO9nY9TpjvZcsMJ9/jJtt3tJlztvGyjxjTtpwzORlL3VZn8/2dtl0bW88xS5mOxrS3Y6mb2+qk3e5kLHXbck7y2sm+99f5eifI7xDRDOfQX375ZWVmZio7O1upqalatGiR0tPTtXv3bnXt2tWj/GuvvaaKitNHrkePHlVKSopuuukmt3JjxozR888/75qOiXHyrXRaQJ8c/+qrr3TbbbcpNjZW8fHxmjZtmkpLS8+4jO2ugHvuuSeQ1QQAhLtKP7zgQn4DAILCH/lNhruQ3wCAoCC//Yr8BgAEjZ/yu6SkxO1VXm67TbXGE088obvuuktTp07VRRddpOzsbLVv317Lli2zlu/UqZMSExNdr/Xr16t9+/YeF8djYmLcyp199tlN2hUBvTh+22236R//+IfWr1+vN954Q1u2bNHdd9/d6HJ33XWXCgoKXK9f/epXgawmAACoh/wGACD8kN8AgEgWil2y+gP5DQAIN8nJyYqLi3O9srKyrOUqKiq0Y8cOpaWluea1atVKaWlp2rZtm6P3Wrp0qW699VZ16NDBbf6mTZvUtWtX9e3bV/fee6+OHj3apG0IWLfqn332mdatW6e//e1vGjZsmCTpqaee0nXXXafHH39cSUlJDS7bvn17JSYmOnqf8vJyt7sSSkpKfKs4ACD8VIpu1f0kWPktkeEA0OL5mt8SGV6L/AYABE0z5HeodsnqK/IbABBUfjqHnp+fr9jYWNfshvLzyy+/VGVlpRISEtzmJyQkaNeuXY2+3YcffqidO3dq6dKlbvPHjBmjG2+8Ub1799a+ffv00EMPKSMjQ9u2bVN0tLOBiwL25Pi2bdsUHx/vCnZJSktLU6tWrfTBBx+ccdkXX3xRnTt31sCBAzV79mx9+61tVKgaWVlZbncoJCcn+20bAABhosoPL0gKXn5LZDgAtHj+yG8yXBL5DQAIombI71DtktVX5DcAIKj8lN+xsbFur0DdXLZ06VINGjRIw4cPd5t/66236vrrr9egQYM0fvx4vfHGG/rb3/6mTZs2OV53wJ4cLyws9Lhzr3Xr1urUqZMKCwsbXO4HP/iBevbsqaSkJP3973/XT3/6U+3evVuvvfaatfzs2bOVmZnpmi4pKSHcQ5zt+Ne8S8NfQw/Z1mPeN2Krj7mc7V6Tk8a07U4TJ/eo+OsOFSftCnO7nGy7bR+ay9nKOPkMvamzt+tBhOPJcb8JVn5LZHgksn0fVxjTbSxlTjhYj5m75jK2dZ9lKWPOs2W1bTmTNxnvJHdtzG23LWOWMaclz8/CyX52upyTYwzAA0+O+w35HXmctGWlwH3f2tZr5qOTLPa2nWxy0i4180qSzNEPbXV28l7eLGc75jH3hzf7wvZeTrLZlvGBKuOvtj5ClB/z23x6OSYmxuMEe12XrLNnz3bN83eXrGeffbauuuoqPfroozrnnHO82CDvkN+Rycl55caWsS1nyzknnJzrNb/byyxl2hrTtu1y0gZ20r40c9eWw07OzZu3jJjbIEnfGNO28wG2TG+Mk/1s2y4n82xZbM6z/b44OafvBBkexoJ8Dr1z586Kjo5WUVGR2/yioqJGez8pKyvTypUr9cgjjzT6Pn369FHnzp21d+9eXX311Y7q1uSL4w8++KB++ctfnrHMZ5991tTVutQfU2XQoEHq1q2brr76au3bt0/nnXeeR3nbQRMAAHAXavktkeEAADSG/AYARDLz4uzcuXM1b948t3mh3CVrQ8hvAACkNm3aaOjQodq4caPGjx8vSaqqqtLGjRs1Y8aMMy77yiuvqLy8XLfffnuj73Pw4EEdPXpU3bp1c1y3Jl8cv//++zVlypQzlunTp48SExP1xRdfuM0/deqUvvrqqyaNh5KamipJ2rt3b4PhDgBo4XhyvFHkNwAg5PDkeKPIbwBAyPFjfjsds9QXZ+qStc6gQYM0ePBgnXfeedq0aZPjp84aQn4DAEJSM5xDz8zM1OTJkzVs2DANHz5cixYtUllZmaZOnSpJmjRpks4991xlZWW5Lbd06VKNHz/eo0eX0tJSzZ8/X9///veVmJioffv2adasWTr//POVnp7uuF5NvjjepUsXdenSpdFyI0aM0LFjx7Rjxw4NHTpUkvTOO++oqqrKFdhO5ObmSlKTrvgDAFqYakX8yXFfkd8AgJBDfjeK/AYAhBw/5nfdWKVnEspdsjaE/AYAhKRmaIPfcsstOnLkiObMmaPCwkINGTJE69atc/UIc+DAAbVq5T4wwu7du7V161a9/fbbHuuLjo7W3//+d73wwgs6duyYkpKSdO211+rnP/95k26yi6qurg7YrsjIyFBRUZGys7N18uRJTZ06VcOGDdOKFSskSYcOHdLVV1+t5cuXa/jw4dq3b59WrFih6667Tuecc47+/ve/67777lP37t21efNmR+9ZUlKiuLg4tZfvNzGi+Xg7Dre/xvh2sh6zjL/W6y1vxvrwduzTYI4n7s16EbqqVTPeT3FxcaMNYCfqvvOLJfmythJJcX6sV7hrjvyWyPBQ56+cczL2qJNxwJ2Mb+ZtGW8y3l+cZLOTcVe9HZvVX+9v46/jBwRfqOa3RIbXR36Ht2C2gb3NPid57a8xtZ1wMha2Oc/J+J82To5DzDK2MUsDtT+8PTbwZuxyb/Oc9n/wRVJ+p6amavjw4Xrqqack1XTJ2qNHD82YMUMPPvhgg8vl5OTonnvu0aFDhxodS/zgwYPq0aOH1qxZo+uvv74pm+MT8ju8+Su//ZW7trGxzTJOxtR2kmHebruTdqmZzbasdpIr3uS3k33ohJMstG2Xv/ZHIM8tOEGG+yZUMzyS2t8BPdf34osvql+/frr66qt13XXX6fLLL9ezzz7r+vnJkye1e/duffvtt5Jq+p/fsGGDrr32WvXr10/333+/vv/97+tPf/pTIKsJAAhzlX544TTyGwAQDP7Ib28yfMmSJerVq5fatm2r1NRUffjhhw2WHTVqlKKiojxeY8eOdZWZMmWKx8/HjBnjRc18Q34DAIKhOfI7MzNTv/vd7/TCCy/os88+07333uvRJevs2bM9ljtTl6w/+clP9P7772v//v3auHGjvve97zW5S1Z/IL8BAMHCOfTTmtytelN06tTJdZebTa9evVT/wfXk5OQm3eEGAIDkezhHUrD7A/kNAAgGfzSum7r8yy+/rMzMTGVnZys1NVWLFi1Senq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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "guided = [i for i, kn in enumerate(results[\"kn\"]) if kn_min < kn.real < kn_max]\n", "if not guided:\n", " guided = list(range(min(4, len(results[\"kn\"]))))\n", "\n", "n_plot = min(4, len(guided))\n", "fig, axes = plt.subplots(2, max(1, n_plot), figsize=(5 * max(1, n_plot), 8))\n", "if n_plot == 1:\n", " axes = axes.reshape(2, 1)\n", "\n", "for j, mode_i in enumerate(guided[:n_plot]):\n", " r = solver.solve(omega, num_modes=10, mode_idx=mode_i + 1)\n", " X, Y, Ex, Ey, Ez = solver.get_field_on_grid(r[\"Et_vec\"], r[\"En_vec\"], nx=80, ny=60)\n", "\n", " Et_mag = np.sqrt(np.abs(Ex) ** 2 + np.abs(Ey) ** 2)\n", " En_mag = np.abs(Ez)\n", "\n", " ax = axes[0, j]\n", " im = ax.pcolormesh(X, Y, Et_mag, cmap=\"hot\", shading=\"auto\")\n", " ax.plot([-a_core/2, a_core/2, a_core/2, -a_core/2, -a_core/2], [-b_core/2, -b_core/2, b_core/2, b_core/2, -b_core/2], \"c--\", linewidth=1.25)\n", " ax.set_title(f\"|Et| mode {mode_i+1}\")\n", " ax.set_aspect(\"equal\")\n", " fig.colorbar(im, ax=ax, fraction=0.046)\n", "\n", " ax = axes[1, j]\n", " im = ax.pcolormesh(X, Y, En_mag, cmap=\"hot\", shading=\"auto\")\n", " ax.plot([-a_core/2, a_core/2, a_core/2, -a_core/2, -a_core/2], [-b_core/2, -b_core/2, b_core/2, b_core/2, -b_core/2], \"c--\", linewidth=1.25)\n", " ax.set_title(f\"|En| mode {mode_i+1}\")\n", " ax.set_aspect(\"equal\")\n", " fig.colorbar(im, ax=ax, fraction=0.046)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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": "3.12.3" }, "papermill": { "default_parameters": {}, "duration": 50.840997, "end_time": "2026-05-27T19:59:52.660311+00:00", "environment_variables": {}, "exception": null, "input_path": "docs/examples/dielectric_waveguide_modes.ipynb", "output_path": "docs/examples/dielectric_waveguide_modes.ipynb", "parameters": {}, "start_time": "2026-05-27T19:59:01.819314+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }