{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Calculate Coupling Coefficients\n", "Two split rings are placed in a broadside coupled configuration. The scalar model of each resonator is augmented by additional coefficients representing the coupling between them.\n", "\n", "In [D. A. Powell et al, Phys. Rev. B 82, 155128 (2010)](http://dx.doi.org/10.1103/PhysRevB.82.155128) similar coefficients were calculated under the quasi-static approximation for a single mode only. Here the effects of retardation and radiation losses are included, as are the contributions of multiple modes of each ring." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "# setup 2D and 3D plotting \n", "%matplotlib inline\n", "from openmodes.ipython import matplotlib_defaults\n", "matplotlib_defaults()\n", "import matplotlib.pyplot as plt\n", "\n", "import numpy as np\n", "\n", "import os.path as osp\n", "\n", "import openmodes\n", "from openmodes.constants import c, eta_0\n", "from openmodes.model import EfieModelMutualWeight\n", "from openmodes.sources import PlaneWaveSource" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Creating geometry\n", "\n", "As in previous examples, we load a pair of SRRs, place them in the simulation and visualise the result." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", " \n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Pruned cell types: vertex, line\n" ] } ], "source": [ "parameters={'inner_radius': 2.5e-3, 'outer_radius': 4e-3}\n", "\n", "sim = openmodes.Simulation(notebook=True)\n", "srr = sim.load_mesh(osp.join(openmodes.geometry_dir, \"SRR.geo\"), \n", " parameters=parameters,\n", " mesh_tol=0.7e-3)\n", "\n", "srr1 = sim.place_part(srr)\n", "srr2 = sim.place_part(srr, location=[0e-3, 0e-3, 2e-3])\n", "srr2.rotate([0, 0, 1], 180)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "
\n", " \n", " Wireframe\n", " Format\n", " \n", " \n", " Arrow Length\n", " \n", " \n", "
\n", "\n", "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sim.plot_3d()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving modes of individual rings\n", "We find the singularities for the two identical rings." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "50da0a866d674b3f9b2dd06b9ce8c44b", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(Label(value='Refining modes'), FloatProgress(value=0.0, max=2.0)))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "start_s = 2j*np.pi*1e9\n", "\n", "num_modes = 3\n", "\n", "estimate = sim.estimate_poles(start_s, modes=num_modes, parts=[srr1, srr2], cauchy_integral=False)\n", "refined = sim.refine_poles(estimate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constructing the models\n", "\n", "We now use these singularities to construct a model for each of the rings, where $n$ represents the ring number and $m$ represents the mode number. $s=j\\omega$ is the complex frequency, $s_{n,m}$ is the complex resonant frequency of each mode and $\\mathbf{V}_{n, m}$ is the corresponding current of the mode. The current on each ring is represented as a sum of modes\n", "\n", "$$\\mathbf{J}_{n} = \\sum_m a_{n,m}\\mathbf{V}_{n, m}$$\n", "\n", "This results in the following coupled equation system for the modal coefficients on each ring\n", "\n", "$$\\frac{s_{n,m}}{s}\\left(s-s_{n,m}\\right)a_{n,m} + \\sum_{n'\\neq n}\\sum_{m'}\\left(sL_{m,n,m',n'} + \\frac{1}{s}S_{m,n,m',n'}\\right)a_{n',m'} = \\mathbf{V}_{n, m}\\cdot\\mathbf{E}_{inc}$$\n", "\n", "* The first term just says that the self-impedance of each mode is calculated directly from the pole expansion.\n", "* The second term is the mutual inductance $L$ and capacitance $C = S^{-1}$ between each modes of different rings. These coefficients are obtained by weighting the relevant parts of the impedance matrix, e.g.:\n", "$$L_{m,n,m',n'} = \\mathbf{V}_{n, m} L_{n,n'}\\mathbf{V}_{n', m'}$$\n", "* The right hand side is just the projection of the incident field onto each mode\n", "\n", "Here we construct two different models, one considering only the fundamental mode of each ring, and another considering the first and third modes. Due to symmetry, the second mode of each ring does not play a part in the hybridised modes which will be considered here." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "dominant_modes = refined.select([0]).add_conjugates()\n", "simple_model = EfieModelMutualWeight(dominant_modes)\n", "\n", "full_modes = refined.select([0, 2]).add_conjugates()\n", "full_model = EfieModelMutualWeight(full_modes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving scattering based on models\n", "Now we iterate through all frequencies, and calculate the model parameters. Their accuracy is demonstrated by using them to calculate the extinction cross-section. For reference purposes, this will be compared with the direct calculation." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1ec39218321b41f595f4eed3d9159c5a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(Label(value='Frequency Sweep'), FloatProgress(value=0.0, max=199.0)))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_freqs = 200\n", "freqs = np.linspace(5e9, 10e9, num_freqs)\n", "\n", "plane_wave = PlaneWaveSource([0, 1, 0], [1, 0, 0], p_inc=1.0)\n", "\n", "extinction_tot = np.empty(num_freqs, np.complex128)\n", "extinction_single = np.empty(num_freqs, np.complex128)\n", "extinction_full_model = np.empty((num_freqs, len(full_modes)), np.complex128)\n", "extinction_simple_model = np.empty((num_freqs, len(dominant_modes)), np.complex128)\n", "\n", "# store the mutual coupling coefficients for plotting purposes\n", "mutual_L = np.empty(num_freqs, np.complex128)\n", "mutual_S = np.empty(num_freqs, np.complex128)\n", "\n", "simple_vr = dominant_modes.vr\n", "simple_vl = dominant_modes.vl\n", "\n", "full_vr = full_modes.vr\n", "full_vl = full_modes.vl\n", " \n", " \n", "for freq_count, s in sim.iter_freqs(freqs):\n", " impedance = sim.impedance(s)\n", " V = sim.source_vector(plane_wave, s)\n", "\n", " # For reference directly calculate extinction for the complete system, and for a single ring \n", " extinction_tot[freq_count] = np.vdot(V, impedance.solve(V)) \n", " extinction_single[freq_count] = np.vdot(V[\"E\", srr1], impedance[srr1, srr1].solve(V[\"E\", srr1]))\n", "\n", " # calculate based on the simple model\n", " Z_model = simple_model.impedance(s)\n", " V_model = simple_vl.dot(V)\n", " I_model = Z_model.solve(V_model)\n", " extinction_simple_model[freq_count] = V.conj().dot(simple_vr*(I_model)) \n", " \n", " # calculate based on the full model\n", " Z_model = full_model.impedance(s)\n", " V_model = full_vl.dot(V)\n", " I_model = Z_model.solve(V_model)\n", " extinction_full_model[freq_count] = V.conj().dot(full_vr*(I_model))\n", " \n", " mutual_L[freq_count] = Z_model.matrices['L'][srr1, srr2][0, 0]\n", " mutual_S[freq_count] = Z_model.matrices['S'][srr1, srr2][0, 0]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Accuracy of the models\n", "\n", "The extinction cross section is now plotted for the pair of rings, using both the simpler model and the direct calculation. Additionally, the cross section of a single ring is shown. It can be seen that this fundamental mode of a single ring is split into two coupled modes. Due to the coupling impedance being complex, the hybridised modes have different widths." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "# normalise the extinction to the cross-sectional area of each ring\n", "area = np.pi*(parameters['outer_radius'])**2\n", "\n", "Q_single = extinction_single/area\n", "Q_pair = extinction_tot/area\n", "Q_full_model = extinction_full_model/area\n", "Q_simple_model = extinction_simple_model/area" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.plot(freqs*1e-9, Q_pair.real, label='pair')\n", "plt.plot(freqs*1e-9, Q_single.real, label='single')\n", "plt.plot(freqs*1e-9, np.sum(Q_simple_model.real, axis=1), label='model')\n", "plt.xlim(freqs[0]*1e-9, freqs[-1]*1e-9)\n", "plt.xlabel('f (GHz)')\n", "plt.legend(loc='upper right')\n", "plt.ylabel('Extinction efficiency')\n", "plt.subplot(122)\n", "plt.plot(freqs*1e-9, Q_pair.imag)\n", "plt.plot(freqs*1e-9, Q_single.imag)\n", "plt.plot(freqs*1e-9, np.sum(Q_simple_model.imag, axis=1))\n", "plt.xlim(freqs[0]*1e-9, freqs[-1]*1e-9)\n", "plt.ylabel('Normalised reactance')\n", "plt.xlabel('f (GHz)')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above figure, it can be seen that the simple model of interaction between the rings gives quite good agreement. This can be improved by using the model which considers the two modes of each ring. While the modes on the same ring are independent of each other, between meta-atoms all modes couple to each other, thus there are 3 distinct coupling impedances, and two distinct self impedance terms.\n", "\n", "The results of this model are plotted below, showing the improved accuracy by accounting for the higher-order mode." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.plot(freqs*1e-9, Q_pair.real, label='exact')\n", "plt.plot(freqs*1e-9, np.sum(Q_simple_model.real, axis=1), label='single mode')\n", "plt.plot(freqs*1e-9, np.sum(Q_full_model.real, axis=1), label='two modes')\n", "plt.legend(loc=\"upper right\")\n", "plt.xlim(5.0, 7)\n", "plt.xlabel('f (GHz)')\n", "plt.subplot(122)\n", "plt.plot(freqs*1e-9, Q_pair.imag)\n", "plt.plot(freqs*1e-9, np.sum(Q_simple_model.imag, axis=1))\n", "plt.plot(freqs*1e-9, np.sum(Q_full_model.imag, axis=1))\n", "plt.xlim(5.3, 6.5)\n", "plt.xlabel('f (GHz)')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coupling coefficients within the model\n", "\n", "Now we can study the coupling coefficients between the dominant modes of the two rings. It can be seen that both $L_{mut}$ and $S_{mut}$ show quite smooth behaviour over this wide frequency range. This justifies the use of a low-order polynomial model for the interaction terms. This frequency variation is due to retardation, which is not very strong for such close separation.\n", "\n", "However, the retardation is still strong enough to make the imaginary parts of these coupling terms non-negligible. These parts corresponds to the real part of the mutual impedance, and mean that the coupling affects not only the stored energy, but also the rate of energy loss due to radiation by the modes." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(freqs*1e-9, mutual_S.real, label='real')\n", "plt.plot(freqs*1e-9, mutual_S.imag, label='imag')\n", "plt.legend(loc=\"center right\")\n", "plt.ylabel('$S_{mut}$ (F$^{-1}$)')\n", "plt.xlabel('f (GHz)')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(freqs*1e-9, mutual_L.real, label='real')\n", "plt.plot(freqs*1e-9, mutual_L.imag, label='imag')\n", "plt.legend(loc=\"center right\")\n", "plt.ylabel('$L_{mut}$ (H)')\n", "plt.xlabel('f (GHz)')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can be seen that these are quite smooth functions, so they could be fitted by a low-order polynomial if required." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }