{
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"# EME solver\n",
"\n",
"This notebook demonstrates basic usage of Tidy3D’s EigenMode Expansion\n",
"(EME) solver. We simulate some example devices and discuss some tips and\n",
"tricks.\n",
"\n",
"EME is a frequency-domain method for propagating electromagnetic fields\n",
"and computing the full bidirectional scattering matrix of a device along\n",
"a fixed axis. It is useful for simulating longer waveguide devices; for\n",
"such devices, it can be much faster than FDTD, although sometimes the\n",
"results can be less accurate. EME is well-suited for devices in which\n",
"the propagation is primarily confined to a particular axis. It is not\n",
"well-suited for free-space or omnidirectional propagation. For example,\n",
"in this notebook, we simulate an evanescent waveguide coupler and a\n",
"waveguide taper, as shown below.\n",
"\n",
"10:24:31 UTC Started working on Batch containing 2 tasks. \n",
"10:24:33 UTC Maximum FlexCredit cost: 0.050 for the whole batch. \n",
" Use 'Batch.real_cost()' to get the billed FlexCredit cost after \n",
" completion. \n",
"10:25:08 UTC Batch complete. \n",
"10:25:11 UTC Created task 'EME taper' with resource_id \n",
" 'eme-d14398ab-1e19-4bd4-88a3-272e60d24463' and task_type 'EME' . \n",
" Tidy3D's EME solver is currently in the beta stage. Cost of EME \n",
" simulations is subject to change in the future. \n",
"10:25:15 UTC Estimated FlexCredit cost: 0.407 . For this solver type, the \n",
" estimate is the final billed cost. \n",
"10:25:16 UTC status = queued \n",
" To cancel the simulation, use 'web.abort(task_id)' or \n",
" 'web.delete(task_id)' or abort/delete the task in the web UI. \n",
" Terminating the Python script will not stop the job running on the \n",
" cloud. \n",
"10:25:53 UTC starting up solver \n",
" running solver \n",
"10:26:46 UTC status = success \n",
"10:26:56 UTC Loading results from simulation_data.hdf5 \n",
"\n",
"\n",
"\n",
" \n",
"\n",
" \n",
" \n",
" \n",
"
<xarray.EMECoefficientDataArray (f: 1, sweep_index: 30, eme_port_index: 2,\n",
" eme_cell_index: 40, mode_index_out: 30,\n",
" mode_index_in: 30)> Size: 35MB\n",
"array([[[[[[ 5.08266942e-01+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j, ...,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j],\n",
" [ 0.00000000e+00+0.00000000e+00j,\n",
" 5.02574360e-01+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j, ...,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j],\n",
" [ 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 4.99999857e-01+0.00000000e+00j, ...,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j],\n",
" ...,\n",
" [ 0.00000000e+00+0.00000000e+00j,\n",
"...\n",
" ...,\n",
" [-6.32779943e-03-4.63581766e-04j,\n",
" -2.03525634e-05+1.91952633e-04j,\n",
" -7.38260629e-06-4.04457556e-06j, ...,\n",
" -1.68821684e-03-3.24394919e-04j,\n",
" -8.01429426e-04-1.41542106e-04j,\n",
" -5.43224459e-04+4.26636645e-04j],\n",
" [ 5.99026315e-04+7.21834198e-03j,\n",
" 9.33103509e-05+1.30685672e-05j,\n",
" 2.66024865e-06+3.08584212e-06j, ...,\n",
" -7.05700554e-04-4.01088930e-04j,\n",
" -2.13653028e-05-1.45123250e-04j,\n",
" 5.34719921e-05+2.63883357e-04j],\n",
" [ 5.98384967e-03-1.80659126e-03j,\n",
" -4.58971442e-05-3.45095206e-05j,\n",
" 2.90031665e-06+5.51793479e-07j, ...,\n",
" -6.78370385e-04+1.08714297e-04j,\n",
" 9.40176154e-06+2.68297573e-04j,\n",
" 3.01954065e-04-2.87396205e-04j]]]]]],\n",
" shape=(1, 30, 2, 40, 30, 30))\n",
"Coordinates:\n",
" * f (f) float64 8B 1.934e+14\n",
" * sweep_index (sweep_index) int64 240B 0 1 2 3 4 5 6 ... 24 25 26 27 28 29\n",
" * eme_port_index (eme_port_index) int64 16B 0 1\n",
" * eme_cell_index (eme_cell_index) int64 320B 0 1 2 3 4 5 ... 35 36 37 38 39\n",
" * mode_index_out (mode_index_out) int64 240B 0 1 2 3 4 5 ... 25 26 27 28 29\n",
" * mode_index_in (mode_index_in) int64 240B 0 1 2 3 4 5 ... 24 25 26 27 28 29\n",
"Attributes:\n",
" long_name: mode expansion coefficient (0.5082669423376676+0j) ... (0.000301954064831497-0.000287396205008...
array([[[[[[ 5.08266942e-01+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j, ...,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j],\n",
" [ 0.00000000e+00+0.00000000e+00j,\n",
" 5.02574360e-01+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j, ...,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j],\n",
" [ 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 4.99999857e-01+0.00000000e+00j, ...,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j,\n",
" 0.00000000e+00+0.00000000e+00j],\n",
" ...,\n",
" [ 0.00000000e+00+0.00000000e+00j,\n",
"...\n",
" ...,\n",
" [-6.32779943e-03-4.63581766e-04j,\n",
" -2.03525634e-05+1.91952633e-04j,\n",
" -7.38260629e-06-4.04457556e-06j, ...,\n",
" -1.68821684e-03-3.24394919e-04j,\n",
" -8.01429426e-04-1.41542106e-04j,\n",
" -5.43224459e-04+4.26636645e-04j],\n",
" [ 5.99026315e-04+7.21834198e-03j,\n",
" 9.33103509e-05+1.30685672e-05j,\n",
" 2.66024865e-06+3.08584212e-06j, ...,\n",
" -7.05700554e-04-4.01088930e-04j,\n",
" -2.13653028e-05-1.45123250e-04j,\n",
" 5.34719921e-05+2.63883357e-04j],\n",
" [ 5.98384967e-03-1.80659126e-03j,\n",
" -4.58971442e-05-3.45095206e-05j,\n",
" 2.90031665e-06+5.51793479e-07j, ...,\n",
" -6.78370385e-04+1.08714297e-04j,\n",
" 9.40176154e-06+2.68297573e-04j,\n",
" 3.01954065e-04-2.87396205e-04j]]]]]],\n",
" shape=(1, 30, 2, 40, 30, 30)) Coordinates: (6)
f
(f)
float64
1.934e+14
units : Hz long_name : frequency sweep_index
(sweep_index)
int64
0 1 2 3 4 5 6 ... 24 25 26 27 28 29
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
" 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) eme_port_index
(eme_port_index)
int64
0 1
long_name : EME port index eme_cell_index
(eme_cell_index)
int64
0 1 2 3 4 5 6 ... 34 35 36 37 38 39
long_name : EME cell index array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
" 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,\n",
" 36, 37, 38, 39]) mode_index_out
(mode_index_out)
int64
0 1 2 3 4 5 6 ... 24 25 26 27 28 29
long_name : mode index out array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
" 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) mode_index_in
(mode_index_in)
int64
0 1 2 3 4 5 6 ... 24 25 26 27 28 29
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
" 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) Attributes: (1)
long_name : mode expansion coefficient 10:27:01 UTC Created task 'EME taper convergence sweep' with resource_id \n",
" 'eme-4f04da03-8b64-442f-9189-cb441ac5a260' and task_type 'EME' . \n",
" Tidy3D's EME solver is currently in the beta stage. Cost of EME \n",
" simulations is subject to change in the future. \n",
"10:27:05 UTC Estimated FlexCredit cost: 0.399 . For this solver type, the \n",
" estimate is the final billed cost. \n",
"10:27:06 UTC status = queued \n",
" To cancel the simulation, use 'web.abort(task_id)' or \n",
" 'web.delete(task_id)' or abort/delete the task in the web UI. \n",
" Terminating the Python script will not stop the job running on the \n",
" cloud. \n",
"10:27:16 UTC starting up solver \n",
" running solver \n",
"10:27:55 UTC status = success \n",
"10:27:59 UTC Loading results from simulation_data.hdf5 \n",
" ![\"Evanescent](\"img/eme_evanescent_coupler.png\")
\n",
"![\"Waveguide](\"img/eme_taper.png\")
\n",
"\n",
"In a translationally invariant waveguide, the eigenmodes propagate\n",
"independently, each with its own propagation constant. At a\n",
"discontinuity in the transverse profile of a device, the forward and\n",
"backward travelling modes on each side couple together; there is\n",
"reflection and transmission described by a scattering matrix, expressed\n",
"in the basis of eigenmodes on each side. The tangential fields are\n",
"continuous at the interface. For a piecewise uniform device, we can\n",
"calculate the scattering matrix at each discontinuity and then combine\n",
"them to obtain the full scattering matrix. For a general device whose\n",
"cross-sectional profile may vary continuously, we can discretize the\n",
"device into cells into along the propagation axis, assuming that the\n",
"cross section is uniform within each cell. If the discretization is fine\n",
"enough, the resulting piecewise uniform geometry approaches the true\n",
"continuously varying geometry.\n",
"\n",
"In our EME solver, the simulation is divided into cells along the\n",
"propagation axis. In each cell, we assume the device is translationally\n",
"invariant and solve for the modes of the device. Between each pair of\n",
"cells, the device cross section and modal basis can change; we impose\n",
"field continuity conditions and solve for the coupling between the two\n",
"modal bases."
],
"id": "e187413c-113a-4a0c-a3f0-37130a8420da"
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import tidy3d as td\n",
"import tidy3d.web as web\n",
"from matplotlib import pyplot as plt\n",
"from tidy3d.plugins import waveguide"
],
"id": "fe19180d"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Evanescent Waveguide Coupler\n",
"\n",
"As a first example, we look at evanescent coupling between a pair of\n",
"waveguides. Using EME, we can efficiently simulate long devices and\n",
"perform length sweeps to help design these devices.\n",
"\n",
"### EME Simulation Setup\n",
"\n",
"We first define the materials and geometries present in the simulation."
],
"id": "1f455fdf-7bee-454e-9e67-58105a971dfb"
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"si = td.material_library[\"cSi\"][\"Li1993_293K\"]\n",
"sio2 = td.material_library[\"SiO2\"][\"Palik_LowLoss\"]\n",
"\n",
"l = 6\n",
"h = 0.22\n",
"w = 0.45\n",
"g = 0.05\n",
"\n",
"geo = td.GeometryGroup(\n",
" geometries=[\n",
" td.Box(size=(w, h, 2 * l), center=(-(w + g) / 2, 0, 0)),\n",
" td.Box(size=(w, h, 2 * l), center=((w + g) / 2, 0, l)),\n",
" ]\n",
")\n",
"\n",
"wvgs = td.Structure(geometry=geo, medium=si)"
],
"id": "a4c24483"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we define the EME simulation.\n",
"\n",
"The EME simulation has a `grid_spec` field and an `eme_grid_spec` field.\n",
"The `grid_spec` field defines a Yee grid like the one present in FDTD\n",
"simulations. This grid is used for mode solving and for storing field\n",
"data. In contrast, the `eme_grid_spec` defines a 1D grid along the\n",
"propagation axis, dividing the simulation into EME cells. The choice of\n",
"EME grid can be important in determining the speed and accuracy of the\n",
"EME simulation. Here, we use an `EMEExplicitGrid` with three cells. We\n",
"make sure that the cell boundaries are aligned with any discontinuities\n",
"in the device profile, and we make sure that the number of modes in each\n",
"cell is large enough to capture the physics of interest.\n",
"\n",
"The EME solver always calculates the full bidirectional scattering\n",
"matrix of the device. The scattering matrix is defined in the modal\n",
"basis of the two ports of the device, which are the boundaries of the\n",
"first and last EME cells. By default these would be the simulation\n",
"bounds along the propagation axis; here, we set `port_offsets` to shift\n",
"these boundaries. We also add an `EMEFieldMonitor` to help visualize the\n",
"field.\n",
"\n",
"Finally, we add a `sweep_spec` to the simulation in order to sweep the\n",
"length of the coupling region. Simple length sweeps can be easier in EME\n",
"simulations than in FDTD simulations – the modes can be reused so there\n",
"is no need to run a new simulation each time. We need to create a\n",
"separate simulation for the sweep, since length sweeps are not\n",
"compatible with `EMEFieldMonitor`."
],
"id": "f6aa51c8-b9ed-444a-b7d6-b75ee1921496"
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
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O1bhx43TVVVfZt+z27dtXdevW9e0A4RUjRoxQzZo1lZGRYZ+GKM0mTJigQ4cO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\n"
}
}
],
"source": [
"eme_grid_spec = td.EMEExplicitGrid(\n",
" boundaries=[0, l],\n",
" mode_specs=[\n",
" td.EMEModeSpec(num_modes=2),\n",
" td.EMEModeSpec(num_modes=4),\n",
" td.EMEModeSpec(num_modes=2),\n",
" ],\n",
")\n",
"\n",
"eme_field_mon = td.EMEFieldMonitor(name=\"field\", size=(td.inf, 0, td.inf))\n",
"\n",
"lengths = np.linspace(l, 6 * l, 100)\n",
"\n",
"eme_sim = td.EMESimulation(\n",
" center=(0, 0, l / 2),\n",
" size=(6 * w, h + 4 * w, l + 4 * w),\n",
" structures=[wvgs],\n",
" medium=sio2,\n",
" symmetry=(0, 1, 0),\n",
" grid_spec=td.GridSpec.auto(min_steps_per_wvl=10),\n",
" monitors=[eme_field_mon],\n",
" eme_grid_spec=eme_grid_spec,\n",
" freqs=[td.C_0 / 1.55],\n",
" axis=2,\n",
" port_offsets=(w, w),\n",
")\n",
"\n",
"eme_sim_sweep = eme_sim.updated_copy(\n",
" sweep_spec=td.EMELengthSweep(scale_factors=list(lengths / l)), monitors=[]\n",
")\n",
"\n",
"_ = eme_sim.plot(y=0, monitor_alpha=0)\n",
"plt.show()"
],
"id": "4bc54658"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we run the simulation."
],
"id": "fe966425-cba9-4773-9076-c0faf705af53"
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"sims = {\"eme_sim\": eme_sim, \"eme_sim_sweep\": eme_sim_sweep}\n",
"batch = web.Batch(simulations=sims, verbose=True)"
],
"id": "15b0730b"
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/html": [
""
]
}
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/html": [
""
]
}
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/html": [
"