{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mode overlap integral between a waveguide mode and a Gaussian mode\n",
    "\n",
    "The evaluation of the overlap integral quantifies the level of matching between two optical field distributions. It is particularly useful, for example, in determining the coupling efficiency to the desired waveguide mode when connecting an optical fiber to an edge coupler.\n",
    "\n",
    "Tidy3D facilitates the analytical computation of field distributions for different beam types including Gaussian beam, astigmatic Gaussian beam, and plane wave. This feature enables swift calculation of mode overlap integral with another mode, likely determined through a mode solver analysis. \n",
    "\n",
    "This notebook presents the optimization of coupling efficiency between a single-mode fiber (represented by a Gaussian mode field) and a silicon edge coupler. The focus is to highlight the usage of built-in functions for the analytical computation of the Gaussian beam profile and overlap integral calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tidy3d as td\n",
    "import tidy3d.web as web\n",
    "from tidy3d.plugins.mode import ModeSolver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate the Gaussian Beam Profile\n",
    "\n",
    "The Gaussian beam is analytically defined by\n",
    "\n",
    "$$\n",
    "E(x,y,z) = \\frac{w_0}{w(z)} \\exp\\left[-\\frac{x^2+y^2}{w(z)^2}\\right] \\exp\\Biggl\\{ i\\Bigl( k_0 z + \\frac{k_0(x^2+y^2)}{2R(z)} - \\psi(z)\\Bigr) \\Biggr\\},\n",
    "$$\n",
    "\n",
    "where the beam parameters are defined as follows:\n",
    "\n",
    "Beam radius:\n",
    "\n",
    "  $$\n",
    "  w(z) = w_0 \\sqrt{1+\\left(\\frac{z+z_0}{z_R}\\right)^2},\n",
    "  $$\n",
    "\n",
    "  with $w_0$ as the waist radius and $z_0$ as the waist distance.\n",
    "\n",
    "Rayleigh range:\n",
    "\n",
    "  $$\n",
    "  z_R = \\frac{k_0 w_0^2}{2}.\n",
    "  $$\n",
    "\n",
    "Radius of curvature:\n",
    "\n",
    "  $$\n",
    "  R(z) = \\frac{(z+z_0)^2+z_R^2}{z+z_0}.\n",
    "  $$\n",
    "\n",
    "Gouy phase:\n",
    "\n",
    "  $$\n",
    "  \\psi(z) = \\arctan\\!\\Bigl(\\frac{z+z_0}{z_R}\\Bigr) - \\arctan\\!\\Bigl(\\frac{z_0}{z_R}\\Bigr).\n",
    "  $$\n",
    "\n",
    "A Gaussian beam field profile can be generated directly through [GaussianBeamProfile](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.GaussianBeamProfile.html). Similarly, an astigmatic Gaussian beam profile can be generated through [AstigmaticGaussianBeamProfile](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.AstigmaticGaussianBeamProfile.html) and a plane wave profile can be generated through [PlaneWaveBeamProfile](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PlaneWaveBeamProfile.html). \n",
    "\n",
    "In this notebook, we want to optimize the coupling between an SMF-28 and a 220 nm SOI edge coupler by adjusting the waveguide width at the end of the edge coupler. This requires us to perform mode analysis on the waveguide cross section with varying widths and then perform mode overlap integral with the fiber mode. For SMF-28, the mode field diameter at 1550 nm is about 10.5 μm. Therefore, we can represent the mode field with a Gaussian beam with a `waist_radius` of 5.25 μm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "lda0 = 1.55  # wavelength of interest\n",
    "freq0 = td.C_0 / lda0  # frequency of interest\n",
    "r_beam = 5.25  # beam radius\n",
    "size = 6 * r_beam  # plane size for the beam profile"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to accurately capture the full profile of the Gaussian beam, it is imperative to ensure the plane size is sufficiently large, at least a few times larger than the beam size. The `size` argument also expects one of the values to be 0. The direction with a zero size is taken as the propagation axis. For example, if `size=(size_x, size_y, 0)`, the Gaussian beam is propagating in the $z$ direction. Additional arguments such as `angle_theta` and `angle_phi` can be specified if the desired propagation direction is not parallel to one of the Cartesian axes, similar to defining a regular [GaussianBeam](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.GaussianBeam.html) source in FDTD.\n",
    "\n",
    "Additionally, it's necessary to align the polarization angle with the desired waveguide mode for effective coupling. In this particular scenario, the target is coupling to the fundamental TE mode that is polarized in the y-direction. \n",
    "\n",
    "The `resolution` parameter is crucial as it defines the sampling resolution and it needs to be appropriately high to ensure precision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate a Gaussian beam\n",
    "gaussian_beam = td.GaussianBeamProfile(\n",
    "    waist_radius=r_beam,\n",
    "    pol_angle=np.pi / 2,  # polarized in the y direction for coupling to the TE mode\n",
    "    size=(size, size, 0),\n",
    "    resolution=200,\n",
    "    freqs=[freq0],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the beam is generated, we can visualize the field profile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaussian_beam.field_data.Ey.abs.plot(cmap=\"hot\", x=\"x\", y=\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conducting Mode Analysis on the Waveguide\n",
    "\n",
    "We will proceed by performing a mode analysis on the waveguide structure at the end facet of the edge coupler. Our aim is to sweep a range of waveguide widths to identify the optimal value, one which would result in the highest coupling efficiency. To accomplish this, we first define a function `make_mode_solver`. This function takes the waveguide width as an input parameter and returns a [ModeSolver]() instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# materials used\n",
    "si = td.material_library[\"cSi\"][\"Li1993_293K\"]\n",
    "sio2 = td.material_library[\"SiO2\"][\"Horiba\"]\n",
    "\n",
    "# thickness of the waveguide\n",
    "h = 0.22\n",
    "\n",
    "\n",
    "def make_mode_solver(w):\n",
    "    waveguide = td.Structure(geometry=td.Box(center=(0, 0, 0), size=(h, w, td.inf)), medium=si)\n",
    "\n",
    "    sim = td.Simulation(\n",
    "        center=(0, 0, 0),\n",
    "        size=(size, size, 1),\n",
    "        grid_spec=td.GridSpec.auto(min_steps_per_wvl=25, wavelength=lda0),\n",
    "        structures=[waveguide],\n",
    "        run_time=1e-12,\n",
    "        medium=sio2,\n",
    "        symmetry=(1, -1, 0),  # symmetry for the fundamental TE mode\n",
    "    )\n",
    "\n",
    "    mode_spec = td.ModeSpec(num_modes=1, target_neff=3.5)\n",
    "    mode_solver = ModeSolver(\n",
    "        simulation=sim,\n",
    "        plane=td.Box(center=(0, 0, 0), size=(size, size, 0)),\n",
    "        mode_spec=mode_spec,\n",
    "        freqs=[freq0],\n",
    "    )\n",
    "\n",
    "    return mode_solver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We investigate the waveguide width from 100 to 200 nm in increment of 10 nm. All 11 mode solvers are submitted via a [Batch]() to run in parallel. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9c7ce3092fec49bf9587b18c47094e3d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">08:29:34 CEST </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">11</span> tasks.                     \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m08:29:34 CEST\u001b[0m\u001b[2;36m \u001b[0mStarted working on Batch containing \u001b[1;36m11\u001b[0m tasks.                     \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">08:29:44 CEST </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.053</span> for the whole batch.               \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m08:29:44 CEST\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.053\u001b[0m for the whole batch.               \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after   \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>the Batch has completed.                                          \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mUse \u001b[32m'Batch.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed FlexCredit cost after   \n",
       "\u001b[2;36m              \u001b[0mthe Batch has completed.                                          \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "dd7e2efb541243fda5e86e20d3302274",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">08:29:53 CEST </span>Batch complete.                                                   \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m08:29:53 CEST\u001b[0m\u001b[2;36m \u001b[0mBatch complete.                                                   \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f2287396b75b480a8eecfe0ca9cee18a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_list = np.linspace(0.1, 0.2, 11)\n",
    "mode_solvers = {f\"w={w:.2f}\": make_mode_solver(w) for w in w_list}\n",
    "\n",
    "batch = web.Batch(simulations=mode_solvers, verbose=True)\n",
    "batch_results = batch.run(path_dir=\"data\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mode Overlap Integral\n",
    "\n",
    "After the batch mode solving, we are ready to perform the mode overlap integral (modal decomposition) between the waveguide mode and the Gaussian mode for each waveguide width. This can be achieved easily with the built-in `outer_dot` method, which implements\n",
    "\n",
    "$$\n",
    "\\frac{1}{4} \\int \n",
    "\\left( \n",
    "    \\mathbf{E}_0 \\times \\mathbf{H}_1^*\n",
    "    + \n",
    "    \\mathbf{H}_0^* \\times \\mathbf{E}_1\n",
    "\\right) \\cdot\n",
    "\\, d\\mathbf {S}.\n",
    "$$\n",
    "\n",
    "\n",
    "After the overlap integrals are calculated, we can plot the coupling efficiency as a function of the waveguide width to identify the optimal value. In this case, the optimal width is between 130 and 140 nm. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "overlap = [\n",
    "    batch_results[f\"w={w:.2f}\"].outer_dot(gaussian_beam.field_data).values.squeeze() for w in w_list\n",
    "]\n",
    "\n",
    "plt.plot(1e3 * w_list, np.abs(overlap) ** 2, \"r\", linewidth=2)\n",
    "plt.xlabel(\"Waveguide width (nm)\")\n",
    "plt.ylabel(\"Coupling efficiency\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For instance, we can examine the mode profile of the waveguide with a width of 130 nm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimal_mode = batch_results[\"w=0.13\"]\n",
    "optimal_mode.Ey.abs.plot(vmax=4, cmap=\"hot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After determining the optimal waveguide geometry, we can examine the impact of misalignment on the coupling efficiency. This scenario becomes relevant as the fiber is often not perfectly aligned with the waveguide in practical situations. To accomplish this, we will employ the `translated_copy(vector)` method, which shifts the mode profile in both the $x$ and $y$ directions. Then we can calculate the overlap integral between the Gaussian beam and the shifted mode profile.\n",
    "\n",
    "As anticipated, the results indicate that the coupling efficiency diminishes when the waveguide mode and Gaussian beam become misaligned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shift_x_list = np.linspace(0, 3, 7)\n",
    "shift_y_list = np.linspace(0, 5, 11)\n",
    "\n",
    "# use a nested list comprehension to build the array of overlaps\n",
    "shifted_overlap = np.array(\n",
    "    [\n",
    "        [\n",
    "            optimal_mode.translated_copy(vector=(shift_x, shift_y, 0))\n",
    "            .outer_dot(gaussian_beam.field_data)\n",
    "            .values.squeeze()\n",
    "            for shift_x in shift_x_list\n",
    "        ]\n",
    "        for shift_y in shift_y_list\n",
    "    ]\n",
    ")\n",
    "\n",
    "# plot the coupling efficiency\n",
    "plt.pcolormesh(shift_x_list, shift_y_list, np.abs(shifted_overlap) ** 2, cmap=\"hot\")\n",
    "plt.xlabel(\"Shift in x (μm)\")\n",
    "plt.ylabel(\"Shift in y (μm)\")\n",
    "plt.title(\"Coupling Efficiency\")\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Final Remarks\n",
    "\n",
    "In this example, we set the size of the Gaussian mode plane and waveguide mode plane to be identical. This is not strictly required for the overlap calculation. As long as both planes are sufficiently large and the mode profiles decay to zero at the boundaries, the result will be accurate. The discretization grids of the two profiles are not required to be identical either, since the `outer_dot` method will automatically interpolate the data. However, we need to ensure both grids are sufficiently fine for the profiles to be accurate and to minimize discretization error in the integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "description": "This notebook demonstrates how to perform an overlap integral between a waveguide mode and a Gaussian beam Tidy3D FDTD.",
  "feature_image": "N/A",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "keywords": "Gaussian beam, waveguide, overlap, edge coupler, Tidy3D, FDTD",
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.13"
  },
  "title": "Mode Overlap Integral between a Waveguide Mode and a Gaussian Mode | Flexcompute"
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
