{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mode solver Fully Vectorial\n",
    "\n",
    "## Strip waveguides \n",
    "\n",
    "Lets compute the modes for different types of waveguides"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "    _________________________________\n",
    "\n",
    "\n",
    "                                    clad_thickness\n",
    "           width\n",
    "         <---------->\n",
    "          ___________    _ _ _ _ _ _\n",
    "         |           |\n",
    "    _____|           |____          |\n",
    "                                    wg_heigth\n",
    "    slab_thickness                     |\n",
    "    _______________________ _ _ _ _ __\n",
    "\n",
    "    sub_thickness\n",
    "    _________________________________\n",
    "    <------------------------------->\n",
    "                 sub_width\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import modes as ms\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ms.waveguide(width=0.5, slab_thickness=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ymargin = 1\n",
    "s = ms.mode_solver_full(plot=True, plot_index=True, logscale=True, n_modes=1, width=0.2, thickness=0.22, fields_to_write=('Ex'), clad_thickness=[ymargin], sub_thickness=ymargin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ymargin = 1.5\n",
    "s = ms.mode_solver_full(plot=True, plot_index=True, logscale=True, n_modes=1, width=0.25, thickness=0.22, fields_to_write=('Ex'), clad_thickness=[ymargin], sub_thickness=ymargin, sub_width=2*ymargin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the mode in logscale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = ms.mode_solver_full(plot=True, plot_index=True, logscale=True, n_modes=1, width=0.5, thickness=0.22, fields_to_write=('Ex'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = ms.mode_solver_full(plot=True, plot_index=True) # by default it will plot at the fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ms.mode_solver_full?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the waveguide parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s.results['n_effs'][0].real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = ms.mode_solver_full(plot=False, n_modes=1, width=0.5, thickness=0.22, fields_to_write=('Ex'), overwrite=True)\n",
    "A, centre, sigma_2 = ms.fit.fit_gaussian(s.wg.xc, s.wg.yc, np.abs(s.modes[0].fields['Ex']))\n",
    "print(f\"Aeff = {A:.2f}, mode_center = {centre}, Sigma2 = ({sigma_2[0]:.2f}, {sigma_2[1]:.2f})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the waveguide geometry that gives the smallest mode area, for the TE polarization at 1550, for a silicon thickness of 220 nm, strip waveguide?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nm = 1e-3\n",
    "widths = np.linspace(250, 600, 15)*nm\n",
    "aeffs = []\n",
    "sigma2x = []\n",
    "sigma2y = []\n",
    "\n",
    "for width in tqdm(widths):\n",
    "    s = ms.mode_solver_full(plot=False,  n_modes=1, width=width, thickness=0.22, fields_to_write=('Ex'), clad_thickness=[ymargin], sub_thickness=ymargin, sub_width=2*ymargin+width, overwrite=True)\n",
    "    A, centre, sigma2 = ms.fit.fit_gaussian(s.wg.xc, s.wg.yc, np.abs(s.modes[0].fields['Ex'])) \n",
    "    aeffs.append(A)\n",
    "    sigma2x.append(sigma2[0])\n",
    "    sigma2y.append(sigma2[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(widths, aeffs, 'o')\n",
    "plt.xlabel('wg width (nm)')\n",
    "plt.ylabel(r'Aeff ($\\mu m^2$)')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(widths, sigma2x)\n",
    "plt.xlabel('wg width (nm)')\n",
    "plt.ylabel(r'$\\sigma_x^2$')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(widths, sigma2y)\n",
    "plt.xlabel('wg width (nm)')\n",
    "plt.ylabel(r'$\\sigma_y^2$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see 350 nm width will give you the smallest mode area for 220nm Silicon strip waveguides\n",
    "\n",
    "\n",
    "## Rib waveguides"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = ms.mode_solver_full(plot=True, plot_index=True, n_modes=1, width=0.5, thickness=0.22, slab_thickness=0.09, fields_to_write=('Ex'), overwrite=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence tests\n",
    "\n",
    "Lets do some convergence tests wherer we reduce the meshsize (20 nm by default)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dx=np.linspace(0.01, 0.02, 3)\n",
    "dx = np.array([5, 10, 20, 40])*1e-3\n",
    "n_effs = [ms.mode_solver_full(n_modes=1, x_step=dxi, y_step=dxi, plot=False).results['n_effs'][0].real for dxi in dx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(dx*1e3, n_effs)\n",
    "plt.xlabel('mesh size (nm)')\n",
    "plt.ylabel('neff0')"
   ]
  }
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