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   "cell_type": "markdown",
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   "source": [
    "# Sweep the coupler gap\n",
    "\n",
    "Analytic calculation of 100% coupling length into two parallel SOI waveguides\n",
    "with a varying gap at different TE wavelengths.\n",
    "\n",
    "An example refractive index profile for the two waveguides spaced 200nm is\n",
    "shown."
   ]
  },
  {
   "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",
    "import opticalmaterialspy as mat\n",
    "from modes.design import directional_coupler_lc\n",
    "\n",
    "wavelength_nm  = 1550\n",
    "width = 0.45\n",
    "thickness = 0.22\n",
    "widths = [width]*2\n",
    "wg_gaps = np.arange(0.15, 0.30, 0.05)\n",
    "wg_gaps = np.array([0.15, 0.2, 0.25])\n",
    "dcs = [ms.waveguide_array(widths=widths, wg_gaps=[wg_gap], sub_width=3, thickness=thickness) for wg_gap in wg_gaps]\n",
    "dcs[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ms.mode_solver_full(wg=dcs[0], n_modes=2, plot=True, plot_index=True, fields_to_write=('Ex'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_effs = [ms.mode_solver_full(wg=wg, n_modes=2).results['n_effs'] for wg in dcs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ne = [ n_eff[0].real for n_eff in n_effs]\n",
    "no = [ n_eff[1].real for n_eff in n_effs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lc = [directional_coupler_lc(wavelength_nm, n_eff_1, n_eff_2) for n_eff_1, n_eff_2 in zip(ne, no)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(wg_gaps*1e3, lc, 'o')\n",
    "plt.xlabel('gap (nm)')\n",
    "plt.ylabel('100% Coupling length (um)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# to increase reduce the gap step we need to reduce the size of the x_step and y_step computing grid\n",
    "\n",
    "wg_gaps = np.arange(0.15, 0.30, 0.02)\n",
    "dcs = [ms.waveguide_array(widths=widths, wg_gaps=[wg_gap], x_step=0.01, y_step=0.01) for wg_gap in wg_gaps]\n",
    "n_effs = [ms.mode_solver_full(wg=wg, n_modes=2).results['n_effs'] for wg in dcs]\n",
    "ne = [ n_eff[0].real for n_eff in n_effs]\n",
    "no = [ n_eff[1].real for n_eff in n_effs]\n",
    "lc = [directional_coupler_lc(wavelength_nm, n_eff_1, n_eff_2) for n_eff_1, n_eff_2 in zip(ne, no)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(wg_gaps*1e3, lc, 'o')\n",
    "plt.xlabel('gap (nm)')\n",
    "plt.ylabel('100% Coupling length (um)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Design a directional coupler with a gap of 250nm that will tap off 10% of the optical power at a wavelength of 1550nm. What length in microns does the directional coupler have to be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "directional_coupler_lc?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "wavelength_nm  = 1550\n",
    "width = 0.5\n",
    "thickness = 0.22\n",
    "widths = [width]*2\n",
    "dc = ms.waveguide_array(widths=widths, wg_gaps=[0.25], sub_width=3, thickness=thickness)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ms.mode_solver_full(wg=dc, n_modes=2, plot=True, plot_index=True, fields_to_write=('Ex'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "directional_coupler_lc(1550, 2.481, 2.464, power_ratio=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise \n",
    "What is the coupler length (in µm) that corresponds with 100% power transfer from the through port (top) to the cross port (bottom)? Assume 500nm x 220nm Si waveguides in SiO2, 1550 nm wavelength, and a 100 nm coupler gap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dc = ms.waveguide_array(widths=widths, wg_gaps=[0.1], sub_width=3, thickness=thickness, x_step=0.01)\n",
    "m = ms.mode_solver_full(wg=dc, n_modes=2, plot=True, fields_to_write=('Ex'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "directional_coupler_lc(1550, np.abs(m.n_effs)[0], np.abs(m.n_effs)[1], power_ratio=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "directional_coupler_lc(1550, 2.498, 2.437, power_ratio=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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