docs/notebooks/32_coupling_efficiency.ipynb

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    "# Coupling efficiency\n",
    "\n",
    "We can compute the mode overlaps between a waveguide and a fiber mode.\n",
    "\n",
    "Fiber modes are usually described with their [MFD Mode field Diameter](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=14203#:~:text=The%20mode%20field%20diameter%20(MFD,achieve%20particularly%20high%20coupling%20efficiency.)\n",
    "\n",
    "or [Numerical Aperture (NA)](https://en.wikipedia.org/wiki/Numerical_aperture)\n",
    "\n",
    "\n",
    "For [standard single mode fiber SMF28](https://www.corning.com/media/worldwide/coc/documents/Fiber/SMF-28%20Ultra.pdf), the MFD is 10.4 for 1.55um wavelength.\n"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import modes\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "widths = np.linspace(0.15, 0.5, 5)\n",
    "ces = np.zeros_like(widths)\n",
    "\n",
    "for i, width in enumerate(widths):\n",
    "    ms = modes.mode_solver_semi(width=width, plot=False)\n",
    "    ce = modes.coupling_efficiency(mode_solver=ms, fibre_mfd=10.4)[0]\n",
    "    ces[i] = ce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "ms = modes.mode_solver_semi()"
   ]
  },
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   "source": [
    "plt.plot(widths, ces*100)\n",
    "plt.title('SMF fiber and 0.22um thick waveguide TE0 mode overlap')\n",
    "plt.xlabel('waveguide width (um)')\n",
    "plt.ylabel('Single mode fiber overlap (%)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many silicon photonics technologies use standard 0.22um thick SOI Silicon, and 0.5um wide waveguides for single mode condition. However, you can only get 15% fiber coupling from a 0.5x0.2 waveguide into a fiber.\n",
    "\n",
    "A common solution is to increase the mode size by tapering down to a narrower waveguide (inverse taper). As you can see, for a single mode fiber, you can reach around 3dB (50%) coupling efficiency with an inverse taper where the tip tapers down to 0.15um.\n",
    "\n",
    "To increse coupling efficiency there are other options:\n",
    "\n",
    "- High NA fibers with reduced MFD\n",
    "- Lens focusing fibers\n",
    "\n",
    "For example, [lensed fibers](https://www.ozoptics.com/ALLNEW_PDF/DTS0080.pdf) have a spot size diameter from 2 to 7.5um"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "widths = np.linspace(0.15, 0.5, 5)\n",
    "ces = np.zeros_like(widths)\n",
    "\n",
    "for i, width in enumerate(widths):\n",
    "    ms = modes.mode_solver_semi(width=width, plot=False)\n",
    "    ce = modes.coupling_efficiency(mode_solver=ms, fibre_mfd=4.)[0]\n",
    "    ces[i] = ce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(widths, ces*100)\n",
    "plt.title('High NA fiber and 0.22um thick waveguide TE0 mode overlap')\n",
    "plt.xlabel('waveguide width (um)')\n",
    "plt.ylabel('Single mode fiber overlap (%)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "wavelength = 1.55\n",
    "MFD = np.linspace(2, 7.5, 10)\n",
    "NA = wavelength/np.pi/(MFD/2)\n",
    "NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ces = np.zeros_like(MFD)\n",
    "width = 0.18\n",
    "\n",
    "for i, mfd in enumerate(MFD):\n",
    "    ms = modes.mode_solver_semi(width=width, plot=False)\n",
    "    ce = modes.coupling_efficiency(mode_solver=ms, fibre_mfd=mfd)[0]\n",
    "    ces[i] = ce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(MFD, ces*100)\n",
    "plt.title('lens fiber 0.18 x 0.22um thick waveguide TE0 mode overlap')\n",
    "plt.xlabel('lensed fiber MFD (um)')\n",
    "plt.ylabel('coupling efficiency (%)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(NA, ces*100)\n",
    "plt.title('lens fiber 0.18 x 0.22um thick waveguide TE0 mode overlap')\n",
    "plt.xlabel('lensed fiber NA')\n",
    "plt.ylabel('coupling efficiency (%)')"
   ]
  }
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