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   "source": [
    "# Additive Backend"
   ]
  },
  {
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   "id": "1",
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   "source": [
    "> The additive backend can be used to obtain pathlengths and group delays."
   ]
  },
  {
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   "execution_count": null,
   "id": "2",
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   "source": [
    "from functools import partial\n",
    "\n",
    "import jax\n",
    "import jax.example_libraries.optimizers as opt\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt  # plotting\n",
    "import sax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3",
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    "tags": []
   },
   "source": [
    "## Parametrized Models"
   ]
  },
  {
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   "id": "4",
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   "source": [
    "def coupler(length=50.0) -> sax.SDict:\n",
    "    sdict = {\n",
    "        (\"in0\", \"out0\"): length,\n",
    "        (\"in0\", \"out1\"): length,\n",
    "        (\"in1\", \"out0\"): length,\n",
    "        (\"in1\", \"out1\"): length,\n",
    "    }\n",
    "    return sax.reciprocal(sdict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5",
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   "source": [
    "def waveguide(length=100.0) -> sax.SDict:\n",
    "    sdict = {\n",
    "        (\"in0\", \"out0\"): length,\n",
    "    }\n",
    "    return sax.reciprocal(sdict)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6",
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    "tags": []
   },
   "source": [
    "## Circuit with additive backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7",
   "metadata": {
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     "duration": 0.080753,
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   "source": [
    "mzi, _ = sax.circuit(\n",
    "    netlist={\n",
    "        \"instances\": {\n",
    "            \"lft\": coupler,\n",
    "            \"top\": partial(waveguide, length=500),\n",
    "            \"btm\": partial(waveguide, length=100),\n",
    "            \"rgt\": coupler,\n",
    "        },\n",
    "        \"connections\": {\n",
    "            \"lft,out0\": \"btm,in0\",\n",
    "            \"btm,out0\": \"rgt,in0\",\n",
    "            \"lft,out1\": \"top,in0\",\n",
    "            \"top,out0\": \"rgt,in1\",\n",
    "        },\n",
    "        \"ports\": {\n",
    "            \"in0\": \"lft,in0\",\n",
    "            \"in1\": \"lft,in1\",\n",
    "            \"out0\": \"rgt,out0\",\n",
    "            \"out1\": \"rgt,out1\",\n",
    "        },\n",
    "    },\n",
    "    backend=\"additive\",\n",
    ")"
   ]
  },
  {
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   "execution_count": null,
   "id": "8",
   "metadata": {
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     "start_time": "2024-06-17T18:16:30.183239",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "mzi()"
   ]
  }
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