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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# YYK Model\n",
    "## S-P pol coupled cavity\n",
    "## Configuration PRMI\n",
    "### With S-to-P TRANS map\n",
    "### without any phase maps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
     ]
    }
   ],
   "source": [
    "%reset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pykat\n",
    "from pykat import finesse\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "pykat.init_pykat_plotting(dpi=90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PRMI Base"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "base = finesse.kat()\n",
    "base.verbose=False\n",
    "base.parse(\"\"\"\n",
    "#------- Main PRMI ---------------------------\n",
    "#---------------------------------------------\n",
    "\n",
    "# clight 299792458.0 \n",
    "\n",
    "l i1 83.74 0  nL                  #I0=780W\n",
    "const fmod1 16.880962M            #f1\n",
    "const fmod2 45.0159M              #f2\n",
    "const fmod3 56.2699M              #f3\n",
    "const PRMtune -13\n",
    "\n",
    "mod eo1 $fmod1 0.1 1 pm 0 nL neo1\n",
    "s seo1 0 neo1 neo2\n",
    "mod eo2 $fmod2 0.1 1 pm 0 neo2 neo3\n",
    "s seo2 0 neo3 neo4\n",
    "mod eo3 $fmod3 0.05 1 am 0 neo4 neo5\n",
    "\n",
    "s eo1refl 0 neo5 neo22\n",
    "bs refl 0.0001 0.9999 0 45 neo22 dump npr nREFL   #REFL\n",
    "s bsm 0 npr nprb\n",
    "\n",
    "m prm 0.90 0.10 $PRMtune nprb nf0\n",
    "\n",
    "s Ls1 14.7615 nf0 nf1 #14.7615 \n",
    "bs PR2 0.9999 0.0001 0 0.6860 nf1 nf2 dump dump # tilted\n",
    "s Ls2 11.0661 nf2 nf3\n",
    "bs PR3 1 0 0 0.6860 nf3 nf4 dump dump # tilted\n",
    "s Ls3 15.7638 nf4 n1\n",
    "\n",
    "bs bs1 0.5 0.5 0 45 n1 n2 n3hr n4hr   #==BS==#\n",
    "\n",
    "s bs1bsAR1 0 n3hr n3hr2\n",
    "m bsAR1 0 1 0 n3hr2 n3ar\n",
    "s subBS1 0.0 1.45 n3ar n3ar2 # BS thickness is ignored \n",
    "m bsAR3 0 1 0 n3ar2 n3\n",
    "s bs1bsAR2 0 n4hr n4hr2\n",
    "m bsAR2 0 1 0 n4hr2 n4ar\n",
    "s subBS2 0.0 1.45 n4ar n4ar2 # BS thickness is ignored \n",
    "m bsAR4 0 1 0 n4ar2 n4\n",
    "\n",
    "s Lmx 26.6649  n3 n6\n",
    "s Lmy 23.3351  n2 n5\n",
    "\n",
    "bs ARx 200e-6 0.9998 0 0.025 n6 nPOX n6ar dump   # wedged ITM\n",
    "bs ARy 200e-6 0.9998 0 0.025 n5 dump n5ar dump   # wedged ITM\n",
    "\n",
    "s subx 0.15 1.754 n6ar n6hr  # thickness 150mm\n",
    "s suby 0.15 1.754 n5ar n5hr  # thickness 150mm\n",
    "\n",
    "m ITMx 0.996 4000e-6 90 n6hr n6hrp1\n",
    "m ITMy 0.996 4000e-6 0 n5hr n5hrp1\n",
    "\n",
    "\n",
    "\n",
    "#----------- P-pol Cavity Part ---------------\n",
    "#---------------------------------------------\n",
    "\n",
    "s spy1 0 n5hrp1 p1y\n",
    "lens compy 2519.89 p1y p2y\n",
    "s spy2 0 p2y p3y\n",
    "lens ly0 -541.619156 p3y p4y\n",
    "s py3 0.0855 p4y p5y\n",
    "bs Lmyp 1 0 0 45 p5y p6y dump dump\n",
    "s py4 23.5127 p6y p4\n",
    "\n",
    "\n",
    "s spx1 0 n6hrp1 p1x\n",
    "lens compx 2519.89 p1x p2x\n",
    "s spx2 0 p2x p3x\n",
    "lens lx0 -541.619156 p3x p4x\n",
    "s px3 0.0855 p4x p5x\n",
    "bs Lmxp 1 0 0 45 p5x p6x dump dump\n",
    "s px4 26.8425 p6x p3\n",
    "\n",
    "bs bsp 0.5 0.5 0 45 p4 dump p6 p3\n",
    "\n",
    "s Lp3 15.7638 p6 nf4p\n",
    "bs PR3p 1 0 0 0.6860 nf4p nf3p dump dump\n",
    "s Lp2 11.0661 nf3p nf2p\n",
    "bs PR2p 0.9999 0.0001 0 0.6860 nf2p nf1p nPOPp dump\n",
    "s Lp1 14.7615 nf1p nf0p\n",
    "m prmp 0.9 0.1 $PRMtune nf0p nREFLp\n",
    "\n",
    "\n",
    "\n",
    "#----------- Gaussian params -----------------\n",
    "#---------------------------------------------\n",
    "\n",
    "\n",
    "gauss input i1 nL 4.3330624e-3 6.809459 4.4088792e-3 7.3067531\n",
    "\n",
    "\n",
    "attr prm Rc -458.1285\n",
    "attr PR2 Rc -3.0764\n",
    "attr PR3 Rc 24.9165\n",
    "\n",
    "attr ARx Rc 0\n",
    "attr ARy Rc 0\n",
    "attr ITMx Rcx -1900\n",
    "attr ITMx Rcy -1900\n",
    "attr ITMy Rcx -1900\n",
    "attr ITMy Rcy -1900\n",
    "\n",
    "\n",
    "attr PR3p Rc 24.9165\n",
    "attr PR2p Rc -3.0764\n",
    "attr prmp Rc 458.1285\n",
    "\n",
    "\n",
    "cav cav_sx prm nf0 ITMx n6hr\n",
    "cav cav_px ITMx n6hrp1 prmp nf0p\n",
    "cav cav_sy prm nf0 ITMy n5hr\n",
    "cav cav_py ITMy n5hrp1 prmp nf0p\n",
    "\n",
    "\n",
    "#----------- Mirror Map (ITMs) ---------------\n",
    "#---------------------------------------------\n",
    "map ITMy ITMY_Rmap.txt\n",
    "map ITMx ITMX_Rmap.txt\n",
    "\n",
    "knm ITMx ITMX_Rmap2\n",
    "conf ITMx save_knm_binary 1\n",
    "conf ITMx interpolation_method 2\n",
    "conf ITMx integration_method 3\n",
    "\n",
    "knm ITMy ITMY_Rmap2\n",
    "conf ITMy save_knm_binary 1\n",
    "conf ITMy interpolation_method 2\n",
    "conf ITMy integration_method 3\n",
    "\n",
    "#---------------- Detectors ------------------\n",
    "#---------------------------------------------\n",
    "\n",
    "ad CR0 0 nf0\n",
    "ad SB1 $fmod1 nf0\n",
    "ad SB2 $fmod2 nf0\n",
    "ad SB3 $fmod3 nf0\n",
    "ad CR0p 0 nf0p\n",
    "ad SB1p $fmod1 nf0p\n",
    "pd1 detectorI $fmod1 0 nprb\n",
    "pd1 detectorQ $fmod1 90 nprb\n",
    "pd1 detectorIp $fmod1 0 nREFLp\n",
    "pd1 detectorQp $fmod1 90 nREFLp\n",
    "\n",
    "\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PRMI BASE check\n",
    "### Sideband lock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
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   "source": [
    "kat=base.deepcopy()\n",
    "kat.parse(\"\"\"\n",
    "xaxis* prm phi lin -180 180 1000\n",
    "cav cav0 prm nf0 ITMx n6hr\n",
    "maxtem 1\n",
    "phase 2\"\"\")\n",
    "\n",
    "out = kat.run()\n",
    "plt.semilogy(out.x, out[\"CR0\"],label=\"Carrier\")\n",
    "plt.semilogy(out.x, out[\"SB1\"],label=\"f1\")\n",
    "plt.semilogy(out.x, out[\"SB2\"],label=\"f2\")\n",
    "plt.semilogy(out.x, out[\"SB3\"],label=\"f3\")\n",
    "plt.xlabel(\"PRM tuning [deg]\")\n",
    "plt.ylabel(\"Amplitude [a.u.]\")\n",
    "plt.legend(loc=0)\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mode of P cav (inside PRC_P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
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    "kat2 = base.deepcopy()\n",
    "kat2.parse(\"\"\"\n",
    "maxtem 8\n",
    "phase 2\n",
    "beam beam1 0 nf0p\n",
    "xaxis beam1 x lin -4 4 100\n",
    "x2axis beam1 y lin -4 4 100\n",
    "\"\"\")\n",
    "\n",
    "out1 = kat2.run()\n",
    "\n",
    "beam_plot(out1)\n"
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  {
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   "source": [
    "## POP_P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
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       "L 113.075415 245.343623 \n",
       "z\n",
       "M 218.697458 172.579791 \n",
       "L 216.593845 171.949461 \n",
       "L 214.241153 171.008848 \n",
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       "L 218.946536 172.670401 \n",
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    "kat3 = base.deepcopy()\n",
    "kat3.parse(\"\"\"\n",
    "maxtem 8\n",
    "phase 2\n",
    "beam beam1 0 nf2p\n",
    "xaxis beam1 x lin -200 200 100\n",
    "x2axis beam1 y lin -200 200 100\n",
    "\"\"\")\n",
    "\n",
    "out3 = kat3.run()\n",
    "\n",
    "beam_plot(out3)\n"
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   "source": [
    "## Fields and Signals when max 0th order, PRM sweep"
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  },
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   "source": [
    "kat4 = base.deepcopy()\n",
    "kat4.parse(\"\"\"\n",
    "maxtem 0\n",
    "xaxis* prm phi lin -180 180 200\n",
    "put* prmp phi $x1\n",
    "\"\"\")\n",
    "\n",
    "out4 = kat4.run()\n",
    "\n",
    "result_plot(out4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
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   "source": [
    "## Total Q signal  (Is Q signal affected?)\n",
    "plt.figure(1)\n",
    "#plt.plot(out1.x, out1[\"detectorI\"]+out1[\"detectorIp\"],label='I signal (S+P)')\n",
    "plt.plot(out4.x, out4[\"detectorQ\"],label='Q signal (S only)')\n",
    "plt.plot(out4.x, out4[\"detectorQ\"]+out4[\"detectorQp\"],label='Q signal (S+P)')\n",
    "plt.xlabel('PRM tuning')\n",
    "plt.ylabel('Signal [a.u.]')\n",
    "plt.legend(loc=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fields and Signals when max 8th order, PRM sweep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
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    "kat5.parse(\"\"\"\n",
    "maxtem 8\n",
    "xaxis* prm phi lin -180 180 200\n",
    "put* prmp phi $x1\n",
    "\"\"\")\n",
    "\n",
    "out5 = kat5.run()\n",
    "\n",
    "result_plot(out5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## With an angular offset (10urad) on PRM\n",
    "### Signals are distorted by HOMs, and the effect from P cav is small"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {},
   "outputs": [
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   "source": [
    "kat6 = base.deepcopy()\n",
    "kat6.parse(\"\"\"\n",
    "attr prm xbeta 10e-6\n",
    "attr prmp xbeta 10e-6\n",
    "maxtem 8\n",
    "xaxis* prm phi lin -180 180 200\n",
    "put* prmp phi $x1\n",
    "\"\"\")\n",
    "\n",
    "out6 = kat6.run()\n",
    "\n",
    "result_plot(out6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {
    "scrolled": true
   },
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   "source": [
    "## Total Q signal  (Is Q signal affected?)\n",
    "plt.figure(1)\n",
    "#plt.plot(out1.x, out1[\"detectorI\"]+out1[\"detectorIp\"],label='I signal (S+P)')\n",
    "plt.plot(out6.x, out6[\"detectorQ\"],label='Q signal (S only)')\n",
    "plt.plot(out6.x, out6[\"detectorQ\"]+out6[\"detectorQp\"],label='Q signal (S+P)')\n",
    "plt.xlabel('PRM tuning')\n",
    "plt.ylabel('Signal [a.u.]')\n",
    "plt.legend(loc=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## With an angular offset (1urad) on ITMs (PIT on IX, YAW on IY\n",
    "### Signals are distorted as much as PRM 10urad, and the effect from the P cavity is still small"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [
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   "source": [
    "kat7 = base.deepcopy()\n",
    "kat7.parse(\"\"\"\n",
    "attr ITMx ybeta 1e-6\n",
    "attr ITMy xbeta 1e-6\n",
    "maxtem 8\n",
    "xaxis* prm phi lin -180 180 200\n",
    "put* prmp phi $x1\n",
    "\"\"\")\n",
    "\n",
    "out7 = kat7.run()\n",
    "\n",
    "result_plot(out7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Angular sweep of PRM\n",
    "### No HOM (up to 1st order)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {},
   "outputs": [],
   "source": [
    "kat8 = base.deepcopy()\n",
    "kat8.parse(\"\"\"\n",
    "pdtype detectorI x-split\n",
    "pdtype detectorQ x-split\n",
    "pdtype detectorIp x-split\n",
    "pdtype detectorQp x-split\n",
    "\n",
    "maxtem 1\n",
    "\n",
    "xaxis* prm xbeta lin -100u 100u 200\n",
    "put* prmp xbeta $x1\n",
    "\"\"\")\n",
    "out8 = kat8.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
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   "source": [
    "result_plot(out8)\n",
    "plt.figure(1)\n",
    "plt.subplot(1,2,1)\n",
    "plt.xlabel('PRM YAW tuning')\n",
    "plt.subplot(1,2,2)\n",
    "plt.xlabel('PRM YAW tuning')\n",
    "plt.figure(2)\n",
    "plt.title('WFS signal (YAW)')\n",
    "plt.xlabel('PRM YAW tuning')\n",
    "plt.figure(3)\n",
    "plt.title('WFS signal (YAW)')\n",
    "plt.xlabel('PRM YAW tuning')"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Angular sweep of PRM\n",
    "### With HOM (up to 8th order)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [],
   "source": [
    "kat9 = base.deepcopy()\n",
    "kat9.parse(\"\"\"\n",
    "pdtype detectorI x-split\n",
    "pdtype detectorQ x-split\n",
    "pdtype detectorIp x-split\n",
    "pdtype detectorQp x-split\n",
    "\n",
    "maxtem 8\n",
    "\n",
    "xaxis* prm xbeta lin -100u 100u 200\n",
    "put* prmp xbeta $x1\n",
    "\"\"\")\n",
    "\n",
    "out9 = kat9.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {},
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   "source": [
    "result_plot(out9)\n",
    "plt.figure(1)\n",
    "plt.subplot(1,2,1)\n",
    "plt.xlabel('PRM YAW tuning')\n",
    "plt.subplot(1,2,2)\n",
    "plt.xlabel('PRM YAW tuning')\n",
    "plt.figure(2)\n",
    "plt.title('WFS signal (YAW)')\n",
    "plt.xlabel('PRM YAW tuning')\n",
    "plt.figure(3)\n",
    "plt.title('WFS signal (YAW)')\n",
    "plt.xlabel('PRM YAW tuning')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def result_plot(out):\n",
    " \t   plt.subplot(1,2,1)\n",
    " \t   plt.semilogy(out.x, out[\"CR0\"],label='CR(S)')\n",
    " \t   plt.semilogy(out.x, out[\"SB1\"],label='SB1 (S)')\n",
    " \t   plt.xlabel('PRM tuning')\n",
    " \t   plt.ylabel('Power')\n",
    " \t   plt.title('S cavity')\n",
    " \t   plt.legend(loc=0)\n",
    " \t   plt.ylim(1e-2,1e2)\n",
    "#\n",
    " \t   plt.subplot(1,2,2)\n",
    " \t   plt.semilogy(out.x, out[\"CR0p\"],label='CR(P)')\n",
    " \t   plt.semilogy(out.x, out[\"SB1p\"],label='SB1(P)')\n",
    " \t   plt.xlabel('PRM tuning')\n",
    " \t   plt.title('P cavity')\n",
    " \t   plt.legend(loc=0)\n",
    "\t   plt.ylim(1e-2,1e2)\n",
    "#\n",
    " \t   plt.figure(2)\n",
    " \t   plt.plot(out.x, out[\"detectorI\"],label='I signal (S)')\n",
    " \t   plt.plot(out.x, out[\"detectorQ\"],label='Q signal (S)')\n",
    " \t   plt.xlabel('PRM tuning')\n",
    " \t   plt.ylabel('Signal [a.u.]')\n",
    " \t   plt.legend(loc=0)\n",
    "#\n",
    " \t   plt.figure(3)\n",
    " \t   plt.plot(out.x, out[\"detectorIp\"],label='I signal (P)')\n",
    " \t   plt.plot(out.x, out[\"detectorQp\"],label='Q signal (P)')\n",
    " \t   plt.xlabel('PRM tuning')\n",
    " \t   plt.ylabel('Signal [a.u.]')\n",
    " \t   plt.legend(loc=0)\n",
    "\n",
    "\n",
    "def beam_plot(out):\n",
    "    \t   X = out.x\n",
    "    \t   Y = out.y\n",
    "    \t   X, Y = np.meshgrid(X, Y)\n",
    "    \t   Z = out[\"beam1\"]\n",
    "    \t   fig1, ax2 = plt.subplots(constrained_layout=True)\n",
    "    \t   CS = ax2.contourf(X, Y, Z, 50, cmap=plt.cm.bone)\n",
    "    \t   ax2.set_aspect('equal', 'datalim')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00017444444444444446"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.01*3.14/180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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