{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "db0337e1-fda0-4de4-ab5e-eb20d8d319de",
   "metadata": {},
   "source": [
    "# Beam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8df40c47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beam \n",
      "  .id: my beam\n",
      "  .matrix:\n",
      "[[0.000000e+00+0.j 6.123234e-17+0.j]\n",
      " [6.123234e-17+0.j 1.000000e+00+0.j]]\n",
      "  .jones_vector:\n",
      "[[nan+nanj]\n",
      " [nan+nanj]]\n",
      "  .profile: g\n",
      "  .fwhm (mm): Var.value = 0.21, .min = 0.0, .max = 1.0, .fit: True, .id: beam fwhm\n",
      "  .Polarization(): 1.0\n",
      "  .Coherence(): nan\n",
      "  .PhaseDifference() [sigma - pi](rad): nan\n",
      "\n",
      "[[0.000000e+00+0.j 6.123234e-17+0.j]\n",
      " [6.123234e-17+0.j 1.000000e+00+0.j]]\n",
      "\n",
      "[[nan+nanj]\n",
      " [nan+nanj]]\n",
      "\n",
      "(nan+nanj)\n"
     ]
    }
   ],
   "source": [
    "import nexus as nx\n",
    "import numpy as np\n",
    "\n",
    "# set beam along pi polarization via initialization parameters\n",
    "beam = nx.Beam(polarization = 1,\n",
    "               mixing_angle = 0,\n",
    "               canting_angle = 90,\n",
    "               id=\"my beam\",\n",
    "               profile = \"g\",   # Gaussian beam profile\n",
    "               fwhm = nx.Var(0.21, min=0, max=1, fit =True, id=\"beam fwhm\")\n",
    "               )\n",
    "\n",
    "print(beam)\n",
    "\n",
    "print(beam.matrix)\n",
    "print(\"\")\n",
    "\n",
    "print(beam.jones_vector)\n",
    "print(\"\")\n",
    "\n",
    "print(beam.ComplexCoherence())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e5d389b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beam \n",
      "  .id: new beam\n",
      "  .matrix:\n",
      "[[ 0.5+0.j  -0. -0.5j]\n",
      " [ 0. +0.5j  0.5+0.j ]]\n",
      "  .jones_vector:\n",
      "[[0.70710678+0.j        ]\n",
      " [0.        +0.70710678j]]\n",
      "  .profile: g\n",
      "  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM\n",
      "  .Polarization(): 1.0\n",
      "  .Coherence(): 0.9999999999999998\n",
      "  .PhaseDifference() [sigma - pi](rad): -1.5707963267948966\n",
      "\n",
      "(-0-0.9999999999999998j)\n"
     ]
    }
   ],
   "source": [
    "beam = nx.Beam(id=\"new beam\")\n",
    "beam.CircularLeft()\n",
    "\n",
    "print(beam)\n",
    "\n",
    "print(beam.ComplexCoherence())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7c24b797",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beam \n",
      "  .id: new beam\n",
      "  .matrix:\n",
      "[[1.+0.j 0.+0.j]\n",
      " [0.+0.j 1.+0.j]]\n",
      "  .jones_vector:\n",
      "[[nan+nanj]\n",
      " [nan+nanj]]\n",
      "  .profile: g\n",
      "  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM\n",
      "  .Polarization(): 0.0\n",
      "  .Coherence(): 0.0\n",
      "  .PhaseDifference() [sigma - pi](rad): 0.0\n",
      "\n",
      "0j\n"
     ]
    }
   ],
   "source": [
    "# set coherency matrix for unpolarized beam\n",
    "beam.SetCoherencyMatrix(np.array([[1,0], [0, 1]], dtype=complex))\n",
    "\n",
    "print(beam)\n",
    "\n",
    "print(beam.ComplexCoherence())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e73cc311-d054-4f2a-a6bc-0381dd279b82",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beam \n",
      "  .id: new beam\n",
      "  .matrix:\n",
      "[[1.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j]]\n",
      "  .jones_vector:\n",
      "[[1.+0.j]\n",
      " [0.+0.j]]\n",
      "  .profile: g\n",
      "  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM\n",
      "  .Polarization(): 1.0\n",
      "  .Coherence(): nan\n",
      "  .PhaseDifference() [sigma - pi](rad): nan\n",
      "\n",
      "(nan+nanj)\n"
     ]
    }
   ],
   "source": [
    "# set Jones vector for a fully sigma polarized beam\n",
    "beam.SetJonesVector(np.array([1,0], dtype=complex))\n",
    "\n",
    "print(beam)\n",
    "\n",
    "print(beam.ComplexCoherence())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1dc5eddf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beam \n",
      "  .id: new beam\n",
      "  .matrix:\n",
      "[[0.5+0.j 0.5+0.j]\n",
      " [0.5+0.j 0.5+0.j]]\n",
      "  .jones_vector:\n",
      "[[0.70710678+0.j]\n",
      " [0.70710678+0.j]]\n",
      "  .profile: g\n",
      "  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM\n",
      "  .Polarization(): 1.0\n",
      "  .Coherence(): 1.0\n",
      "  .PhaseDifference() [sigma - pi](rad): 0.0\n",
      "\n",
      "(1+0j)\n"
     ]
    }
   ],
   "source": [
    "beam.LinearSigma()\n",
    "\n",
    "beam.Rotate(45)\n",
    "\n",
    "print(beam)\n",
    "\n",
    "print(beam.ComplexCoherence())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d67db1ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beam \n",
      "  .id: new beam\n",
      "  .matrix:\n",
      "[[ 0.5+0.j  -0. -0.5j]\n",
      " [ 0. +0.5j  0.5+0.j ]]\n",
      "  .jones_vector:\n",
      "[[0.70710678+0.j        ]\n",
      " [0.        +0.70710678j]]\n",
      "  .profile: g\n",
      "  .fwhm (mm): Var.value = 0.0, .min = 0.0, .max = inf, .fit: False, .id: FWHM\n",
      "  .Polarization(): 1.0\n",
      "  .Coherence(): 0.9999999999999998\n",
      "  .PhaseDifference() [sigma - pi](rad): -1.5707963267948966\n",
      "\n",
      "1.0\n",
      "0.9999999999999998\n",
      "-1.5707963267948966\n",
      "(-0-0.9999999999999998j)\n"
     ]
    }
   ],
   "source": [
    "beam.CircularLeft()\n",
    "\n",
    "print(beam)\n",
    "\n",
    "print(beam.Polarization())\n",
    "\n",
    "print(beam.Coherence())\n",
    "\n",
    "print(beam.PhaseDifference())\n",
    "\n",
    "print(beam.ComplexCoherence())"
   ]
  }
 ],
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