Fig2 - purcell_factor.ipynb

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   "source": [
    "# Code for Fig. 2"
   ]
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   "source": [
    "%load_ext autoreload\n",
    "%autoreload 1\n",
    "%aimport general_functions"
   ]
  },
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm.auto import tqdm\n",
    "from joblib import Parallel, delayed\n",
    "\n",
    "from general_functions import (compute_energies, purcell_factor, complete_dynamics, g0_fun)"
   ]
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   "source": [
    "The coupling between the impurity atomns and the lattice dipoles is given by $H=H_a+H_{am}+H_m$, where $H_m$ is the lattice Hamiltonian given in the previous notebook, and \n",
    "\n",
    "\\begin{equation}\n",
    "    \\frac{H_a}{\\hbar} = \\left(\\omega_a-i\\frac{\\Gamma_a}{2}\\right)\\sigma_{ee}^a,\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "    \\frac{H_{am}}{\\hbar} = \\sum_{i=1}^{N}\\left(J_{ai} - i\\frac{\\sqrt{\\Gamma_0\\Gamma_a}}{2}\\right)\\sigma_{eg}^a\\sigma_{ge}^i + (i\\leftrightarrow a).\n",
    "\\end{equation}"
   ]
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   "source": [
    "## Semi-analytical Purcell factor (a-b, solid lines)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "There is a semi-analytical method to compute the Purcell factor, denoting the coupling between the impurity atom and the lattice. Under the Markov approximation\n",
    "\\begin{equation}\n",
    "    P_a = \\frac{\\frac{9d^2}{2k_0^2}\\Im\\left(\\iint _{|\\mathbf{k}|> k_0}d^2\\mathbf{k}\\frac{\\hat{\\boldsymbol{\\wp}}^*_a \\boldsymbol{\\alpha}_\\mathbf{k}(\\mathbf{r}_a)\\otimes \\boldsymbol{\\beta}_\\mathbf{k}(\\mathbf{r}_a)\\hat{\\boldsymbol{\\wp}}_a}{(\\omega_\\mathbf{k}-\\omega_\\mathbf{k})/\\Gamma_0}\\right)}{1 + \\frac{9d^2}{2k_0^2}\\Im\\left(\\iint _{|\\mathbf{k}|\\leq k_0}d^2\\mathbf{k}\\frac{\\hat{\\boldsymbol{\\wp}}^*_a \\boldsymbol{\\alpha}_\\mathbf{k}(\\mathbf{r}_a)\\otimes \\boldsymbol{\\beta}_\\mathbf{k}(\\mathbf{r}_a)\\hat{\\boldsymbol{\\wp}}_a}{(\\omega_\\mathbf{k}-\\omega_\\mathbf{k})/\\Gamma_0}\\right)},\n",
    "\\end{equation}\n",
    "with the field eigenmodes evaluated at the impurity atom position\n",
    "\\begin{equation}\n",
    "    \\boldsymbol{\\alpha}_\\mathbf{k}(\\mathbf{r}) = \\sum_{j=1}^N\\mathbf{G}_0(\\mathbf{r}, \\mathbf{r}_j, \\omega_0)\\cdot \\hat{\\boldsymbol{\\wp}}_0e^{i\\mathbf{r}_j\\cdot\\mathbf{k}},\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "    \\boldsymbol{\\beta}_\\mathbf{k}(\\mathbf{r}) = \\sum_{j=1}^N\\hat{\\boldsymbol{\\wp}}_0^*\\mathbf{G}_0(\\mathbf{r}_j, \\mathbf{r}, \\omega_0)\\cdot e^{-i\\mathbf{r}_j\\cdot\\mathbf{k}}.\n",
    "\\end{equation}\n",
    "Since we are working in the single exitation manifold, and assuming that initiallya and excitated impurity atom, the wavefunction at any time reads\n",
    "\\begin{align}\n",
    "|\\Psi(t)\\rangle=\\left(C_a(t)\\sigma^a_{eg}+\\sum_{j=1}^N C_{\\mathbf{r}_j}(t)\\sigma_{eg}^j\\right)|\\mathrm{vac}\\rangle,\n",
    "\\end{align}\n",
    "where the complex coefficients are obtained by solving the time dependent Schrödinger equation $i\\hbar\\partial_t|\\Psi(t)\\rangle = H |\\Psi(t)\\rangle$. Since the Hamiltonian is time indiependet, the dynamics of the system reduce to computing the matrix exponential $|\\Psi(t)\\rangle = e^{-i\\hbar H t}|\\Psi(0)\\rangle$."
   ]
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    "pol_lat = np.array([[0, 1, 0]]).T  # Lattice polarization\n",
    "pol_emi = np.array([[1, 1, 0]]).T / np.sqrt(2)  # Impurity polarization\n",
    "\n",
    "d = 1  # Lattice constant\n",
    "lambda0 = d / 0.3  # Wave-lenght of transition\n",
    "k0 = 2 * np.pi / lambda0\n",
    "\n",
    "aho = 0.1 * d  # Cut-off in momentums\n",
    "\n",
    "n = 2 ** 9 + 1  # Number of sites for the reciprocal lattice (total sites is N = n²)\n",
    "nmax = 9  # Number of reciprocal lattice in the summatory\n",
    "\n",
    "# Reciprocal lattice vectors\n",
    "b1 = 2 * np.pi / d * np.array([1, 0])\n",
    "b2 = 2 * np.pi / d * np.array([0, 1])\n",
    "A = d ** 2\n",
    "\n",
    "G0 = g0_fun(k0, aho)  # Renormalizated Green function in k = 0\n",
    "\n",
    "k_x = np.linspace(-np.pi, np.pi, n) / d\n",
    "k_X, k_Y = np.meshgrid(k_x, k_x)\n",
    "\n",
    "k = np.vstack((k_X.flatten(), k_Y.flatten())).T\n",
    "\n",
    "x = np.arange(0, n) - n / 2 + d / 2\n",
    "y = np.arange(0, n) - n / 2 + d / 2\n",
    "x, y = np.meshgrid(x, y)\n",
    "z = np.zeros((n, n))\n",
    "r_lat = [x, y, z]"
   ]
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   "source": [
    "# Compute the eigenenergies in momentum space\n",
    "J, Gamma = compute_energies(b1, b2, A, nmax, k0, aho, k, G0=G0, polarizations=[pol_lat])\n",
    "omega_k = (J - 0.5j * Gamma).reshape(n, n)\n",
    "\n",
    "# Energy in the X-point X=(π/d, 0)\n",
    "omega_q = np.real(omega_k).reshape(n, n)[n // 2, -1]  # Note that the first index is for y, and the second for x"
   ]
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"
    }
   },
   "cell_type": "markdown",
   "id": "9bdd621d-cd2e-4c11-9832-f88b91a53c39",
   "metadata": {},
   "source": [
    "We study the Purcell factor as the impurity attom moves in the $z$ axis. The code is written for the situation in which the impurity in on top of a dipole of the array (left figure), where $r_a = (0, 0, z)$. For the situation in which the impurity atom in in the center of a plaquette (right figure) just change the impurity position to $r_a=(0.5d, 0.5d, z)$.\n",
    "\n",
    "![impurity_location.png](attachment:a452ec47-f268-444a-b8a9-ed3598d810d0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "96faa08f-8275-4c28-bd94-c72c556ea6f2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-03T14:43:08.716806Z",
     "iopub.status.busy": "2022-02-03T14:43:08.716806Z",
     "iopub.status.idle": "2022-02-03T14:43:08.725803Z",
     "shell.execute_reply": "2022-02-03T14:43:08.725803Z",
     "shell.execute_reply.started": "2022-02-03T14:43:08.716806Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "n_pos = 100  # Number of points to evaluate the Purcell\n",
    "\n",
    "x_vector = np.ones(n_pos) * 0 * d\n",
    "y_vector = np.ones(n_pos) * 0 * d\n",
    "z_vector = np.linspace(0.1, 1.5, n_pos) * d\n",
    "\n",
    "r_emi_vector = np.array([x_vector, y_vector, z_vector])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "06527672-820a-4c80-a699-3aed59b274b7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-03T14:43:09.086727Z",
     "iopub.status.busy": "2022-02-03T14:43:09.086727Z",
     "iopub.status.idle": "2022-02-03T14:43:48.401396Z",
     "shell.execute_reply": "2022-02-03T14:43:48.401396Z",
     "shell.execute_reply.started": "2022-02-03T14:43:09.086727Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5d4cf668ce0149b8a2c68d2eca73f6a9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Computing Purcell:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbar = tqdm(range(n_pos), desc='Computing Purcell')  # Progress bar\n",
    "# Compute the Purcell factor in parallel using all the cores of the CPU\n",
    "results = Parallel(n_jobs=-1, backend='multiprocessing')(\n",
    "    delayed(purcell_factor)(r_lat, r_emi_vector[:, j], [k_X, k_Y],\n",
    "                            omega_k, omega_q, k0, pol_lat, pol_emi) for j in pbar)\n",
    "\n",
    "results = np.array(results)\n",
    "optical_depth = results[:, 1] / results[:, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "816355bf-2a24-4ea5-a438-33c6666cdeab",
   "metadata": {},
   "source": [
    "## Numerical Purcell factor (a-b, dashed lines)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9973d1d2-8b93-4e66-a94c-31ce87b99cb6",
   "metadata": {},
   "source": [
    "Another possibility is to compute the Purcell factor via numericall methods. For that purpose we need to compute the dynamics of the system, and then compute the expression\n",
    "\\begin{align}\n",
    "    P(t)\\approx \\frac{\\mathcal{P}_L(t) + L_b(t)}{L_T(t) - L_b(t)},\n",
    "\\end{align}\n",
    "where the following quantities have been defined. The population of the lattice $\\mathcal{P}_L(t)=\\sum_j|C_{\\mathbf{r}_j}(t)|^2$, the cumulative loss in population due to the adiabatic absorbing boundaries \n",
    "\\begin{align}\n",
    "    L_b(t)\\approx \\sum_{|\\mathbf{r}_j| \\geq r_{\\textrm{min}}}\\int_0^t dt' [\\Gamma_0(\\mathbf{r}_j) - \\Gamma_0]|C_{\\mathbf{r}_j(t')}|^2\\,.\n",
    "\\end{align}\n",
    "Finally, the total free space decay in the system is computed as\n",
    "\\begin{equation}\n",
    "    L_T(t) =\\sum_\\alpha L_\\alpha (t)=\\sum_{\\alpha} \\int _0^t dt'\\gamma_\\alpha |\\langle\\phi_\\alpha|\\Psi(t')\\rangle|^2.\n",
    "\\end{equation}\n",
    "The value $P(t)$ converges to a finite value, which is what we define as the numerical Purcell factor $P_n = P(t\\rightarrow \\infty)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "57c353c9-e8ef-475c-a381-61005b252f11",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-03T15:36:47.433580Z",
     "iopub.status.busy": "2022-02-03T15:36:47.433580Z",
     "iopub.status.idle": "2022-02-03T15:36:47.453581Z",
     "shell.execute_reply": "2022-02-03T15:36:47.453581Z",
     "shell.execute_reply.started": "2022-02-03T15:36:47.433580Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "pol_lat = np.array([[0, 1, 0]]).T  # Lattice polarization\n",
    "pol_emi = [np.array([[1, 1, 0]]).T / np.sqrt(2)]  # Impurity polarization\n",
    "\n",
    "border = 15  # Distance from the borer of the array where the absorving boundary starts\n",
    "max_gamma = 15  # Maximum extra decay rate at the borders of the lattice\n",
    "\n",
    "d = 1  # Lattice constant\n",
    "lambda0 = d / 0.3  # Wave-lenght of transition\n",
    "k0 = 2 * np.pi / lambda0\n",
    "\n",
    "# If N_x is odd, there is a lattice atom at r=(0, 0, 0)\n",
    "N_x = 51  # Number of sites in the lattice in each direction (total number = N_x * N_y)\n",
    "N_y = N_x\n",
    "x_pos = np.arange(0, N_x) - N_x / 2 + d / 2\n",
    "y_pos = np.arange(0, N_y) - N_y / 2 + d / 2\n",
    "x_pos, y_pos = np.meshgrid(x_pos, y_pos)\n",
    "x_pos = x_pos.flatten()\n",
    "y_pos = y_pos.flatten()\n",
    "z_pos = np.zeros(len(x_pos))\n",
    "r_pos = [x_pos, y_pos, z_pos]\n",
    "\n",
    "gamma_emi = 0.002  # Free space decay rate for emitter\n",
    "\n",
    "# Transition energy for emitter\n",
    "omega_emi = -0.999  # (ω_X - ω_0)/Γ_0 for  d / lambda_0 = 0.3\n",
    "# omega_emi = -15.368  # (ω_X - ω_0)/Γ_0 for d / lambda_0 = 0.1\n",
    "\n",
    "dt = 2e-3 / gamma_emi  # Time step\n",
    "tf = dt * 2 ** 12  # Total time of simulation\n",
    "\n",
    "# Initial wavefunction, with the excitation in the impurity\n",
    "psi0 = np.zeros(len(x_pos) + 1)\n",
    "psi0[-1] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "db26a146-bdad-4cd8-aa7e-7fea978507a0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-03T15:45:27.696700Z",
     "iopub.status.busy": "2022-02-03T15:45:27.696700Z",
     "iopub.status.idle": "2022-02-03T16:35:42.352311Z",
     "shell.execute_reply": "2022-02-03T16:35:42.352311Z",
     "shell.execute_reply.started": "2022-02-03T15:45:27.696700Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "08e986a7173e4dadbebbfa50941bf488",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Computing dynamics:   0%|          | 0/106 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_z = 106  # Number of points to evaluate the Purcell\n",
    "z_emitter = np.linspace(0.1, 1.5, n_z) * d\n",
    "\n",
    "purcell_numerical = np.zeros(n_z)\n",
    "real_space_emission = np.zeros((n_z, N_y, N_x))\n",
    "\n",
    "pbar = tqdm(total=n_z, desc='Computing dynamics')\n",
    "for i in range(n_z):\n",
    "    emitter = [[0, 0, z_emitter[i]]]\n",
    "    \n",
    "    # Compute the dynamics of the system and the numerical Purcell factor\n",
    "    results = complete_dynamics(r_pos, k0, pol_lat, dt, tf, psi0, N_x, N_y, emitter, pol_emi, gamma_emi,\n",
    "                      omega_emi, border, max_gamma=max_gamma)\n",
    "    \n",
    "    purcell_numerical[i] = results['Q_n'][-1]\n",
    "    \n",
    "    # Save the real space emission for the time in wich the lattice is maximally excited \n",
    "    population = np.abs(results['psi'][:, :-1].reshape((-1, N_y, N_x))) ** 2\n",
    "    index_max = np.argmax(np.sum(population, axis=(1, 2)))\n",
    "    real_space_emission[i] = population[index_max]\n",
    "    \n",
    "    pbar.update()    \n",
    "pbar.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "af240d59-1d70-4130-9a15-09531b1928f5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-03T16:35:42.353311Z",
     "iopub.status.busy": "2022-02-03T16:35:42.353311Z",
     "iopub.status.idle": "2022-02-03T16:35:42.635314Z",
     "shell.execute_reply": "2022-02-03T16:35:42.635314Z",
     "shell.execute_reply.started": "2022-02-03T16:35:42.353311Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(z_vector, optical_depth, 'b', label='semi-analytical')\n",
    "ax.plot(z_emitter, purcell_numerical, 'b--', label='numerical')\n",
    "ax.legend()\n",
    "\n",
    "ax.set_xlim(min(z_emitter), max(z_emitter))\n",
    "\n",
    "ax.set_yscale('log')\n",
    "\n",
    "ax.set_xlabel(r'z/d')\n",
    "ax.set_ylabel(r'$P_n$');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4d3dd61c-01d4-408f-a5f8-6ce1da6c6d0a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-03T16:38:51.234019Z",
     "iopub.status.busy": "2022-02-03T16:38:51.234019Z",
     "iopub.status.idle": "2022-02-03T16:38:51.314018Z",
     "shell.execute_reply": "2022-02-03T16:38:51.314018Z",
     "shell.execute_reply.started": "2022-02-03T16:38:51.234019Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of z / d = 0.300\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_target = 0.3\n",
    "index = np.argmin(np.abs(z_target - z_emitter))\n",
    "print('The value of z / d = {:.3f}'.format(z_emitter[index]))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(real_space_emission[index], origin='lower', aspect='equal', cmap='jet',\n",
    "          extent=[min(x_pos), max(x_pos), min(y_pos), max(y_pos)], vmin=0)\n",
    "\n",
    "ax.set_xlabel('x/d')\n",
    "ax.set_ylabel('y/d');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a6c4220-d943-4961-8a9d-31bd70af8e88",
   "metadata": {},
   "source": [
    "## Chirality (c-d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ff0412b9-3ff0-4487-862f-fee22aad5dba",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-04T10:14:36.754984Z",
     "iopub.status.busy": "2022-02-04T10:14:36.754406Z",
     "iopub.status.idle": "2022-02-04T10:14:36.761232Z",
     "shell.execute_reply": "2022-02-04T10:14:36.760903Z",
     "shell.execute_reply.started": "2022-02-04T10:14:36.754914Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "pol_lat = np.array([[0, 1, 0]]).T\n",
    "\n",
    "border = 15\n",
    "max_gamma = 15\n",
    "r_circles = np.arange(border, border + 5)  # Concentric circles to compute the directionality\n",
    "\n",
    "d = 1\n",
    "lambda0 = d / 0.3\n",
    "k0 = 2 * np.pi / lambda0\n",
    "\n",
    "N_x = 61\n",
    "N_y = N_x\n",
    "x_pos = np.arange(0, N_x) - N_x / 2 + d / 2\n",
    "y_pos = np.arange(0, N_y) - N_y / 2 + d / 2\n",
    "x_pos, y_pos = np.meshgrid(x_pos, y_pos)\n",
    "x_pos = x_pos.flatten()\n",
    "y_pos = y_pos.flatten()\n",
    "z_pos = np.zeros(len(x_pos))\n",
    "r_pos = [x_pos, y_pos, z_pos]\n",
    "\n",
    "gamma_emi = 0.002\n",
    "omega_emi = -0.999  # For d / lambda_0 = 0.3\n",
    "# omega_emi = -15.368  # For d / lambda_0 = 0.1\n",
    "\n",
    "emitter = [[0, 0, 0.3]]\n",
    "\n",
    "dt = 2e-3 / gamma_emi\n",
    "tf = dt * 2 ** 10\n",
    "\n",
    "psi0 = np.zeros(len(x_pos) + 1)\n",
    "psi0[-1] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e78455df-8901-4ca9-b91a-4c88ac27c93f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-04T10:14:59.820988Z",
     "iopub.status.busy": "2022-02-04T10:14:59.820410Z",
     "iopub.status.idle": "2022-02-04T12:19:12.111179Z",
     "shell.execute_reply": "2022-02-04T12:19:12.110836Z",
     "shell.execute_reply.started": "2022-02-04T10:14:59.820916Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cf968e5aa8434ba8887a99eb2f7915da",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Computing dynamics:   0%|          | 0/101 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_theta = 101\n",
    "theta = np.linspace(0, 2 * np.pi, n_theta) * d\n",
    "\n",
    "chi_1D = np.zeros(n_theta)\n",
    "real_space_emission = np.zeros((n_theta, N_y, N_x))\n",
    "\n",
    "pbar = tqdm(total=n_theta, desc='Computing dynamics')\n",
    "for i in range(n_theta):    \n",
    "    pol_emi = [np.array([[np.cos(theta[i]), np.sin(theta[i]), 0]]).T]\n",
    "    \n",
    "    # Fix the angle of reference for the directionality to π/4\n",
    "    results = complete_dynamics(r_pos, k0, pol_lat, dt, tf, psi0, N_x, N_y, emitter,\n",
    "                                pol_emi, gamma_emi, omega_emi, border, max_gamma=max_gamma, \n",
    "                                theta_max=np.pi / 4, r_circles=r_circles)\n",
    "    \n",
    "    chi_1D[i] = np.average(results['chirality'])\n",
    "    \n",
    "    population = np.abs(results['psi'][:, :-1].reshape((-1, N_y, N_x))) ** 2\n",
    "    index_max = np.argmax(np.sum(population, axis=(1, 2)))\n",
    "    real_space_emission[i] = population[index_max]\n",
    "    \n",
    "    pbar.update()    \n",
    "pbar.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "708b4f01-3427-4615-8e9a-bd0461d22dd5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-04T12:19:12.131972Z",
     "iopub.status.busy": "2022-02-04T12:19:12.131843Z",
     "iopub.status.idle": "2022-02-04T12:19:12.356722Z",
     "shell.execute_reply": "2022-02-04T12:19:12.356281Z",
     "shell.execute_reply.started": "2022-02-04T12:19:12.131945Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(theta / np.pi, chi_1D)\n",
    "\n",
    "ax.set_xlim(0, 2)\n",
    "ax.set_ylim(-1, 1)\n",
    "\n",
    "ax.set_xlabel(r'$\\theta / \\pi$')\n",
    "ax.set_ylabel(r'$\\chi_\\mathrm{1D}$');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6f753708-9cab-4c77-8fc9-58d2e49cbf8f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-05T11:53:28.085426Z",
     "iopub.status.busy": "2022-02-05T11:53:28.085153Z",
     "iopub.status.idle": "2022-02-05T11:53:28.150233Z",
     "shell.execute_reply": "2022-02-05T11:53:28.149913Z",
     "shell.execute_reply.started": "2022-02-05T11:53:28.085394Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of theta / pi = 1.000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta_target = np.pi\n",
    "index = np.argmin(np.abs(theta_target - theta))\n",
    "print('The value of theta / pi = {:.3f}'.format(theta[index] / np.pi))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.imshow(real_space_emission[index], origin='lower', aspect='equal', cmap='jet',\n",
    "          extent=[min(x_pos), max(x_pos), min(y_pos), max(y_pos)], vmin=0)\n",
    "\n",
    "ax.set_xlabel('x/d')\n",
    "ax.set_ylabel('y/d');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}