{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[{"file_id":"1zTtXm1vTteOqb8r50tO8VM0fN7EhX7H_","timestamp":1694342620432},{"file_id":"1JrJRijkDwZ11GZ0Mg68TmlwUZKdbbDjS","timestamp":1693486578147}],"toc_visible":true,"authorship_tag":"ABX9TyPOVgUuCE/w/YT9hg6MqEKI"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["<a href=\"https://colab.research.google.com/github/IrisFDTD/OPTICS-UNIZAR/blob/main/Topic_1/chapter1_coherence_and_interferences.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"],"metadata":{"id":"JAAnG_Wf1ALR"}},{"cell_type":"markdown","source":["<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"><img alt=\"Licencia Creative Commons\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\"></span> The following notes written by  <span xmlns:cc=\"http://creativecommons.org/ns#\" property=\"cc:attributionName\">Sergio Gutiérrez Rodrigo (<sergut@unizar.es>) </span>. Distributed under  <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\">License Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional</a>\n","\n"],"metadata":{"id":"tYZjdh8TvE7-"}},{"cell_type":"markdown","source":["```\n","Departamento de Física Aplicada\n","Universidad de Zaragoza\n","Instituto de Nanociencia y Materiales de Aragón (INMA)\n","C/ Pedro Cerbuna, 12, 50009, Zaragoza, España\n","```\n","\n","\n","\n","\n"],"metadata":{"id":"j2H5UHGe1Uf8"}},{"cell_type":"markdown","source":["---\n","# **Óptica - Tema 1 -Coherence and interference phenomena**\n","\n","---"],"metadata":{"id":"D7vYGeB21ZQU"}},{"cell_type":"markdown","source":["# Coherencia"],"metadata":{"id":"_m0cuMqAE0Wr"}},{"cell_type":"markdown","source":["## Definición de ondas planas y pulsos (gaussiano, sinc)"],"metadata":{"id":"EKXxFj93IlzT"}},{"cell_type":"code","source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","def onda_plana(t, A, σ, ω_0, φ):\n","    \"\"\"\n","    Genera una onda plana dada la frecuencia central y fase.\n","    Las unidades han de ser consistentes entre t, σ y ω_0.\n","    El pulso está normalizado.\n","\n","    La onda plana se caracteriza por un término exponencial complejo que depende de la frecuencia central de la onda\n","    y la fase de la envolvente de la onda portadora.\n","\n","    E(t) = E * exp(i * ω_0 * t) * exp(i * φ(t)) = A * exp(-t² / 2*σ) * exp(i * ( ω_0 * t + φ(t) ) )\n","\n","    Argumentos:\n","        t (float): vector de tiempos\n","        A (float): amplitud del pulso\n","        σ (float): anchura del pulso\n","        ω_0 (float): frecuencia central (radianes / unidad de tiempo)\n","        φ (float): fase de la envolvente de la onda portadora (rad)\n","\n","    Devuelve:\n","        E_pulso (float): forma del pulso gaussiano en el tiempo especificado\n","    \"\"\"\n","\n","    return A * np.exp(1j * ( ω_0 * t + φ ))\n","\n","def pulso_gaussiano(t, A, σ, ω_0, φ):\n","    \"\"\"\n","    Genera un pulso gaussiano dada su duración, frecuencia central y fase.\n","    Las unidades han de ser consistentes entre t, σ y ω_0.\n","    El pulso está normalizado.\n","\n","    Un pulso gaussiano viene caracterizado por una envolvente en forma de gaussiana de expresión:\n","\n","    E_envolvente = A * exp(-t² / 2*σ)\n","\n","    Donde σ es la duración temporal del pulso, que está relacionada con el ancho de banda por la expresión:\n","\n","    σ = FWHM / (2 * √log(2))\n","\n","    FHWM es la anchura a media altura (full width half maximum).\n","\n","    La envolvente viene modulada por un término exponencial complejo que depende de la frecuencia central de la onda,\n","    de manera que el pulso vendrá dado por el producto de la envolvente y esta exponencial, además del producto\n","    con la exponencial compleja que lleva la fase de la envolvente de la onda portadora.\n","\n","    E(t) = E_envolvente * exp(i * ω_0 * t) * exp(i * φ(t)) = A * exp(-t² / 2*σ) * exp(i * ( ω_0 * t + φ(t) ) )\n","\n","    Argumentos:\n","        t (float): vector de tiempos\n","        A (float): amplitud del pulso\n","        σ (float): anchura del pulso\n","        ω_0 (float): frecuencia central (radianes / unidad de tiempo)\n","        φ (float): fase de la envolvente de la onda portadora (rad)\n","\n","    Devuelve:\n","        E_pulso (float): forma del pulso gaussiano en el tiempo especificado\n","    \"\"\"\n","\n","    return A * np.exp(-t*t / (2 * σ)) * np.exp(1j * ( ω_0 * t + φ ))\n","\n","def pulso_sinc(t, A, σ, ω_0, φ):\n","    \"\"\"\n","    Genera un pulso tipo sinc() gaussiano dada su duración, frecuencia central y fase.\n","    Las unidades han de ser consistentes entre t, σ y ω_0.\n","    El pulso está normalizado.\n","\n","    Un pulso gaussiano viene caracterizado por una envolvente en forma de gaussiana de expresión:\n","\n","    E_envolvente = A * sinc(t /*σ)\n","\n","\n","    La envolvente viene modulada por un término exponencial complejo que depende de la frecuencia central de la onda,\n","    de manera que el pulso vendrá dado por el producto de la envolvente y esta exponencial, además del producto\n","    con la exponencial compleja que lleva la fase de la envolvente de la onda portadora.\n","\n","    E(t) = E_envolvente * exp(i * ω_0 * t) * exp(i * φ(t)) =A * sinc(t /σ) * exp(i * ( ω_0 * t + φ(t) ) )\n","\n","    Los primeros mínimos se encuentran en +-pi*σ\n","\n","    Argumentos:\n","        t (float): vector de tiempos\n","        A (float): amplitud del pulso\n","        σ (float): anchura del pulso\n","        ω_0 (float): frecuencia central (radianes / unidad de tiempo)\n","        φ (float): fase de la envolvente de la onda portadora (rad)\n","\n","    Devuelve:\n","        E_pulso (float): forma del pulso gaussiano en el tiempo especificado\n","    \"\"\"\n","\n","    return  A*np.sinc(t / (np.pi* σ))*np.exp(1j * ( ω_0 * t + φ )) #np.sinc(x) = np.sin(pi*x)/(pi*x)) https://numpy.org/doc/stable/reference/generated/numpy.sinc.html"],"metadata":{"id":"SIBMiOXCE2at"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Parámetros"],"metadata":{"id":"aX-287CO6Vzc"}},{"cell_type":"code","source":["c=299792458.0     #m/s\n","pasos_temporales = 4000\n","\n","# -- Parámetros del pulso --\n","A = 1 # Amplitud del pulso\n","λ_0 = 100.55 # Longitud de onda de ejemplo (en micrómetros)\n","ω_0 = 2 * np.pi * c * 1e-12 / (λ_0 * 1e-6) # Frecuencia angular del pulso (rad / ps)\n","σ = 0.2 # Duración del pulso (ps)\n","t, Δt = np.linspace(0, 200*σ, num=pasos_temporales, retstep=True) # Vector de tiempos (centrado en cero, ps). Guardamos la separación entre datos\n","to=np.max(t)/2\n","print(\"Δt (ps)=\",Δt)\n","fs=1/Δt\n","print(\"fs=1/Δt sampling rate (1/ps)=\",fs)\n"],"metadata":{"id":"5G8qOMEg5281","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1702312331399,"user_tz":-60,"elapsed":4,"user":{"displayName":"SERGIO GUTIERREZ RODRIGO","userId":"07959720391705098820"}},"outputId":"d112615a-933d-427d-9641-c66435e2d9fe"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Δt (ps)= 0.010002500625156289\n","fs=1/Δt sampling rate (1/ps)= 99.97500000000001\n"]}]},{"cell_type":"markdown","source":["## Cálculo del pulso"],"metadata":{"id":"cMS7UyuXIVPV"}},{"cell_type":"code","source":["tipo_onda='gaussiana'\n","if(tipo_onda=='onda plana'):\n","  # Fase\n","  φ_0 =  0* np.ones(pasos_temporales) # Fase (constante en este caso)\n","  #φ_0 = (t-to)**2 # Variable con t\n","  onda =onda_plana(t-to, A, σ, ω_0, φ_0)\n","\n","\n","if(tipo_onda=='gaussiana'):\n","  φ_0 =  0* np.ones(pasos_temporales) # Fase (constante en este caso)\n","  onda=pulso_gaussiano(t-to, A, σ, ω_0, φ_0) # Vector con el campo complejo del pulso\n","\n","\n","if(tipo_onda=='sinc'):\n","  φ_0 =  0* np.ones(pasos_temporales) # Fase (constante en este caso)\n","  onda=pulso_sinc(t-to, A, σ, ω_0, φ_0) # Vector con el campo complejo del pulso\n","\n"],"metadata":{"id":"J16BhzHbG7PF"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Representación gráfica"],"metadata":{"id":"iILvcQsGIZ7P"}},{"cell_type":"code","source":["plt.figure(figsize=(16, 4))\n","plt.plot(t,np.real(onda),label='$Re(E(t))$')\n","plt.plot(t,np.abs(onda),label='$|E(t)|$')\n","delay=0.0\n","plt.plot(t+delay,np.real(onda),label=r'$Re(E(t+\\tau))$',\n","                                color='red',linestyle='--')\n","plt.axhline(0.0,color='grey',linestyle='--')\n","plt.xlabel(r'$t$ (ps)')\n","plt.ylabel(r'$Re(E)$')\n","plt.axvline(to+np.pi*σ,color='grey',linestyle='--',label=r'$\\pi \\sigma$')\n","#plt.xlim(10,10+2*np.pi*1)\n","plt.legend()\n","plt.show()"],"metadata":{"id":"1-vL5MdFHG22","colab":{"base_uri":"https://localhost:8080/","height":392},"executionInfo":{"status":"ok","timestamp":1702312358341,"user_tz":-60,"elapsed":1579,"user":{"displayName":"SERGIO GUTIERREZ RODRIGO","userId":"07959720391705098820"}},"outputId":"ad2e1f12-85f6-44eb-a429-d50c27b8b46b"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 1600x400 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["# Cálculo numérico del grado de coherencia $\\gamma(\\tau)$ a partir de $E(t)$"],"metadata":{"id":"ZKuGqP3xrx0M"}},{"cell_type":"markdown","source":["$\\gamma(\\tau)=\\dfrac{\\Gamma(\\tau)}{Y}=\\dfrac{<E^*(t)|E(t+\\tau)>}{<E^*(t)|E(t)>}$"],"metadata":{"id":"5kXZWEzLrxmr"}},{"cell_type":"markdown","source":["**Comentario**: para ondas planas, con o sin fase temporal, el resultado es sólo aproximado. Para poder realizarlo hay que truncar ambas ondas. Serían en realidad paquetes de onda extensos en el tiempo, en lugar de verdaderas ondas planas."],"metadata":{"id":"1xfiy6_ZMV98"}},{"cell_type":"code","source":["def introduce_wave(x,N,pos):\n","    '''\n","    Genera un vector x \"expandido\" incrustando el original en un vector\n","    con más pasos temporales e iniciado con ceros\n","    '''\n","    n=x.shape[0]\n","    y=np.zeros((N*n),dtype=complex)\n","    if n > y.shape[0]:\n","        raise ValueError(\"n should be less than or equal to the number of columns in y.\")\n","    # Copy the y array to avoid modifying it in-place\n","    x_expand = y.copy()\n","    # Determine the starting index for insertion\n","    # Range: 0, y.shape[0] - n + 1\n","    # Substitute the values from x into y\n","    x_expand[ pos:pos + n] = x\n","    return x_expand\n","\n","def gamma_tau(E,tau,shape_ini,times_shape_ini,tau0):\n","  '''\n","  Calcula la función de correlación (promedio temporal de E*(t)|E(t+tau))\n","  salvo factores ctes (tiempo de simulación T y dt )\n","  '''\n","  N=times_shape_ini  # Los vectores de campo expandido tendrá N veces el tamaño original\n","  Et=introduce_wave(E,N,tau0) # Campo E(t)\n","  Ettau=introduce_wave(E,N,tau)     # Campo E(t+tau)\n","  promedio_temporal=np.sum(np.conjugate(Et)*Ettau) # \"Integral (suma)\" de <E*(t)|E(t+tau)>\n","  return promedio_temporal\n","\n","'''\n","Se calcula la función de correlación, \\Gamma, para muchos valores de tau\n","La idea es \"barrer\" E(t+tau) sobre el campo E(t)\n","'''\n","E=onda # Se ha definido previamente el campo en el array onda\n","n=E.shape[0]\n","N=10\n","tau0=int(N*n/2)\n","Gamma =[]\n","for tau in range(0, n*N - n + 1):\n","  Gamma.append(gamma_tau(E,tau,n,N,tau0))\n","Gamma=np.array(Gamma)\n","gamma=Gamma/Gamma[tau0] # Se calcula el grado de coherencia temporal \\gamma"],"metadata":{"id":"QRYQn8WhuRIK"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Ejemplo de campo \"expandido\""],"metadata":{"id":"NC13hMkGwnJe"}},{"cell_type":"code","source":["Et=introduce_wave(E,N,int(N*n/2)) #int(N*n/2))\n","t_rango_expand=Δt*(np.linspace(0,Et.shape[0],Et.shape[0]))\n","plt.plot(t_rango_expand,np.real(Et),label=r'Re($E(t))$',\n","                                color='red',linestyle='-')\n","plt.xlabel(r'$t$ (ps)')\n","#plt.xlim(0,0.3)\n","plt.legend()\n","plt.show()"],"metadata":{"id":"-AwRrhnvjMfZ","colab":{"base_uri":"https://localhost:8080/","height":453},"executionInfo":{"status":"ok","timestamp":1702312380724,"user_tz":-60,"elapsed":453,"user":{"displayName":"SERGIO GUTIERREZ RODRIGO","userId":"07959720391705098820"}},"outputId":"4dc49ae2-d090-4d6f-ef4c-093d043047f8"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["## Representación de $\\gamma (\\tau)$"],"metadata":{"id":"8ircnlPgwrLI"}},{"cell_type":"code","source":["t_max=np.argmax(Gamma)\n","texpand=Δt*(np.linspace(0,Gamma.shape[0],Gamma.shape[0])-t_max)\n","plt.plot(texpand,np.abs(gamma),label=r'|$\\gamma(\\tau)|$',\n","                              color='red',linestyle='-')\n","plt.xlabel(r'$\\tau-\\tau_0$ (ps)')\n","plt.xlim(-100*σ,100*σ)\n","plt.legend()\n","plt.show()"],"metadata":{"id":"jP-yBlwfsyC8","executionInfo":{"status":"ok","timestamp":1702312384259,"user_tz":-60,"elapsed":1209,"user":{"displayName":"SERGIO GUTIERREZ RODRIGO","userId":"07959720391705098820"}},"outputId":"ff46f1d0-821c-42ba-a08e-210edce9192f","colab":{"base_uri":"https://localhost:8080/","height":453}},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"iVBORw0KGgoAAAANSUhEUgAAAiwAAAG0CAYAAAARqnxaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAA3bElEQVR4nO3deXRU9f3/8VcSkgkRSJCQhCUQUIkgq7GJkdpCzZeIFKG2HrT9CfJFPCq4xVbBBVyK8AVBWopSqaDfYxXUU6kVvlQbjRtRKouIVQqWzUASQEkgIQuZ+/tjmGFCJoGZuXfuJPN8nDPnTu7c5X2Zmrz6+Xzu50YZhmEIAAAgjEXbXQAAAMDZEFgAAEDYI7AAAICwR2ABAABhj8ACAADCHoEFAACEPQILAAAIe+3sLuBcOJ1OHThwQB07dlRUVJTd5QAAgHNgGIaOHTum7t27Kzo6uDaSVhFYDhw4oPT0dLvLAAAAAdi/f7969uwZ1DFaRWDp2LGjJNcFd+rUyeZqAADAuaisrFR6errn73gwWkVgcXcDderUicACAEArY8ZwDgbdAgCAsEdgAQAAYY/AAgAAwl6rGMMCAIBZGhoaVF9fb3cZbUJsbKxiYmJCci4CCwAgIhiGodLSUh09etTuUtqUpKQkpaWlWT5PGoEFABAR3GElJSVFCQkJTEQaJMMwVF1drfLycklSt27dLD0fgQUA0OY1NDR4wkqXLl3sLqfNaN++vSSpvLxcKSkplnYPMegWANDmucesJCQk2FxJ2+P+N7V6XBCBBQAQMegGMl+o/k0JLAAAIOz5HVg++OADjR07Vt27d1dUVJTWrFlz1n2Kiop06aWXyuFw6MILL9QLL7wQQKkAACBS+R1YqqqqNGTIEC1duvSctt+9e7fGjBmjkSNHauvWrbrnnnt0yy236O9//7vfxQIAgMjk911Co0eP1ujRo895+2XLlqlPnz5auHChJKl///766KOP9PTTTys/P9/f0wNoa6qrpfh4KZoeagDNs/w3RHFxsfLy8hqty8/PV3FxcbP71NbWqrKystELQBv09ttSUpJ02WVSba3d1QBhqaioSBkZGX7tc+TIEaWkpGjPnj3nvM8NN9zgaVwI9vxWsDywlJaWKjU1tdG61NRUVVZW6sSJEz73mTt3rhITEz2v9PR0q8sEYIennpLq66UtW6S33rK7GqDNmDNnjsaNG+dX0Hj44Yc1Z84cVVRUWFdYEMKyDXbmzJmqqKjwvPbv3293SQDMdvy4VFR0+uf1620rBRHIMKSqKntehmHppVVXV+v555/XlClT/Npv4MCBuuCCC/TSSy9ZVFlwLJ/pNi0tTWVlZY3WlZWVqVOnTp4Z8s7kcDjkcDisLg2Anb74wtW64rZ1q22lIAJVV0sdOthz7uPHpfPOC3j3fv36qUuXLnr33Xc9f0cNw1Bubq5GjhyprKwsORwOXX755Y32GzdunN58802fx/zrX/+qa6+9VmPHjtWqVas0bdq0gOuziuUtLLm5uSosLGy07p133lFubq7VpwYQzr780rXs08e1/OIL6eRJ++oBWonVq1dr8+bN+vjjjz3r/vznP2vv3r168MEH9eGHHyorK6vJfitWrNDBgwe1c+dOSdK6det08OBBHTx4UNdcc40kKTs7Wxs3blRtGI4p87uF5fjx49q1a5fn5927d2vr1q06//zz1atXL82cOVMlJSX63//9X0nSbbfdpj/84Q+6//779d///d9699139eqrr2rt2rXmXQWA1udf/3Itx46V/vhH16Db/ftPBxjASgkJrpYOu84dhGHDhmno0KH6+uuvlZeXp+rqas2cOVO//e1v1bFjR+3du1fdu3dvsp/7GUrFxcWKiorSlVdeqQ5ntDJ1795ddXV1Ki0tVe/evYOq02x+B5bPPvtMI0eO9PxcUFAgSZo0aZJeeOEFHTx4UPv27fN83qdPH61du1b33nuvfve736lnz57605/+xC3NQKTbvdu1zMyUeveW/v1vac8eAgtCIyoqqG4Zu/Xr1087duyQJM2fP1/JycmaPHmyJOnEiROKj49vdt9t27YpIyOjSViRTj/MsLq62oKqg+N3YBkxYoSMFgYM+ZrFdsSIEdqyZYu/pwLQlrkH06enu0KKO7AAOKvMzEx98MEH+vbbb7VgwQKtXbtW0afmMkpOTtb333/f7L7btm3T4MGDfX723XffSZK6du1qftFBCsu7hABEgG+/dS179pTct166W10AtMjdwjJjxgyNGjVKI0aM8Hw2bNgw/cvd5erDnj17lJmZ6fOz7du3q2fPnkpOTja75KARWACEXm2t5L57MD3d9ZKkkhL7agJakX79+mn//v16/fXXtWDBgkaf5efn68svv2y2lcXpdGrv3r0qKSlp0mPy4YcfatSoUZbVHQwCC4DQcweT+HipSxcpLc31c2mpfTUBrUi/fv0kSdOnT9eFF17Y6LNBgwbp0ksv1auvvupz37vuuksff/yxMjMzGwWWmpoarVmzRlOnTrWu8CAQWACEnjuw9OjhGvzoDixnzNkEwLeamhoZhqGJEyf6/HzWrFn63e9+J6fT2eSz0aNHa//+/Tp+/Lhn3IskrVy5UtnZ2U3mbwkXlk8cBwBNHDrkWqakuJbux3fQwgKck88//1xxcXHq37+/z8/HjBmjnTt3qqSk5JwfbxMbG6slS5aYWaapCCwAQu/wYdfSfSeCdwuL08mTm4Gz+PzzzzVgwADFxsY2u80999zj1zFvueWWIKuyFr8VAISeu4XFfSeCu6Xl5Enp1G2VAFwyMjKahI977rknZNOF+Dq/HQgsAELvzBaWuDjp/PNd7+kWAhqxOzDYfX43AguA0HMHFu+5HtzvjxwJfT0Awh6BBUDondklJLlub5boEoKlWpqpHYEJ1b8pgQVA6J3ZJSSd7hIisMAC7sGp4fiMnNbO/W/a0gBgM3CXEIDQ89UlRGCBhWJiYpSUlKTy8nJJUkJCgqKiomyuqnUzDEPV1dUqLy9XUlKSYmJiLD0fgQVA6PnqEiKwwGJpp26fd4cWmCMpKcnzb2slAguA0Kqudr2kxl1C7jEsDLqFRaKiotStWzelpKSovr7e7nLahNjYWMtbVtwILABCy92C0q6d1LHj6fW0sCBEYmJiQvZHFuZh0C2A0Dp61LVMSnI9R8iNwAKgBQQWAKHlHVi8EVgAtIDAAiC0Kipcy8TExuuZhwVACwgsAELLHVjObGHp3Nm1JLAA8IHAAiC03F1CZ7awdOrkWlZVSQ0NIS0JQPgjsAAIrea6hNyBRZKOHQtdPQBaBQILgNBqrkvI4XC9vLcBgFMILABCq7kuIe91BBYAZyCwAAit5rqEpNPdQpWVoasHQKtAYAEQWs11CUm0sABoFoEFQGi11CVECwuAZhBYAIQWLSwAAkBgARBajGEBEAACC4DQ4i4hAAEgsAAInZMnXTPZSr67hGhhAdAMAguA0PEOIt4z27rRwgKgGQQWAKHjDizx8VJsbNPPaWEB0AwCC4DQOX7ctezY0ffntLAAaAaBBUDonC2wuFtYCCwAzkBgARA67qcwd+jg+3N3CwtdQgDOQGABEDruFpazBRZaWACcgcACIHTOFljc693bAcApBBYAoXO2MSzuwFJT45qzBQBOIbAACJ2zjWHxXu+eYA4ARGABEEpn6xJyOKSYGNd7AgsALwQWAKFzti6hqCjGsQDwicACIHTO1sLi/RmBBYAXAguA0DnbGBbvzwgsALwQWACEDi0sAAJEYAEQOmcbwyIRWAD4RGABEDq0sAAIEIEFQOgwhgVAgAgsAEKHFhYAASKwAAidcxnDct55jbcFABFYAISKYdDCAiBgBBYAoVFTIzU0uN4TWAD4icACIDS8A4i728cXd2DhWUIAvBBYAISGO7Ccd54U3cKvHlpYAPhAYAEQGucyfsX7cwILAC8EFgChcS5zsHh/TmAB4IXAAiA0aGEBEAQCC4DQOJc5WCQCCwCfAgosS5cuVUZGhuLj45WTk6ONGze2uP3ixYuVmZmp9u3bKz09Xffee69qamoCKhhAK0ULC4Ag+B1YVq9erYKCAs2ePVubN2/WkCFDlJ+fr/Lycp/bv/zyy5oxY4Zmz56tr776Ss8//7xWr16tBx98MOjiAbQigYxhMQxrawLQavgdWBYtWqSpU6dq8uTJGjBggJYtW6aEhAStWLHC5/YbNmzQ8OHD9ctf/lIZGRkaNWqUbrzxxhZbZWpra1VZWdnoBaCV87eFxel0TTYHAPIzsNTV1WnTpk3Ky8s7fYDoaOXl5am4uNjnPldccYU2bdrkCSj/+c9/tG7dOl1zzTXNnmfu3LlKTEz0vNLT0/0pE0A4qq52LVuaNE6SEhJOv6dbCMApfgWWw4cPq6GhQampqY3Wp6amqrS01Oc+v/zlL/X444/rhz/8oWJjY3XBBRdoxIgRLXYJzZw5UxUVFZ7X/v37/SkTQDhyBxbvQOJLTIzUvr3rPYEFwCmW3yVUVFSkJ598Us8884w2b96sv/zlL1q7dq2eeOKJZvdxOBzq1KlToxeAVs491f7ZAovEwFsATbTzZ+Pk5GTFxMSorKys0fqysjKlpaX53OeRRx7RTTfdpFtuuUWSNGjQIFVVVenWW2/VQw89pOiWpugG0Haca5eQdDrUuPcBEPH8SgtxcXHKyspSYWGhZ53T6VRhYaFyc3N97lNdXd0klMTExEiSDO4AACLHuXYJSadDDYEFwCl+tbBIUkFBgSZNmqTLLrtM2dnZWrx4saqqqjR58mRJ0sSJE9WjRw/NnTtXkjR27FgtWrRIw4YNU05Ojnbt2qVHHnlEY8eO9QQXABHAny4h9zY8sRnAKX4HlgkTJujQoUOaNWuWSktLNXToUK1fv94zEHffvn2NWlQefvhhRUVF6eGHH1ZJSYm6du2qsWPHas6cOeZdBYDw50+XEC0sAM4QZbSCfpnKykolJiaqoqKCAbhAa5WdLf3zn9Lf/ib99Kctb3vNNdL//Z+0cqV0880hKQ+A+cz8+82IVwCh4c8YFrqEAJyBwAIgNOgSAhAEAguA0Ahk0C2BBcApBBYAoRHIbc10CQE4hcACwHqGwcRxAIJCYAFgvdpa19OXJQbdAggIgQWA9bxbSpjpFkAACCwArOcOHnFxUrtzmK+SLiEAZyCwALCeP3cISQy6BdAEgQWA9fy5Q8h7O1pYAJxCYAFgPX/uEJIYdAugCQILAOsF2iVECwuAUwgsAKxHlxCAIBFYAFiPLiEAQSKwALBeMF1ChmFNTQBaFQILAOsF2iXU0CDV1VlTE4BWhcACwHr+dgl5b8c4FgAisAAIBX+7hGJjT8+IS2ABIAILgFDwt0vIe1sG3gIQgQVAKPjbJeS9LS0sAERgARAK/nYJeW9LYAEgAguAUAikS4gHIALwQmABYL1AuoRoYQHghcACwHrBdAnRwgJABBYAoRBMlxAtLABEYAEQCnQJAQgSgQWA9QLpEmLQLQAvBBYA1gtm4jhaWACIwAIgFNytJIF0CdHCAkAEFgBWczqlEydc7xl0CyBABBYA1qqpOf2eLiEAASKwALCWd5cOg24BBIjAAsBa7haS+Hgp2o9fObSwAPBCYAFgrUDuEPLenhYWACKwALBaIHcIeW9PCwsAEVgAWC3YFhYCCwARWABYjS4hACYgsACwVrBdQgQWACKwALBasC0s7knnAEQ0AgsAa5kxhsUwzK0JQKtDYAFgrWC7hCRaWQAQWABYLNAWlvbtmx4DQMQisACwVqCBJSZGcjgaHwNAxCKwALBWoF1CEnOxAPAgsACwVqAtLN77cGszEPEILACsFUxgYXp+AKcQWABYy906EkwLC4EFiHgEFgDWcocNxrAACAKBBYC1zBjDQmABIh6BBYC1zBjDwqBbIOIRWABYixYWACYgsACwFoEFgAkILACsRWABYAICCwBrMXEcABMQWABYx+k8/aRlJo4DEAQCCwDr1NScfk+XEIAgBBRYli5dqoyMDMXHxysnJ0cbN25scfujR49q2rRp6tatmxwOh/r166d169YFVDCAVsQ7aLRv7//+BBYAp7Tzd4fVq1eroKBAy5YtU05OjhYvXqz8/Hzt2LFDKSkpTbavq6vTf/3XfyklJUWvv/66evToob179yopKcmM+gGEM3fQcDikmBj/9yewADjF78CyaNEiTZ06VZMnT5YkLVu2TGvXrtWKFSs0Y8aMJtuvWLFC3333nTZs2KDY2FhJUkZGRovnqK2tVW1trefnyspKf8sEEA6CGXArMXEcAA+/uoTq6uq0adMm5eXlnT5AdLTy8vJUXFzsc58333xTubm5mjZtmlJTUzVw4EA9+eSTamhoaPY8c+fOVWJioueVnp7uT5kAwkWwgYUWFgCn+BVYDh8+rIaGBqWmpjZan5qaqtLSUp/7/Oc//9Hrr7+uhoYGrVu3To888ogWLlyo3/72t82eZ+bMmaqoqPC89u/f70+ZAMIFgQWASfzuEvKX0+lUSkqKnnvuOcXExCgrK0slJSVasGCBZs+e7XMfh8Mhh8NhdWkArEZgAWASvwJLcnKyYmJiVFZW1mh9WVmZ0tLSfO7TrVs3xcbGKsZrwF3//v1VWlqquro6xcXFBVA2gFbBrMDCGBYg4vnVJRQXF6esrCwVFhZ61jmdThUWFio3N9fnPsOHD9euXbvkdDo96/7973+rW7duhBWgrTNr0C0tLEDE83seloKCAi1fvlwvvviivvrqK91+++2qqqry3DU0ceJEzZw507P97bffru+++0533323/v3vf2vt2rV68sknNW3aNPOuAkB4MrNLyDDMqQlAq+T3GJYJEybo0KFDmjVrlkpLSzV06FCtX7/eMxB33759io4+nYPS09P197//Xffee68GDx6sHj166O6779YDDzxg3lUACE9mBRbJNWtuIJPPAWgTAhp0O336dE2fPt3nZ0VFRU3W5ebm6pNPPgnkVABaMzMDS3U1gQWIYDxLCIB13IHFPRbFXzExrllyJQbeAhGOwALAOsG2sHjvy8BbIKIRWABYh8ACwCQEFgDWIbAAMAmBBYB13ONOggksPAARgAgsAKxECwsAkxBYAFiHwALAJAQWANYhsAAwCYEFgHXMDCyMYQEiGoEFgHXMCCw8ABGACCwArESXEACTEFgAWIfAAsAkBBYA1iGwADAJgQWANerrpZMnXe+ZOA5AkAgsAKzh3SJCCwuAIBFYAFjDHTCio6W4uMCPQ2ABIAILAKt4j1+Jigr8OAQWACKwALCKGQNuvfdnDAsQ0QgsAKxhVmBh4jgAIrAAsIrZLSwEFiCiEVgAWIPAAsBEBBYA1iCwADARgQWANawYw2IYwR0LQKtFYAFgDbNbWAxDqqkJ7lgAWi0CCwBrmBVY2rdvekwAEYfAAsAaZgWWdu1Oz5RLYAEiFoEFgDXMCizex2DyOCBiEVgAWMPMwMLkcUDEI7AAsIYVLSwEFiBiEVgAWMMdLtytI8EgsAARj8ACwBq0sAAwEYEFgDWsGMPCoFsgYhFYAFjDHS5oYQFgAgILAGvQJQTARAQWANYgsAAwEYEFgDWYOA6AiQgsAKzBxHEATERgAWANuoQAmIjAAsB8Tqd04oTrPYEFgAkILADMV1Nz+j2BBYAJCCwAzOcdLNq3D/54TBwHRDwCCwDzuQOLwyHFxAR/PFpYgIhHYAFgPjMH3Hofh8ACRCwCCwDzmTktv/dxCCxAxCKwADCfO7C4x54Ei4njgIhHYAFgPrMDCxPHARGPwALAfO7A0qGDOcejSwiIeAQWAOY7fty1NLtLqLpaMgxzjgmgVSGwADCfVWNYDEOqrTXnmABaFQILAPNZFVi8jw0gohBYAJjP7MDSrp0UF+d6zzgWICIRWACYz+zAIjHwFohwBBYA5jP7LiGJwAJEOAILAPOZfZeQxORxQIQjsAAwnxVdQkweB0Q0AgsA8zGGBYDJAgosS5cuVUZGhuLj45WTk6ONGzee036rVq1SVFSUxo8fH8hpAbQWBBYAJvM7sKxevVoFBQWaPXu2Nm/erCFDhig/P1/l5eUt7rdnzx79+te/1pVXXhlwsQBaCSsDC2NYgIjkd2BZtGiRpk6dqsmTJ2vAgAFatmyZEhIStGLFimb3aWho0K9+9Ss99thj6tu3b1AFA2gFGMMCwGR+BZa6ujpt2rRJeXl5pw8QHa28vDwVFxc3u9/jjz+ulJQUTZky5ZzOU1tbq8rKykYvAK2I+y4hbmsGYBK/Asvhw4fV0NCg1NTURutTU1NVWlrqc5+PPvpIzz//vJYvX37O55k7d64SExM9r/T0dH/KBGA3xrAAMJmldwkdO3ZMN910k5YvX67k5ORz3m/mzJmqqKjwvPbv329hlQBMZRgEFgCma+fPxsnJyYqJiVFZWVmj9WVlZUpLS2uy/TfffKM9e/Zo7NixnnVOp9N14nbttGPHDl1wwQVN9nM4HHI4HP6UBiBc1NVJDQ2u9wy6BWASv1pY4uLilJWVpcLCQs86p9OpwsJC5ebmNtn+4osv1hdffKGtW7d6Xtdee61GjhyprVu30tUDtEXegYJBtwBM4lcLiyQVFBRo0qRJuuyyy5Sdna3FixerqqpKkydPliRNnDhRPXr00Ny5cxUfH6+BAwc22j8pKUmSmqwH0Ea4A0tsrOtlFrqEgIjmd2CZMGGCDh06pFmzZqm0tFRDhw7V+vXrPQNx9+3bp+hoJtAFIpYVDz6UCCxAhPM7sEjS9OnTNX36dJ+fFRUVtbjvCy+8EMgpAbQWVjz40Pt47uMDiCg0hQAwlxV3CEmnW2wYdAtEJAILAHNZHVhoYQEiEoEFgLkILAAsQGABYC4CCwALEFgAmMuqu4S8A4thmHtsAGGPwALAXFbdJeQOLE6ndOKEuccGEPYILADMZVWXkPfx6BYCIg6BBYC5rAos0dHMxQJEMAILAHNZFVgkBt4CEYzAAsBcBBYAFiCwADCXVXcJeR/z2DHzjw0grBFYAJjLqruEJFpYgAhGYAFgLiu7hDp2dC0JLEDEIbAAMJc7TFjZJURgASIOgQWAudzjS9ytIWYisAARi8ACwFwEFgAWILAAMJc7sNAlBMBEBBYA5qmvl2prXe+tbGHhtmYg4hBYAJjHu+WDLiEAJiKwADCPu+UjLs71Mhu3NQMRi8ACwDxWDriVaGEBIhiBBYB5CCwALEJgAWAeAgsAixBYAJgnVIGFu4SAiENgAWAeWlgAWITAAsA8oQwshmHNOQCEJQILAPNYOcutdDoIOZ1STY015wAQlggsAMxjdQtLQsLp93QLARGFwALAPFYHlpiY06GFwAJEFAILAPO4Q4RVgUVi4C0QoQgsAMxjdQuLxK3NQIQisAAwTygCS6dOrmVlpXXnABB2CCwAzENgAWARAgsA84QisCQmupYVFdadA0DYIbAAMA8tLAAsQmABYJ5QtrAQWICIQmABYB6rZ7qVTrew0CUERBQCCwBz1NZK9fWu93QJATAZgQWAObznRWHQLQCTEVgAmMMdWOLjpXbtrDsPLSxARCKwADCHO0C4A4VVGHQLRCQCCwBzuLto3IHCKgy6BSISgQWAOdwBIinJ2vPQwgJEJAILAHMcPepa0sICwAIEFgDmCHWXUHW1dPKktecCEDYILADMEaouIe9Bvd63UgNo0wgsAMwRqhaWuDjXrdPe5wTQ5hFYAJgjVGNYvM/BwFsgYhBYAJgjVF1CEgNvgQhEYAFgjlB1CXmfgxYWIGIQWACYI5RdQkzPD0QcAgsAc9AlBMBCBBYA5qBLCICFCCwAzGFHlxAtLEDEILAACF59vXTihOt9KLqE3KGIwAJEDAILgOB5BwfvmWit4g5FBBYgYgQUWJYuXaqMjAzFx8crJydHGzdubHbb5cuX68orr1Tnzp3VuXNn5eXltbg9gFbIHRw6dJDatbP+fJ07u5bffWf9uQCEBb8Dy+rVq1VQUKDZs2dr8+bNGjJkiPLz81VeXu5z+6KiIt1444167733VFxcrPT0dI0aNUolJSVBFw8gTIRy/IoknX++a0lgASKG34Fl0aJFmjp1qiZPnqwBAwZo2bJlSkhI0IoVK3xu/+c//1l33HGHhg4dqosvvlh/+tOf5HQ6VVhYGHTxAMJEKO8Qkk63sHz/fWjOB8B2fgWWuro6bdq0SXl5eacPEB2tvLw8FRcXn9MxqqurVV9fr/Pd/w/Jh9raWlVWVjZ6AQhjoZyDRaKFBYhAfgWWw4cPq6GhQampqY3Wp6amqrS09JyO8cADD6h79+6NQs+Z5s6dq8TERM8rPT3dnzIBhFqou4S8W1gMIzTnBGCrkN4lNG/ePK1atUpvvPGG4t2Ph/dh5syZqqio8Lz2798fwioB+M3dNeMOElZzt7CcPCkdPx6acwKwlV/D+ZOTkxUTE6OysrJG68vKypSWltbivk899ZTmzZunf/zjHxo8eHCL2zocDjkcDn9KA2CnI0dcyy5dQnO+9u2luDiprs4Vljp2DM15AdjGrxaWuLg4ZWVlNRow6x5Am5ub2+x+8+fP1xNPPKH169frsssuC7xaAOHJPZakhbFppoqKYhwLEGH8njChoKBAkyZN0mWXXabs7GwtXrxYVVVVmjx5siRp4sSJ6tGjh+bOnStJ+p//+R/NmjVLL7/8sjIyMjxjXTp06KAOHTqYeCkAbBPqFhbJ1f1UWsqdQkCE8DuwTJgwQYcOHdKsWbNUWlqqoUOHav369Z6BuPv27VN09OmGm2effVZ1dXX6xS9+0eg4s2fP1qOPPhpc9QDCQ6hbWLzPRQsLEBECmpJy+vTpmj59us/PioqKGv28Z8+eQE4BoDWxo4WFwAJEFJ4lBCB4drSwMHkcEFEILACC525hoUsIgEUILACCU1srVVW53od60K1ECwsQIQgsAILjbuGIjg7dTLcSLSxAhCGwAAiOOzB07uwKLaFCCwsQUQgsAIJjx/gV7/PRwgJEBAILgOC4A0Mox694n+/w4dCeF4AtCCwAgmNXC0vXrq7loUM8sRmIAAQWAMGxq4UlJcW1rKnhic1ABCCwAAiOu0sm1C0s553nemqz5GplAdCmEVgABKe83LU89TyxkHK3srhrANBmEVgABKeszLV0h4dQ8h7HAqBNI7AACA4tLABCgMACIDjusEALCwALEVgABM4wTncJ0cICwEIEFgCBq6yU6upc792tHaHkDiy0sABtHoEFQODcLRsdOkgJCaE/vzsk0cICtHkEFgCBs7M7SKKFBYggBBYAgbNzwK1ECwsQQQgsAAJndwuL+7zl5ZLTaU8NAEKCwAIgcHZOGidJaWlSVJRUX89Tm4E2jsACIHAHDriW3bvbc/7Y2NNhqaTEnhoAhASBBUDg3CGhRw/7anCfm8ACtGkEFgCB+/Zb15LAAsBiBBYAgXOHhJ497avB3R1FYAHaNAILgMDU1EhHjrje08ICwGIEFgCBcQeE+Hipc2f76iCwABGBwAIgMN4DbqOi7KuDwAJEBAILgMCEw/gVicACRAgCC4DAhMMtzd7n//57qbra3loAWIbAAiAwe/a4lr162VqGkpKkjh1d7/fts7UUANYhsAAIzH/+41pecIG9dURFSX37ut67awLQ5hBYAATGHQ7cYcFOBBagzSOwAPCf0ynt3u16T2ABEAIEFgD+O3BAqquT2rWz/y4hicACRAACCwD/uYNB796u0GI3AgvQ5hFYAPgvnMavSI0Di2HYWwsASxBYAPhv507XMlwCS+/eUnS0VFUlHTxodzUALEBgAeC/f/3LtRwwwN463ByO07dXu2sD0KYQWAD478svXctwCSySdMklrqW7NgBtCoEFgH9qaqRvvnG9d4eEcDBwoGu5fbu9dQCwBIEFgH927HDNw9K5s5SWZnc1p9HCArRpBBYA/vniC9dywADXtPjhwjuwcKcQ0OYQWAD457PPXMtLL7W3jjNlZkqxsVJl5elZeAG0GQQWAP755z9dyx/8wN46zhQXJw0b5nr/6af21gLAdAQWAOfu5ElpyxbX++xse2vx5fLLXctPPrG3DgCmI7AAOHdffCGdOCF16iRddJHd1TSVm+taEliANofAAuDcvfeeazl8uGtm2XDjbmHZskWqrra3FgCmCsPfOADC1j/+4Vrm5dlbR3N695Z69ZLq66WiIrurAWAiAguAc1NXJ33wgev9VVfZW0tzoqKka65xvV+3zt5aAJiKwALg3Lzzjuvhgmlp0qBBdlfTPO/AwnwsQJtBYAFwblavdi2vvz48x6+4/eQnUny8ay4W95wxAFq9MP6tAyBsVFRIb7zhej9hgr21nM1550k//7nr/YoV9tYCwDQEFgBn9/zz0vHjUv/+p28dDmeTJ7uWL70kHTliby0ATEFgAdCyY8ekp55yvS8oCO/uILef/EQaMsQVshYutLsaACZoBb95ANhq1izp4EGpb1/p//0/u6s5N1FR0qOPut4vXMgTnIE2IKDAsnTpUmVkZCg+Pl45OTnauHFji9u/9tpruvjiixUfH69BgwZpHbcbAq3Diy9Kixe73v/+967BrK3FuHHST3/quh173DiptNTuigAEwe/Asnr1ahUUFGj27NnavHmzhgwZovz8fJWXl/vcfsOGDbrxxhs1ZcoUbdmyRePHj9f48eO1ffv2oIsHYJGKCumBB6Sbb3b9/OtfS2PG2FqS36KipOXLpYwM6ZtvXA9r5FZnoNWKMgz//uvNycnRD37wA/3hD3+QJDmdTqWnp+vOO+/UjBkzmmw/YcIEVVVV6a233vKsu/zyyzV06FAtW7bsnM5ZWVmpxMREVWzbpk4dO/re6GyXwed8zufNq6lxdfvs3+960vHbb5+e2v6ee1zdKq1h7Iovu3a55mbZudP184UXSvn50iWXSD17SomJrmcjtWsnxcS4XtHRp5cAAlZ57JgSBw1SRUWFOnXqFNSx2vmzcV1dnTZt2qSZM2d61kVHRysvL0/FxcU+9ykuLlZBQUGjdfn5+VqzZk2z56mtrVVtba3n58rKStebwYP9KRdAMC65RHrySenaa+2uJDgXXuiaj+WJJ6SlS10BZtcuu6sC4Ce/Asvhw4fV0NCg1NTURutTU1P19ddf+9yntLTU5/alLfQnz507V4899ljTD+LjXc28zWnpMz7ncz5v/rPYWKlbN9dr6FDpxz92daGc7ZitRadO0oIFrgHEf/+7qxXpq6+k8nLp6FGpslJqaJCczsZLuo/ODf9OaI5hSF4NEMHwK7CEysyZMxu1ylRWVio9PV0qK3P94gGAQHTsKP3iF64XAOtVVrq6XU3gV2BJTk5WTEyMysrKGq0vKytTWlqaz33S0tL82l6SHA6HHA6HP6UBAIA2zK8RZXFxccrKylJhYaFnndPpVGFhoXKbmf0yNze30faS9M477zS7PQAAwJn87hIqKCjQpEmTdNlllyk7O1uLFy9WVVWVJp+aCnvixInq0aOH5s6dK0m6++679eMf/1gLFy7UmDFjtGrVKn322Wd67rnnzL0SAADQZvkdWCZMmKBDhw5p1qxZKi0t1dChQ7V+/XrPwNp9+/Yp2utWwCuuuEIvv/yyHn74YT344IO66KKLtGbNGg0cONC8qwAAAG2a3/Ow2MEzD4sJ93EDAIDQMPPvN7MiAQCAsEdgAQAAYY/AAgAAwh6BBQAAhD0CCwAACHsEFgAAEPYILAAAIOwRWAAAQNgjsAAAgLDn99T8dnBPxltZWWlzJQAA4Fy5/26bMal+qwgsR44ckSSlp6fbXAkAAPDXkSNHlJiYGNQxWkVgOf/88yW5HqwY7AW3JpWVlUpPT9f+/fsj6hlKXDfXHQm4bq47ElRUVKhXr16ev+PBaBWBxf3058TExIj6ot06derEdUcQrjuycN2RJVKv2/13PKhjmFAHAACApQgsAAAg7LWKwOJwODR79mw5HA67SwkprpvrjgRcN9cdCbju4K87yjDjXiMAAAALtYoWFgAAENkILAAAIOwRWAAAQNgjsAAAgLAX1oFlz549mjJlivr06aP27dvrggsu0OzZs1VXV9dou23btunKK69UfHy80tPTNX/+fJsqNs+cOXN0xRVXKCEhQUlJST63iYqKavJatWpVaAs12blc9759+zRmzBglJCQoJSVFv/nNb3Ty5MnQFmqxjIyMJt/tvHnz7C7LdEuXLlVGRobi4+OVk5OjjRs32l2SpR599NEm3+vFF19sd1mm++CDDzR27Fh1795dUVFRWrNmTaPPDcPQrFmz1K1bN7Vv3155eXnauXOnPcWa6GzXffPNNzf5/q+++mp7ijXR3Llz9YMf/EAdO3ZUSkqKxo8frx07djTapqamRtOmTVOXLl3UoUMH/fznP1dZWZlf5wnrwPL111/L6XTqj3/8o7788ks9/fTTWrZsmR588EHPNpWVlRo1apR69+6tTZs2acGCBXr00Uf13HPP2Vh58Orq6nT99dfr9ttvb3G7lStX6uDBg57X+PHjQ1OgRc523Q0NDRozZozq6uq0YcMGvfjii3rhhRc0a9asEFdqvccff7zRd3vnnXfaXZKpVq9erYKCAs2ePVubN2/WkCFDlJ+fr/LycrtLs9Qll1zS6Hv96KOP7C7JdFVVVRoyZIiWLl3q8/P58+fr97//vZYtW6ZPP/1U5513nvLz81VTUxPiSs11tuuWpKuvvrrR9//KK6+EsEJrvP/++5o2bZo++eQTvfPOO6qvr9eoUaNUVVXl2ebee+/V3/72N7322mt6//33deDAAV133XX+nchoZebPn2/06dPH8/MzzzxjdO7c2aitrfWse+CBB4zMzEw7yjPdypUrjcTERJ+fSTLeeOONkNYTKs1d97p164zo6GijtLTUs+7ZZ581OnXq1Oh/A61d7969jaefftruMiyVnZ1tTJs2zfNzQ0OD0b17d2Pu3Lk2VmWt2bNnG0OGDLG7jJA68/eU0+k00tLSjAULFnjWHT161HA4HMYrr7xiQ4XW8PX7edKkSca4ceNsqSeUysvLDUnG+++/bxiG6/uNjY01XnvtNc82X331lSHJKC4uPufjhnULiy8VFRWNHqJUXFysH/3oR4qLi/Osy8/P144dO/T999/bUWJITZs2TcnJycrOztaKFStMeYR3OCsuLtagQYOUmprqWZefn6/Kykp9+eWXNlZmvnnz5qlLly4aNmyYFixY0Ka6verq6rRp0ybl5eV51kVHRysvL0/FxcU2Vma9nTt3qnv37urbt69+9atfad++fXaXFFK7d+9WaWlpo+8+MTFROTk5bf67l6SioiKlpKQoMzNTt99+u44cOWJ3SaarqKiQdPrBxZs2bVJ9fX2j7/ziiy9Wr169/PrOW8XDD9127dqlJUuW6KmnnvKsKy0tVZ8+fRpt5/5jVlpaqs6dO4e0xlB6/PHH9ZOf/EQJCQl6++23dccdd+j48eO666677C7NMqWlpY3CitT4+24r7rrrLl166aU6//zztWHDBs2cOVMHDx7UokWL7C7NFIcPH1ZDQ4PP7/Lrr7+2qSrr5eTk6IUXXlBmZqYOHjyoxx57TFdeeaW2b9+ujh072l1eSLj/O/X13bel/4Z9ufrqq3XdddepT58++uabb/Tggw9q9OjRKi4uVkxMjN3lmcLpdOqee+7R8OHDNXDgQEmu7zwuLq7JuER/v3NbWlhmzJjhc8Co9+vMX1olJSW6+uqrdf3112vq1Kl2lB20QK67JY888oiGDx+uYcOG6YEHHtD999+vBQsWWHgFgTH7ulsrf/4dCgoKNGLECA0ePFi33XabFi5cqCVLlqi2ttbmq0AwRo8ereuvv16DBw9Wfn6+1q1bp6NHj+rVV1+1uzSEwA033KBrr71WgwYN0vjx4/XWW2/pn//8p4qKiuwuzTTTpk3T9u3bLbkBxJYWlvvuu08333xzi9v07dvX8/7AgQMaOXKkrrjiiiaDadPS0pqMNHb/nJaWZk7BJvH3uv2Vk5OjJ554QrW1tWH1vAozrzstLa3JnSTh+n2fKZh/h5ycHJ08eVJ79uxRZmamBdWFVnJysmJiYnz+txvu36OZkpKS1K9fP+3atcvuUkLG/f2WlZWpW7dunvVlZWUaOnSoTVXZo2/fvkpOTtauXbt01VVX2V1O0KZPn6633npLH3zwgXr27OlZn5aWprq6Oh09erRRK4u//73bEli6du2qrl27ntO2JSUlGjlypLKysrRy5UpFRzduFMrNzdVDDz2k+vp6xcbGSpLeeecdZWZmhl13kD/XHYitW7eqc+fOYRVWJHOvOzc3V3PmzFF5eblSUlIkub7vTp06acCAAaacwyrB/Dts3bpV0dHRnmtu7eLi4pSVlaXCwkLPnW1Op1OFhYWaPn26vcWF0PHjx/XNN9/opptusruUkOnTp4/S0tJUWFjoCSiVlZX69NNPz3pXZFvz7bff6siRI42CW2tkGIbuvPNOvfHGGyoqKmoyTCMrK0uxsbEqLCzUz3/+c0nSjh07tG/fPuXm5vp1orD17bffGhdeeKFx1VVXGd9++61x8OBBz8vt6NGjRmpqqnHTTTcZ27dvN1atWmUkJCQYf/zjH22sPHh79+41tmzZYjz22GNGhw4djC1bthhbtmwxjh07ZhiGYbz55pvG8uXLjS+++MLYuXOn8cwzzxgJCQnGrFmzbK48OGe77pMnTxoDBw40Ro0aZWzdutVYv3690bVrV2PmzJk2V26eDRs2GE8//bSxdetW45tvvjFeeuklo2vXrsbEiRPtLs1Uq1atMhwOh/HCCy8Y//rXv4xbb73VSEpKanQHWFtz3333GUVFRcbu3buNjz/+2MjLyzOSk5ON8vJyu0sz1bFjxzz/7UoyFi1aZGzZssXYu3evYRiGMW/ePCMpKcn461//amzbts0YN26c0adPH+PEiRM2Vx6clq772LFjxq9//WujuLjY2L17t/GPf/zDuPTSS42LLrrIqKmpsbv0oNx+++1GYmKiUVRU1OjvdHV1tWeb2267zejVq5fx7rvvGp999pmRm5tr5Obm+nWesA4sK1euNCT5fHn7/PPPjR/+8IeGw+EwevToYcybN8+mis0zadIkn9f93nvvGYZhGP/3f/9nDB061OjQoYNx3nnnGUOGDDGWLVtmNDQ02Ft4kM523YZhGHv27DFGjx5ttG/f3khOTjbuu+8+o76+3r6iTbZp0yYjJyfHSExMNOLj443+/fsbTz75ZKv/pebLkiVLjF69ehlxcXFGdna28cknn9hdkqUmTJhgdOvWzYiLizN69OhhTJgwwdi1a5fdZZnuvffe8/nf8aRJkwzDcN3a/MgjjxipqamGw+EwrrrqKmPHjh32Fm2Clq67urraGDVqlNG1a1cjNjbW6N27tzF16tQ2EdCb+zu9cuVKzzYnTpww7rjjDqNz585GQkKC8bOf/axR48O5iDp1MgAAgLDV6uZhAQAAkYfAAgAAwh6BBQAAhD0CCwAACHsEFgAAEPYILAAAIOwRWAAAQNgjsAAAgLBHYAEAAGGPwAIAAMIegQVAq3LkyBGlpKRoz549ph3zhhtu0MKFC007HgDz8SwhAK1KQUGBjh07puXLl5t2zO3bt+tHP/qRdu/ercTERNOOC8A8tLAAaDWqq6v1/PPPa8qUKaYed+DAgbrgggv00ksvmXpcAOYhsAARbNy4cYqKivL5evPNN8PuHOvWrZPD4dDll1/eaP2IESM0ffp0TZ8+XYmJiUpOTtYjjzwidwPy66+/rkGDBql9+/bq0qWL8vLyVFVV1egYY8eO1apVq4K7WACWaWd3AQDss2LFCtXX1+v48eO66KKLtG7dOg0bNkySlJycHHbn+PDDD5WVleXzsxdffFFTpkzRxo0b9dlnn+nWW29Vr1699NOf/lQ33nij5s+fr5/97Gc6duyYPvzwQ53ZG56dna05c+aotrZWDocjsIsFYBkCCxDBunTpIkkqLi5WVFSUrrzySnXo0CGk53jrrbd03333yel06oEHHtAtt9zS7LH27t2r7t27+/wsPT1dTz/9tKKiopSZmakvvvhCTz/9tLKysnTy5Eldd9116t27tyRp0KBBTfbv3r276urqVFpa6tkOQPigSwiAtm3bpoyMjBbDyowZM5rt2nG/vv76a7/OcfLkSRUUFOjdd9/Vli1btGDBAh05cqTZY5w4cULx8fE+P7v88ssVFRXl+Tk3N1c7d+7UkCFDdNVVV2nQoEG6/vrrtXz5cn3//fdN9m/fvr0k1zgZAOGHFhYA2rZtmwYPHtziNvfdd59uvvnmFrfp27evX+fYuHGjLrnkEvXo0UOSNHr0aL399tu68cYbfR4jOTnZZ9g4m3feeUcbNmzQ22+/rSVLluihhx7Sp59+qj59+ni2+e677yRJXbt29fv4AKxHYAGgPXv2aODAgS1u07Vr16D+mPs6x4EDBzxhRZJ69OihkpKSZo8xbNiwZu/k+fTTTxv9/Mknn+iiiy5STEyMJGn48OEaPny4Zs2apd69e+uNN95QQUGBZ/vt27erZ8+epo3dAWAuuoQAyOl0au/evSopKWkyGDWczpGfn68vv/zSZyvLvn37VFBQoB07duiVV17RkiVLdPfdd+vTTz/Vk08+qc8++0z79u3TX/7yFx06dEj9+/dvtP+HH36oUaNGBVQXAOsRWADorrvu0scff6zMzEzLAouvc3Tv3r1Ri0pJSUmzg2ol12DZSy+9VK+++mqTzyZOnKgTJ04oOztb06ZN0913361bb71VnTp10gcffKBrrrlG/fr108MPP6yFCxdq9OjRnn1ramq0Zs0aTZ061cQrBmAmZroFYJuTJ0+qf//+KioqUmJiorKysrRhwwbPnUW+rF27Vr/5zW+0fft2RUe7/j/XiBEjNHToUC1evDigOp599lm98cYbevvttwPaH4D1GMMCwDbt2rXTwoULNXLkSDmdTt1///0thhVJGjNmjHbu3KmSkhKlp6ebUkdsbKyWLFliyrEAWIMWFgCtXrAtLADCH4EFAACEPQbdAgCAsEdgAQAAYY/AAgAAwh6BBQAAhD0CCwAACHsEFgAAEPYILAAAIOwRWAAAQNgjsAAAgLBHYAEAAGHv/wNOG1F3aLfJzgAAAABJRU5ErkJggg==\n"},"metadata":{}}]},{"cell_type":"markdown","source":["## Caso de onda tipo $sinc()$: comparación cálculo numérico vs analítico"],"metadata":{"id":"6U1zr-2ksW4s"}},{"cell_type":"markdown","source":["### Función analítica $\\gamma (\\tau)$ para una distribución espectral tipo salto"],"metadata":{"id":"1fNKIaqzw0Rh"}},{"cell_type":"markdown","source":["![image.png](data:image/png;base64,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)"],"metadata":{"id":"plJW_4w3ttE2"}},{"cell_type":"code","source":["def gamma_sinc_analitica(tau,ω_0):\n","  '''\n","  Podemos obtener gamma analítica para la distribución espectral de tipo salto\n","  Sabiendo que su transformada de Fourier, el pulso E(t), es una función proporcional\n","  a sinc(t).\n","  Definida la onda tipo sinc(t), la ventana de la distribución escalar es:\n","  delta_nu=1/(pi*sigma), donde el mínimo de la onda sinc() ocurre en σ*np.pi\n","  '''\n","  delta_nu=1.0/(σ*np.pi) # en t=σ*np.pi ocurre el mínimo de la onda sinc()\n","  return np.sinc(np.pi*delta_nu*tau*Δt/np.pi)*np.exp(1j*ω_0*tau*Δt) #np.sin(np.pi*delta_nu*tau*Δt)*np.exp(1j*ω_0*tau*Δt)/(np.pi*delta_nu*tau*Δt)\n","\n","Gamma_sinc =[]\n","for tau in range(0, n*N - n + 1):\n","  Gamma_sinc.append(gamma_sinc_analitica(tau,ω_0))\n","\n","Gamma_sinc=np.array(Gamma_sinc)"],"metadata":{"id":"BZATFBW-xTdz"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["### Representación de $\\gamma (\\tau)$"],"metadata":{"id":"3eSLnr1dxHfo"}},{"cell_type":"code","source":["if (tipo_onda=='sinc'):\n","  t_max=np.argmax(Gamma)\n","  texpand=Δt*(np.linspace(0,Gamma.shape[0],Gamma.shape[0])-t_max)\n","  plt.plot(texpand,np.abs(gamma),label=r'|$\\gamma(\\tau)|$ numérica' ,\n","                                color='red',linestyle='-')\n","  texpand=Δt*(np.linspace(0,Gamma.shape[0],Gamma.shape[0]))\n","  plt.plot(texpand,np.abs(Gamma_sinc),label=r'|$\\gamma(\\tau)|$ analítica',\n","                                color='blue',linestyle='--')\n","\n","  plt.axvline(np.pi*σ,color='grey',linestyle='--',label=r'$1/\\Delta \\nu=\\pi \\sigma$')\n","  plt.xlabel(r'$\\tau-\\tau_0$ (ps)')\n","  #plt.ylabel(r'$\\gamma(\\tau)$')\n","  plt.xlim(0,5*np.pi*σ)\n","  plt.legend()\n","  plt.show()"],"metadata":{"id":"pvutgPN186JN"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# Interferencias: franjas de Young"],"metadata":{"id":"ub2w4ZjaszqB"}},{"cell_type":"markdown","source":["Intensidad franjas de Young para espectro simétrico:\n","\n","$$I=I_1+I_2+2\\sqrt{I_1 I_2}\\gamma_c(\\tau_s+\\tau) \\cos(\\delta)$$ donde $\\delta=\\omega_0(\\tau_s+\\tau)$"],"metadata":{"id":"7KHu05U6hX5-"}},{"cell_type":"markdown","source":["Siendo $$\\gamma_c(\\tau) = \\int_{-\\infty}^{+\\infty}g(x)cos(2\\pi \\, x \\, \\tau)\\,dx$$ donde $x=\\nu -\\nu_0$"],"metadata":{"id":"LG-DZo2_gvC-"}},{"cell_type":"markdown","source":["## Observación en función de las coordenadas $x,y$ de la pantalla."],"metadata":{"id":"eTZ1bSydshTY"}},{"cell_type":"markdown","source":["![image.png](data:image/png;base64,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)"],"metadata":{"id":"kGcdc_ipzoc3"}},{"cell_type":"markdown","source":["Delta se puede escribir como: $\\delta=\\omega_0(\\tau_s+\\tau)=\\dfrac{2\\pi \\, n}{\\lambda_0}(\\Delta_s+\\Delta)$\n","donde\n","+ $\\Delta_s=\\overline{SS_2}-\\overline{SS_1}$\n","+ $\\Delta_s=\\overline{S_2P}-\\overline{S_1P}$\n","\n","\n","Aproximaciones:\n","1. $x_s,d << D_1$ : fuente \"casi\" alineada con el eje $z$. Distancia entre aperturas pequeña en comparación con la distancia entre el plano de la fuente y el de las aperturas.\n","2. $x,y,d << D_2$ : puntos de observación cercanos al eje $z$. Distancia entre aperturas pequeña en comparación con la distancia entre el plano de la de las aperturas y el plano de observación.\n","\n","Utilizando estas aproximaciones se llega a que\n","+ $\\Delta_s=\\dfrac{x_s d}{D_1}$\n","+ $\\Delta_s=\\dfrac{x d}{D_2}$\n","\n","---\n","*En el código $(x,y)=(x_p,y_p)$*"],"metadata":{"id":"u1Ts2nFHx-wn"}},{"cell_type":"markdown","source":["## Ejemplo $g(\\nu)\\rightarrow$ Tipo \"perfil cuadrado\" (simétrico)"],"metadata":{"id":"4ISaf6YksUSQ"}},{"cell_type":"markdown","source":["![image.png](data:image/png;base64,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)"],"metadata":{"id":"-IPsgFunnuZM"}},{"cell_type":"markdown","source":["$\\gamma(\\tau)=e^{\\imath 2 \\pi \\nu_0 \\tau} \\dfrac{\\sin{(\\pi \\Delta \\nu \\, \\tau)}}{\\pi \\Delta \\nu \\, \\tau}$\n","\n","$\\implies \\gamma_c(\\tau)=\\dfrac{\\sin{(\\pi \\Delta \\nu \\, \\tau)}}{\\pi \\Delta \\nu \\, \\tau}$"],"metadata":{"id":"Oc-EILeqzt-R"}},{"cell_type":"markdown","source":["## Función de Python para calcular la intensidad de las franjas de Young (aproximación)"],"metadata":{"id":"CiEdVeSX1Dve"}},{"cell_type":"code","source":["import numpy as np\n","\n","def intensidad_young(xp,I1,I2,lambda_nm,n,d,D1,D2,xs,gamma_tipo='onda plana'):\n","  # Longitud de onda, k y frecuencia angular\n","  c=299792458.0     #m/s\n","  lambda0=lambda_nm*1e-9\n","  k = 2.0 * np.pi / lambda0\n","  omega0=c*k\n","\n","  # Cálculo de delta\n","  delta= (2.0*np.pi*n/lambda0)*(xs*d/D1+xp*d/D2)\n","\n","  # Se selecciona el tipo de onda (gamma_c)\n","  # Por defecto 'onda plana'\n","  # Se pueden añadir tantas como se quiera\n","  if(gamma_tipo=='onda plana'):\n","    gamma_c=1.0\n","\n","  if(gamma_tipo=='perfil cuadrado'):\n","    tau=delta/omega0\n","    delta_lambda=20.0 #nm # delta_lambda=0.0 --> onda plana\n","    lambda_i=lambda0-delta_lambda*1e-9\n","    lambda_f=lambda0+delta_lambda*1e-9\n","    delta_nu =c*(lambda_i-lambda_f)/(lambda_f*lambda_i)\n","    gamma_c= np.sinc(np.pi*delta_nu*tau/np.pi) #np.sinc(x)=sin(pi*x)/(pi*x)\n","\n","  # Cálculo de la intensidad\n","  return I1+I2+2.0*np.sqrt(I1*I2)*gamma_c*np.cos(delta)"],"metadata":{"id":"dIwVLUsVe7L7"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# Parámetros geométricos"],"metadata":{"id":"31WL-PawSmg-"}},{"cell_type":"markdown","source":["+ $D_1$   (distancia entre el plano de la fuente en $S$ y el plano que contiene a las aperturas)\n","+ $D_2$  (distancia entre el plano que contiene a las aperturas y la \"pantalla\" de observación)\n","+ $d$  (distancia entre las aperturas)\n","+ $x_s$  (coordenada de la fuente en el eje $x$ )\n","+ $\\lambda$ (longitud de onda)\n","+ $n$ (índice de refracción del medio)"],"metadata":{"id":"_r612Tx2Q3eY"}},{"cell_type":"code","source":["# Intensidades\n","I1,I2=1.0,1.0 # Unidades arbitrarias\n","\n","# Índice de refracción\n","n=1.0\n","\n","# Distancias\n","D1=1.0  # m\n","D2=1.0  # m\n","d=0.001 # m\n","xs=0.0 # m\n","\n","# Parámetros electromagnéticos\n","c=299792458.0     #m/s\n","lambda_nm = 600.0 # nm\n","lambda0=lambda_nm*1e-9\n","k = 2.0 * np.pi / lambda0\n","omega0=c*k\n","\n","print(\"Frecuencia central=\",np.round(omega0*1e-12/(2.0*np.pi),2),\"THz\")\n","\n","# gamma_c\n","gamma_tipo='perfil cuadrado'"],"metadata":{"id":"zeQjDEdwSplf"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# Experimento de Young en la dirección $x$ ($y=0$)"],"metadata":{"id":"Hs2F_KgvDsaS"}},{"cell_type":"markdown","source":["## Cálculo de la intensidad"],"metadata":{"id":"x6yoGDdvZ9R7"}},{"cell_type":"code","source":["def calc_intensity_pattern():\n","    Xp=400\n","    m=10\n","    xpm = (2*m+1)*lambda0*D2/(2.0*d)-xs*D2/D1\n","    diff_pattern = []\n","    for i in range(Xp):\n","      print(\"x iteration\",i,' of ',Xp)\n","      xp=xpm * (Xp - 2 * i) / Xp\n","      I_analytic=intensidad_young(xp,I1,I2,lambda_nm,n,d,D1,D2,xs,\n","                                  gamma_tipo=gamma_tipo)\n","      diff_pattern.append([xp,I_analytic])\n","    return np.array(diff_pattern)\n","\n","# Calculo de la intensidad\n","intensity_pattern=calc_intensity_pattern()"],"metadata":{"id":"wPzGpwenEAp2"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Figura estática"],"metadata":{"id":"mgEJ9uPPr5y-"}},{"cell_type":"code","source":["import matplotlib.pyplot as plt\n","x=intensity_pattern[:,0]\n","y_analytic=intensity_pattern[:,1]\n","plt.plot(x,y_analytic,label='Analytic',color='red')\n","\n","plt.axvline((2*0+1)*lambda0*D2/(2.0*d)-xs*D2/D1,color='grey',linestyle='--',label=r'$x_{min}(m=0)$')\n","plt.axvline((1)*lambda0*D2/d-xs*D2/D1,color='orange',linestyle='--',label=r'$x_{max}(m=1)$')\n","plt.xlabel(r'$x$ (m)')\n","plt.ylabel('Intensity')\n","plt.legend()\n","plt.show()"],"metadata":{"id":"T6Py4-VcDspb"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["# Experimento de Young plano $XY$"],"metadata":{"id":"40xc5XwuN2dy"}},{"cell_type":"markdown","source":["## Cálculo de la intensidad"],"metadata":{"id":"c-6vG45PaHdx"}},{"cell_type":"code","source":["def calc_intensity_pattern_2D():\n","    Xp,Yp=400,400\n","    m=10\n","    xpm = (2*m+1)*lambda0*D2/(2.0*d)-xs*D2/D1\n","    ypm = xpm\n","    diff_pattern = []\n","    for i in range(Xp):\n","      print(\"x iteration\",i,' of ',Xp)\n","      xp=xpm * (Xp - 2 * i) / Xp\n","      for j in range(Yp):\n","        yp=ypm * (Yp - 2 * j) / Yp\n","        I_analytic=intensidad_young(xp,I1,I2,lambda_nm,n,d,D1,D2,xs,\n","                                  gamma_tipo=gamma_tipo)\n","        diff_pattern.append([xp,yp,I_analytic])\n","    return np.array(diff_pattern)\n","\n","intensity_pattern_2D=calc_intensity_pattern_2D()"],"metadata":{"id":"qm2CKK5dro-J"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Figura estática"],"metadata":{"id":"4qE5xkHUU9Ry"}},{"cell_type":"code","source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","# Generate some sample data (replace this with your numpy array)\n","data =intensity_pattern_2D\n","\n","# Extract x, y, and the value from the data\n","x = data[:, 0]\n","y = data[:, 1]\n","value = data[:, 2]\n","\n","# Reshape the value to a 2D grid for contour plotting\n","x_unique = np.unique(x)\n","y_unique = np.unique(y)\n","X, Y = np.meshgrid(x_unique, y_unique)\n","Z = value.reshape(len(y_unique), len(x_unique))\n","\n","\n","# Create a contour plot\n","plt.figure(figsize=(12, 2))\n","max_value=np.max(Z)/1.0\n","contour = plt.contourf(X, Y,  np.rot90(Z), levels=500, cmap='viridis',\n","                       vmax=max_value)\n","plt.colorbar(contour)  # Use scientific notation for colorbar\n","\n","\n","plt.xlabel('X (m)')\n","plt.ylabel('Y (m)')\n","plt.title('Intensity')\n","plt.show()\n"],"metadata":{"id":"i1N1KpD4NaGo"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Figura dinámica"],"metadata":{"id":"qGrtluxkT2Wf"}},{"cell_type":"code","source":["import matplotlib.pyplot as plt\n","import numpy as np\n","import ipywidgets as widgets\n","from ipywidgets import interactive\n","from ipywidgets import SelectionSlider\n","\n","def plot_function_with_sliders(f, labels, x_min, y_min,ref_x,max_y,value_scale):\n","    # Extract the parameter names from the function signature, excluding 'x'\n","    # and the last\n","    parameters = list(f.__code__.co_varnames)[1:f.__code__.co_argcount-1]\n","\n","    # Create sliders for each parameter\n","    # Define the base, min exponent, and max exponent for the slider\n","    sliders = {}\n","    i=0\n","    for param in parameters:\n","        #print(\"parameter=\",param)\n","        #print(\"[initial value, min, max, step]=\",value_scale[i])\n","        sliders[param] = widgets.FloatSlider(value=value_scale[i][0],\n","                                             min=value_scale[i][1],\n","                                             max=value_scale[i][2],\n","                                             step=value_scale[i][3],\n","                                             description=param,\n","                                             readout_format='.4f')\n","        i+=1\n","    # Create sliders for x_max and y_max\n","    #print(\"x max\")\n","    #print(\"[initial value, min, max, step]=\",value_scale[i])\n","    x_max_slider = widgets.FloatSlider(value=value_scale[i][0],\n","                                       min=value_scale[i][1],\n","                                       max=value_scale[i][2],\n","                                       step=value_scale[i][3],\n","                                       description='x scale',\n","                                       readout_format='.4f')\n","    i+=1\n","    #print(\"y max\")\n","    #print(\"[initial value, min, max, step]=\",value_scale[i])\n","    y_max_slider = widgets.FloatSlider(value=value_scale[i][0],\n","                                       min=value_scale[i][1],\n","                                       max=value_scale[i][2],\n","                                       step=value_scale[i][3],\n","                                       description='y scale',\n","                                       readout_format='.4f')\n","\n","    # Define a function to update the plot\n","    def update_plot(**kwargs):\n","        N=200\n","        # Extract x, y, and the value from the data\n","        x = np.linspace(x_min-x_max_slider.value, abs(x_min)+x_max_slider.value, N)\n","        y = np.linspace(y_min-y_max_slider.value, abs(y_min)+y_max_slider.value, N)\n","\n","        # Pass slider values as keyword arguments to the input function\n","        params = {param: slider.value for param, slider in sliders.items()}\n","        params['gamma_tipo'] = value_scale[-1][0]\n","\n","        # Cálculo de la función\n","        Z =f(x, **params)\n","\n","        # Reshape the value to a 2D grid for contour plotting\n","        x_unique = np.unique(x)\n","        y_unique = np.unique(y)\n","        X, Y = np.meshgrid(x_unique, y_unique)\n","\n","        # Repeat the row N times to create a (N,N) array\n","        Z = np.tile(Z, (N, 1))\n","\n","        # Result as a (N, N) array\n","        Z = Z.T  # Transpose the array\n","        Z = Z.reshape(len(y_unique), len(x_unique))\n","\n","        # Create a contour plot\n","        plt.figure(figsize=(12, 2))\n","        max_value=np.max(Z)\n","        print(\"Valor mínimo=\",np.min(Z))\n","        print(\"Valor máximo=\",max_value)\n","        contour = plt.contourf(X, Y,  np.rot90(Z), levels=50, cmap='viridis')\n","\n","        # Set the minimum and maximum values for the colorbar\n","        contour.set_clim(0.0,max_value)  # Set the desired min and max values here\n","\n","        plt.colorbar(contour)\n","\n","        plt.xlim((x_min-x_max_slider.value)/ref_x, (abs(x_min)+x_max_slider.value)/ref_x)\n","        plt.ylim((y_min-y_max_slider.value)/ref_x, (abs(y_min)+y_max_slider.value)/ref_x)\n","        plt.xlabel(labels[0])\n","        plt.ylabel(labels[1])\n","        plt.title('Intensity')\n","        plt.show()\n","\n","    # Create an interactive plot with the sliders\n","    interactive_plot = interactive(update_plot, **sliders, x_max=x_max_slider, y_max=y_max_slider)\n","    return interactive_plot"],"metadata":{"id":"HXhPvAk_T2cu"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["# Example of an input function\n","function=intensidad_young\n","\n","\n","# Define labels, axis limits, and initial parameter values\n","labels = [r'$x(m)$', r'$y(m)$']\n","m=10\n","xpm = (2*m+1)*lambda0*D2/(2.0*d)-xs*D2/D1\n","x_min = -xpm\n","y_min = -xpm\n","max_y = 1.0\n","ref_x = 1.0 #lambda0*D2/d\n","# value_scale (each): [initial value, min,max,step]\n","value_scale=[[I1,1e-4*I1,10*I1,0.01*I1], # I1\n","             [I2,1e-4*I2,10*I2,0.01*I2], # I2\n","             [lambda_nm,0.1*lambda_nm,3.0*lambda_nm,0.1*lambda_nm],      # lambda (wavelength) in nm\n","             [n,1.0,3.5,0.1],           # n\n","             [d,0.1*d,10*d,0.05*d],     # d\n","             [D1,0.1*D1,10*D1,0.05*D1], # D1\n","             [D2,0.1*D2,10*D2,0.05*D2], # D2\n","             [xs,0.0,1e-2,1e-3],        # xs\n","             [-xpm,0.1*xpm,10*xpm,0.05*xpm],    # x scale\n","             [-xpm,0.1*xpm,10*xpm,0.05*xpm],    # y scale\n","             [gamma_tipo]]       # tipo gamma\n","\n","# Create the interactive plot\n","interactive_plot = plot_function_with_sliders(function,\n","                                              labels,\n","                                              x_min, y_min,\n","                                              ref_x,max_y,\n","                                              value_scale)\n","\n","# Display the interactive plot\n","interactive_plot"],"metadata":{"id":"-yGvE2xSXuHI"},"execution_count":null,"outputs":[]}]}