FI-static.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "from matplotlib.patches import Rectangle\n",
    "import matplotlib.patches as patches\n",
    "from IPython.display import HTML\n",
    "from matplotlib.widgets import Slider\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dcc36ef63b1d47a98b19ae84b328043d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatLogSlider(value=2.0, description='Compress wave packet', max=2.0, min=-10.0, step=0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "from matplotlib.patches import Rectangle\n",
    "import matplotlib.patches as patches\n",
    "from IPython.display import HTML\n",
    "from matplotlib.widgets import Slider\n",
    "import ipywidgets as widgets\n",
    "\n",
    "      \n",
    "# functions that will used to interfere two waves at the second beam splitter\n",
    "# interfere_amplitudes calcualtes the effective final amplitude given two waves with their amplitudes and phases\n",
    "# interfere_phases calcualtes the effective final phase given two waves with their amplitudes and phases\n",
    "def interfere_amplitudes(a1,phi1,a2,phi2):\n",
    "    return np.sqrt(np.power((a1*np.sin(phi1)+a2*np.sin(phi2)),2)+np.power((a1*np.cos(phi1)+a2*np.cos(phi2)),2))\n",
    "\n",
    "def interfere_phases(a1,phi1,a2,phi2):\n",
    "    return np.arctan((a1*np.sin(phi1)+a2*np.sin(phi2))/(a1*np.cos(phi1)+a2*np.cos(phi2)))\n",
    "\n",
    "def sym (lim1,lim2,si):\n",
    "    return si*lim1-lim2*0**si\n",
    "    \n",
    "def linspace(lim1,lim2,si):\n",
    "    return np.linspace(sym (lim1,lim2,si),sym(lim2,lim1,si),100)\n",
    "\n",
    "# si = 0 creates left side of the Franson interferometer, si = 0 creates right side of the Franson interferometer\n",
    "def create_figure(a,vg,c,t,ax,width1,width2,xglass,eta,k,Amp,t1,t2):\n",
    "    \n",
    "    \n",
    "    r1 = np.sqrt(1-t1*t1); # reflectivity of the first beam splitter\n",
    "    r2 = np.sqrt(1-t2*t2); # reflectivity of the first beam splitter\n",
    "    \n",
    "    # RIGHT\n",
    "    si=1   \n",
    "    width=width2\n",
    "    \n",
    "    x1r = linspace(0, 1,si)\n",
    "    x2r = linspace(1, xglass,si)\n",
    "    x3r = linspace(xglass, xglass+width,si)\n",
    "    x4r = linspace(xglass+width,5,si)\n",
    "    x5r = linspace(1,5,si)\n",
    "    x6r = linspace(5,9,si)\n",
    "    y1r = np.linspace(0,4,100)\n",
    "    y2r = np.linspace(0,4,100)\n",
    "    y3r = np.linspace(4,8,100)\n",
    "    # preparing light waves\n",
    "    rx1,=ax.plot([], [], 'r')\n",
    "    rx2,=ax.plot([], [], 'r')\n",
    "    rx3,=ax.plot([], [], 'b')\n",
    "    rx4,=ax.plot([], [], 'r')\n",
    "    rx5,=ax.plot([], [], 'r')\n",
    "    rx6,=ax.plot([], [], 'r')\n",
    "    ry1,=ax.plot([], [], 'r')\n",
    "    ry2,=ax.plot([], [], 'r')\n",
    "    ry3,=ax.plot([], [], 'r')  \n",
    "    \n",
    "       \n",
    "    # the interferometer paths Syntax: (xdata), (ydata) for the various points\n",
    "    rup = plt.Line2D((sym(1,9,si),sym(9,1,si)),(4,4),color=\"whitesmoke\")\n",
    "    rdo = plt.Line2D((sym(0,5,si),sym(5,0,si)),(0,0),color=\"whitesmoke\")\n",
    "    rle = plt.Line2D((sym(1,1,si),sym(1,1,si)),(0,4),color=\"whitesmoke\")\n",
    "    rri = plt.Line2D((sym(5,5,si),sym(5,5,si)),(0,8),color=\"whitesmoke\")\n",
    " \n",
    "\n",
    "    #mirrors\n",
    "    rm1 = plt.Line2D((-(-1)**si*0.5,-(-1)**si*1.5),(3.5,4.5),color=\"black\") # mirror at top left corner\n",
    "    rm2 = plt.Line2D((-(-1)**si*4.5,-(-1)**si*5.5),(-0.5,0.5),color=\"black\") # mirror at bootom right corner\n",
    "\n",
    "    # beam spitters  (For calcualtions, first beam splitter will have reflecting surface on the left side, Seond will have reflectivng surface on the right side)\n",
    "    rbs1 = plt.Line2D((-(-1)**si*0.5,-(-1)**si*1.5),(-0.5,0.5),color=\"grey\",linestyle='dashed',lw=2.5)\n",
    "    rbs2 = plt.Line2D((-(-1)**si*4.5,-(-1)**si*5.5),(3.5,4.5),color=\"grey\",linestyle='dashed',lw=2.5)\n",
    "\n",
    "    \n",
    "    # adding elements to the figures \n",
    "    # creating the glass slide in the lower arm of the Mach-Zehnder\n",
    "    rpatch = patches.Rectangle((si*xglass-(xglass+width)*0**si,-0.625), width, 1.25, facecolor='white',edgecolor='black')\n",
    "    rglass=ax.add_patch(rpatch)\n",
    "    ax.add_line(rup)\n",
    "    ax.add_line(rdo)\n",
    "    ax.add_line(rle)\n",
    "    ax.add_line(rri)\n",
    "    ax.add_line(rm1)\n",
    "    ax.add_line(rm2)\n",
    "    ax.add_line(rbs1)\n",
    "    ax.add_line(rbs2)\n",
    "    \n",
    "    \n",
    "    # creating incoming sine wave    \n",
    "    rx1.set_data(x1r, Amp*np.sin(k*(x1r+(-1)**si*c*t))*np.exp(-a*(x1r+(-1)**si*vg*t)**2))\n",
    "\n",
    "    # creating the wave transmitted through the first beam splitter    \n",
    "    rx2.set_data(x2r, t1*Amp*np.sin(k*(x2r+(-1)**si*c*t))*np.exp(-a*(x2r+(-1)**si*vg*t)**2))\n",
    "\n",
    "    # creating the wave travelling inside the glass slide    \n",
    "    rx3.set_data(x3r,t1*Amp*np.sin(eta*k*(x3r+(-1)**si*xglass+(-1)**si*c*t/eta)-(-1)**si*k*xglass)*np.exp(-a*(x3r+(-1)**si*vg*t+(eta-1)*(x3r+(-1)**si*xglass))**2))\n",
    "\n",
    "    # creating the wave emerging from the glass slide and htiing mirror m2    \n",
    "    rx4.set_data(x4r,t1*Amp*np.sin(k*(x4r+(-1)**si*c*t) -(-1)**si*(eta-1)*k*width)*np.exp(-a*(x4r+(-1)**si*vg*t-(-1)**si*(eta-1)*width)**2))\n",
    "\n",
    "    # creating the wave reflecting off the first beamsplitter (pi phase shift will occur on reflection here)    \n",
    "    ry1.set_data(-(-1)**si -(-1)**si*r1*Amp*np.sin(k*(y1r-0-c*t) + np.pi + k*1)*np.exp(-a*(1+y1r-0-vg*t)**2),y1r)\n",
    "\n",
    "    # creating the wave reflecting off the mirror m2 (pi phase shift will occur on reflection here)    \n",
    "    ry2.set_data(-(-1)**si*5 -(-1)**si*t1*Amp*np.sin(k*(y2r-0-c*t) + np.pi + k*5 + (eta-1)*k*width )*np.exp(-a*(5+(eta-1)*width+y2r-0-vg*t)**2),y2r)\n",
    "\n",
    "    # creating the wave reflecting off the mirror m1 (pi phase shift will occur on reflection here)    \n",
    "    rx5.set_data(x5r,4+r1*Amp*np.sin(k*(x5r+(-1)**si*c*t)-(-1)**si* k*4)*np.exp(-a*(-(-1)**si*4+x5r+(-1)**si*vg*t)**2))\n",
    "\n",
    "    # creating the wave emerging on the horizontal path after the second beam splitter \n",
    "    #(pi phase shift occurs for the wave in the lower path that is reflected to the right)    \n",
    "    rx6.set_data(x6r,4 + Amp*interfere_amplitudes(r1*t2*np.exp(-a*(-(-1)**si*4+x6r+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*r2*np.exp(-a*(-(-1)**si*4-(-1)**si*(eta-1)*width+x6r+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width)*np.sin(k*(x6r+(-1)**si*5+(-1)**si*c*t)+interfere_phases(r1*t2*np.exp(-a*(-(-1)**si*4+x6r+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*r2*np.exp(-a*(-(-1)**si*4-(-1)**si*(eta-1)*width+x6r+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width)))\n",
    "\n",
    "    # creating the wave emerging on the vertical path after the second beam splitter \n",
    "    #(NO phase shift occurs when the wave moving right is reflected upwards by the beam splitter. \n",
    "    # This is because we had chosen the convention that the second beam splitter has mirrored surface on the right hand side)\n",
    "    ry3.set_data(-(-1)**si*5+Amp*interfere_amplitudes(r1*r2*np.exp(-a*(-(-1)**si*5-(-1)**si*y3r+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*t2*np.exp(-a*(-(-1)**si*5-(-1)**si*(eta-1)*width-(-1)**si*y3r+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width-(-1)**si*np.pi)*np.sin(k*((-1)**si*y3r+(-1)**si*4+(-1)**si*c*t)+interfere_phases(r1*r2*np.exp(-a*(-(-1)**si*5-(-1)**si*y3r+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*t2*np.exp(-a*(-(-1)**si*5-(-1)**si*(eta-1)*width-(-1)**si*y3r+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width-(-1)**si*np.pi)),y3r)\n",
    "    \n",
    "    \n",
    "    #LEFT\n",
    "    si=0  \n",
    "    width=width1\n",
    "    \n",
    "    x1l = linspace(0, 1,si)\n",
    "    x2l = linspace(1, xglass,si)\n",
    "    x3l = linspace(xglass, xglass+width,si)\n",
    "    x4l = linspace(xglass+width,5,si)\n",
    "    x5l = linspace(1,5,si)\n",
    "    x6l = linspace(5,9,si)\n",
    "    y1l = np.linspace(0,4,100)\n",
    "    y2l = np.linspace(0,4,100)\n",
    "    y3l = np.linspace(4,8,100)\n",
    "    # preparing light waves\n",
    "    lx1,=ax.plot([], [], 'r')\n",
    "    lx2,=ax.plot([], [], 'r')\n",
    "    lx3,=ax.plot([], [], 'b')\n",
    "    lx4,=ax.plot([], [], 'r')\n",
    "    lx5,=ax.plot([], [], 'r')\n",
    "    lx6,=ax.plot([], [], 'r')\n",
    "    ly1,=ax.plot([], [], 'r')\n",
    "    ly2,=ax.plot([], [], 'r')\n",
    "    ly3,=ax.plot([], [], 'r')  \n",
    "    \n",
    "       \n",
    "    # the interferometer paths Syntax: (xdata), (ydata) for the various points\n",
    "    lup = plt.Line2D((sym(1,8,si),sym(8,1,si)),(4,4),color=\"whitesmoke\")\n",
    "    ldo = plt.Line2D((sym(0,5,si),sym(5,0,si)),(0,0),color=\"whitesmoke\")\n",
    "    lle = plt.Line2D((sym(1,1,si),sym(1,1,si)),(0,4),color=\"whitesmoke\")\n",
    "    lri = plt.Line2D((sym(5,5,si),sym(5,5,si)),(0,9),color=\"whitesmoke\")\n",
    " \n",
    "\n",
    "    #mirrors\n",
    "    lm1 = plt.Line2D((-(-1)**si*0.5,-(-1)**si*1.5),(3.5,4.5),color=\"black\") # mirror at top left corner\n",
    "    lm2 = plt.Line2D((-(-1)**si*4.5,-(-1)**si*5.5),(-0.5,0.5),color=\"black\") # mirror at bootom right corner\n",
    "\n",
    "    # beam spitters  (For calcualtions, first beam splitter will have reflecting surface on the left side, Seond will have reflectivng surface on the right side)\n",
    "    lbs1 = plt.Line2D((-(-1)**si*0.5,-(-1)**si*1.5),(-0.5,0.5),color=\"grey\",linestyle='dashed',lw=2.5)\n",
    "    lbs2 = plt.Line2D((-(-1)**si*4.5,-(-1)**si*5.5),(3.5,4.5),color=\"grey\",linestyle='dashed',lw=2.5)\n",
    "\n",
    "    \n",
    "    # adding elements to the figures \n",
    "    # creating the glass slide in the lower arm of the Mach-Zehnder\n",
    "    lpatch = patches.Rectangle((si*xglass-(xglass+width)*0**si,-0.625), width, 1.25, facecolor='white',edgecolor='black')\n",
    "    lglass=ax.add_patch(lpatch)\n",
    "    ax.add_line(lup)\n",
    "    ax.add_line(ldo)\n",
    "    ax.add_line(lle)\n",
    "    ax.add_line(lri)\n",
    "    ax.add_line(lm1)\n",
    "    ax.add_line(lm2)\n",
    "    ax.add_line(lbs1)\n",
    "    ax.add_line(lbs2)\n",
    "    \n",
    "    # creating incoming sine wave    \n",
    "    lx1.set_data(x1l, Amp*np.sin(k*(x1l+(-1)**si*c*t))*np.exp(-a*(x1l+(-1)**si*vg*t)**2))\n",
    "\n",
    "    # creating the wave transmitted through the first beam splitter    \n",
    "    lx2.set_data(x2l, t1*Amp*np.sin(k*(x2l+(-1)**si*c*t))*np.exp(-a*(x2l+(-1)**si*vg*t)**2))\n",
    "\n",
    "    # creating the wave travelling inside the glass slide    \n",
    "    lx3.set_data(x3l,t1*Amp*np.sin(eta*k*(x3l+(-1)**si*xglass+(-1)**si*c*t/eta)-(-1)**si*k*xglass)*np.exp(-a*(x3l+(-1)**si*vg*t+(eta-1)*(x3l+(-1)**si*xglass))**2))\n",
    "\n",
    "    # creating the wave emerging from the glass slide and htiing mirror m2    \n",
    "    lx4.set_data(x4l,t1*Amp*np.sin(k*(x4l+(-1)**si*c*t) -(-1)**si*(eta-1)*k*width)*np.exp(-a*(x4l+(-1)**si*vg*t-(-1)**si*(eta-1)*width)**2))\n",
    "\n",
    "    # creating the wave reflecting off the first beamsplitter (pi phase shift will occur on reflection here)    \n",
    "    ly1.set_data(-(-1)**si -(-1)**si*r1*Amp*np.sin(k*(y1l-c*t) + np.pi + k*1)*np.exp(-a*(1+y1l-vg*t)**2),y1l)\n",
    "\n",
    "    # creating the wave reflecting off the mirror m2 (pi phase shift will occur on reflection here)    \n",
    "    ly2.set_data(-(-1)**si*5 -(-1)**si*t1*Amp*np.sin(k*(y2l-c*t) + np.pi + k*5 + (eta-1)*k*width )*np.exp(-a*(5+(eta-1)*width+y2l-vg*t)**2),y2l)\n",
    "\n",
    "    # creating the wave reflecting off the mirror m1 (pi phase shift will occur on reflection here)    \n",
    "    lx5.set_data(x5l,4+r1*Amp*np.sin(k*(x5l+(-1)**si*c*t)-(-1)**si*k*4)*np.exp(-a*(-(-1)**si*4+x5l+(-1)**si*vg*t)**2))\n",
    "\n",
    "    # creating the wave emerging on the horizontal path after the second beam splitter \n",
    "    #(pi phase shift occurs for the wave in the lower path that is reflected to the right)    \n",
    "    lx6.set_data(x6l,4 + Amp*interfere_amplitudes(r1*t2*np.exp(-a*(-(-1)**si*4+x6l+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*r2*np.exp(-a*(-(-1)**si*4-(-1)**si*(eta-1)*width+x6l+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width)*np.sin(k*(x6l+(-1)**si*5+(-1)**si*c*t)+interfere_phases(r1*t2*np.exp(-a*(-(-1)**si*4+x6l+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*r2*np.exp(-a*(-(-1)**si*4-(-1)**si*(eta-1)*width+x6l+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width)))\n",
    "\n",
    "    # creating the wave emerging on the vertical path after the second beam splitter \n",
    "    #(NO phase shift occurs when the wave moving right is reflected upwards by the beam splitter. \n",
    "    # This is because we had chosen the convention that the second beam splitter has mirrored surface on the right hand side)\n",
    "    ly3.set_data(-(-1)**si*5+Amp*interfere_amplitudes(r1*r2*np.exp(-a*(-(-1)**si*5-(-1)**si*y3l+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*t2*np.exp(-a*(-(-1)**si*5-(-1)**si*(eta-1)*width-(-1)**si*y3l+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width-(-1)**si*np.pi)*np.sin(k*((-1)**si*y3l+(-1)**si*4+(-1)**si*c*t)+interfere_phases(r1*r2*np.exp(-a*(-(-1)**si*5-(-1)**si*y3l+(-1)**si*vg*t)**2),-(-1)**si*k*9,t1*t2*np.exp(-a*(-(-1)**si*5-(-1)**si*(eta-1)*width-(-1)**si*y3l+(-1)**si*vg*t)**2),-(-1)**si*k*9 -(-1)**si*(eta-1)*k*width-(-1)**si*np.pi)),y3l)\n",
    "    \n",
    "    \n",
    "    \n",
    "    #COMMON\n",
    "    ax.add_patch(plt.Circle((0, 0), .125))\n",
    "    \n",
    "    # Axis scaling turned on so that aspect ratio is maintained\n",
    "    plt.axis(\"scaled\")\n",
    "    # Axis turned off \n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "\n",
    "style = {'description_width': 'initial'}    #to be abto to show full description of the sliders\n",
    "@widgets.interact(a=widgets.FloatLogSlider(\n",
    "    value=2,\n",
    "    base=10,\n",
    "    min=-10, # max exponent of base\n",
    "    max=2, # min exponent of base\n",
    "    step=0.2, # exponent step\n",
    "    description='Compress wave packet',style=style\n",
    "    ),vg_factor=widgets.FloatSlider(\n",
    "    value=1,\n",
    "    min=0,\n",
    "    max=1, \n",
    "    step=0.001, \n",
    "    description='f (where group velocity = f x c)',style=style\n",
    "    ),t=widgets.FloatSlider(\n",
    "    value=1,\n",
    "    min=0,\n",
    "    max=100, \n",
    "    step=0.001, \n",
    "    description='time'\n",
    "    ),c=(0,1,0.001),width1=widgets.FloatSlider(\n",
    "    value=0.78,\n",
    "    min=0,\n",
    "    max=1, \n",
    "    step=0.001, \n",
    "    description='width of the left phase shifter',style=style\n",
    "    ),width2=widgets.FloatSlider(\n",
    "    value=0.43,\n",
    "    min=0,\n",
    "    max=1, \n",
    "    step=0.001, \n",
    "    description='width of the right phase shifter',style=style\n",
    "    ),xglass=widgets.FloatSlider(\n",
    "    value=2.5,\n",
    "    min=1.5,\n",
    "    max=3.5, \n",
    "    step=0.001, \n",
    "    description='Position of the phase shifters',style=style\n",
    "    ),eta=widgets.FloatSlider(\n",
    "    value=3,\n",
    "    min=1,\n",
    "    max=3, \n",
    "    step=0.001, \n",
    "    description='Refractive index',style=style\n",
    "    ),k=(1,30,0.1),Amp=(0.062,0.25,0.001),t1=widgets.FloatSlider(\n",
    "    value=0.707,\n",
    "    min=0.001,\n",
    "    max=0.999, \n",
    "    step=0.001, \n",
    "    description='Transmittivity of first BS',style=style\n",
    "    ),t2=widgets.FloatSlider(\n",
    "    value=0.707,\n",
    "    min=0.001,\n",
    "    max=0.999, \n",
    "    step=0.001, \n",
    "    description='Transmittivity of second BS',style=style\n",
    "    ))\n",
    "def update(a=0.8,vg_factor=1,c=0.2,t=0,width1 = 0.78,width2 =0.707,xglass=2.5,eta=3,k=22.2,Amp=0.125,t1=0.707,t2=0.707):\n",
    "    ax=plt.gca() #clear old figure\n",
    "    vg=vg_factor*c\n",
    "    create_figure(a,vg,c,t,ax,width1,width2,xglass,eta,k,Amp,t1,t2)\n",
    "    #select axis object contining old figure\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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