{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 8: Fiber Optics"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 1.1: Critical_angle.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"n1=1.50          //Core refractive index\n",
"n2=1.47          //Cladding refractive index\n",
"\n",
"//Calculations\n",
"C_a=asin(n2/n1)        //Critical angle       \n",
"N_a=(n1**2-n2**2)**(1/2)\n",
"A_a=asin(N_a)\n",
"\n",
"//Results\n",
"printf('The Critical angle =%0.3f degrees\n',(C_a*180/%pi))\n",
"printf('The numerical aperture =%0.3f \n',(N_a))\n",
"printf('The acceptance angle =%0.3f degrees\n',(A_a*180/%pi))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.10: Numerical_aperture_and_Acceptance_angle.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"n1=1.53\n",
"delta=0.0196\n",
"\n",
"//Calculations\n",
"N_a=n1*(2*delta)**(1/2)\n",
"A_a=asin(N_a)\n",
"//Result\n",
"printf('Numerical aperture =%0.3f \n',(N_a))\n",
"printf('Acceptance angle =%0.3f degrees \n',(A_a*180/%pi))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.11: Core_radius.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"n1=1.480\n",
"n2=1.465\n",
"V=2.405\n",
"lamda=850*10**-9\n",
"\n",
"//Calculations\n",
"delta=(n1**2-n2**2)/(2*n1**2)\n",
"a=(V*lamda*10**-9)/(2*%pi*n1*sqrt(2*delta))\n",
"\n",
"//Results\n",
"printf('delta =%0.3f \n',(delta))\n",
"printf('Core radius,a =%0.3f micro m\n',(a*10**15))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.12: Total_dist_travelled_by_light_over_one_metre_of_fiber.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"n1=1.5\n",
"n2=1.49\n",
"a=25\n",
"\n",
"//Calculations\n",
"C_a=asin(n2/n1)           //Critical angle\n",
"L=2*a*tan(C_a)             \n",
"N_r=10**6/L                    \n",
"\n",
"//Result\n",
"printf('Critical angle=%0.3f degrees\n',(C_a*180/%pi))\n",
"printf('Fiber length covered in one reflection=%0.3f micro m\n',(L))\n",
"printf('Total no.of reflections per metre=%0.3f \n',(N_r))\n",
"printf('Since L=1m, Total dist. travelled by light over one metre of fiber =%0.3f m \n',(1/sin(C_a)))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.13: No_of_modes.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"alpha=1.85\n",
"lamda=1.3*10**-6\n",
"a=25*10**-6\n",
"N_a=0.21\n",
"\n",
"//Calculations\n",
"V_n=((2*%pi**2)*a**2*N_a**2)/lamda**2\n",
"N_m=(alpha/(alpha+2))*V_n\n",
"\n",
"printf('No.of modes =%0.3f =155(approx)\n',(N_m))\n",
"printf('Taking the two possible polarizations, Total No.of nodes =%0.3f \n',(N_m*2))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.14: ignal_attention_per_unit_length.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"P_i=100\n",
"P_o=2\n",
"L=10\n",
"\n",
"//Calculations\n",
"S=(10/L)*log(P_i/P_o)\n",
"O=S*L\n",
"\n",
"//Result\n",
"printf('a.Signal attention per unit length =%0.3f dB km**-1\n',(S))\n",
"printf('b.Overall signal attenuation =%0.3f dB\n',(O))\n",
"printf('//Answer given in the textbook is wrong')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.15: Bandwidth_length_product.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"L=10\n",
"n1=1.55\n",
"delta=0.026\n",
"C=3*10**5\n",
"\n",
"//Calculations\n",
"delta_T=(L*n1*delta)/C\n",
"B_W=10/(2*delta_T)\n",
"\n",
"//Result\n",
"printf('Total dispersion =%0.3f ns\n',(delta_T/10**-9))\n",
"printf('Bandwidth length product =%0.3f Hz-km\n',(B_W/10**5))\n",
"printf('//Answer given in the text book is wrong')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.2: No_of_modes_propogated_inside_the_fiber.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"d=50                //diameter\n",
"N_a=0.2             //Numerical aperture\n",
"lamda=1             //wavelength\n",
"\n",
"//Calculations\n",
"N=4.9*(((d*10**-6*N_a)/(lamda*10**-6))**2)\n",
"\n",
"//Result\n",
"printf('N =%0.3f \n',N)\n",
"printf('Fiber can support%0.3f guided modes \n',N)\n",
"printf('In graded index fiber, No.of modes propogated inside the fiber =%0.3f only',N/2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.3: Numerical_aperture.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"d=50                //diameter\n",
"n1=1.450\n",
"n2=1.447\n",
"lamda=1             //wavelength\n",
"\n",
"//Calculations\n",
"N_a=(n1**2-n2**2)   //Numerical aperture\n",
"N=4.9*(((d*10**-6*N_a)/(lamda*10**-6))**2)\n",
"\n",
"//Results\n",
"printf('Numerical aperture =%0.3f ',N_a)\n",
"printf('No. of modes that can be propogated =%0.3f \n',(N))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.4: Numerical_aperture.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"delta=0.05          \n",
"n1=1.46\n",
"\n",
"//Calculation\n",
"N_a=n1*(2*delta)**(1/2)     //Numerical aperture\n",
"\n",
"//Result\n",
"printf('Numerical aperture =%0.3f \n',(N_a))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.5: maximum_no_of_modes_propogating_through_fiber.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"a=5\n",
"n1=1.450\n",
"n2=1.447\n",
"lamda=1             //wavelength\n",
"\n",
"//Calculations\n",
"N_a=(n1**2-n2**2)   //Numerical aperture\n",
"\n",
"N=4.9*((a*10**-6*sqrt(N_a)/(lamda*10**-6))**2)\n",
"\n",
"//Result\n",
"\n",
"printf('maximum no.of modes propogating through fiber =%0.3f \n',(N))\n",
"printf('Correction needed')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.6: Number_of_modes.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"a=100\n",
"N_a=0.3               //Numerical aperture\n",
"lamda=850             //wavelength\n",
"\n",
"//Calculations\n",
"V_n=(2*(%pi**2*a**2*10**-12*N_a**2)/lamda**2*10**-18)\n",
"//Result\n",
"printf('Number of modes =%0.3f modes\n',(V_n/10**-36))\n",
"printf('No.of modes is doubled to account for the two possible polarisations')\n",
"printf('Total No.of modes =%0.3f \n',(V_n/10**-36)*2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.7: Cutoff_Wavellength.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"a=5;\n",
"n1=1.48;\n",
"delta=0.01;\n",
"V=25;\n",
"\n",
"//Calculation\n",
"lamda=(%pi*(a*10**-6)*n1*sqrt(2*delta))/V   // Cutoff Wavelength\n",
"\n",
"//Result\n",
"printf('Cutoff Wavellength =%0.3f micro m. \n',(lamda*10**7))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.8: Maximum_core_radius.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"V=2.405\n",
"lamda=1.3\n",
"N_a=0.05\n",
"\n",
"//Calculations\n",
"a_max=(V*lamda)/(2*%pi*N_a)\n",
"\n",
"//Result\n",
"printf('Maximum core radius=%0.3f micro m\n',(a_max))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.9: Acceptance_angle.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//variable declaration\n",
"N_a=0.3\n",
"gamma=45\n",
"\n",
"//Calculations\n",
"theta_a=asin(N_a)\n",
"theta_as=asin((N_a)/cos(gamma))\n",
"\n",
"//Results\n",
"printf('Acceptance angle, theta_a =%0.3f degrees\n',(theta_a*180/%pi))\n",
"printf('For skew rays,theta_as %0.3f degrees\n',(theta_as*180/%pi))\n",
"printf('//Answer given in the textbook is wrong')"
   ]
   }
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			{
			 "text": "MetaKernel Magics",
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