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diff --git a/Applied_Physics_for_Engineers/Chapter_9.ipynb b/Applied_Physics_for_Engineers/Chapter_9.ipynb new file mode 100755 index 00000000..579b6def --- /dev/null +++ b/Applied_Physics_for_Engineers/Chapter_9.ipynb @@ -0,0 +1,555 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9: Fibre Optics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.1, Page 463" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu_1 = 1.55; # Refractive index of the core \n", + "mu_2 = 1.50; # Refractive indices of cladding \n", + "\n", + "#Calculations\n", + "NA = mu_1*sqrt(2*(mu_1-mu_2)/mu_1); \n", + "print \"The NA of the optical fibre = %5.3f\"%NA\n", + "theta_a = degrees(asin(NA)); # The acceptance angle of optical fibre, degrees\n", + "\n", + "#Result\n", + "print \"The acceptance angle of the optical fibre is = %.1f degrees\"%theta_a\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The NA of the optical fibre = 0.394\n", + "The acceptance angle of the optical fibre is = 23.2 degrees\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.2, Page 463" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu_1 = 1.50; # Refractive index of the core \n", + "mu_2 = 1.45; # Refractive index cladding\n", + "\n", + "#Calculations&Results\n", + "NA = mu_1*sqrt(2*(mu_1-mu_2)/mu_1); # Numerical aperture of optical fibre\n", + "print \"The NA of the optical fibre = %5.3f\"%NA\n", + "theta_a = degrees(asin(NA)); # The acceptance angle of optical fibre, degrees\n", + "print \"The acceptance angle of the optical fibre = %5.2f degrees\"%theta_a\n", + "theta_c = degrees(asin(mu_2/mu_1)); # The critical angle of the optical fibre, degrees\n", + "print \"The acceptance angle of the optical fibre = %4.1f degrees\"%theta_c\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The NA of the optical fibre = 0.387\n", + "The acceptance angle of the optical fibre = 22.79 degrees\n", + "The acceptance angle of the optical fibre = 75.2 degrees\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.3, Page 464" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu0 = 1; # Refactive index of fibre in air\n", + "mu2 = 1.59; # Refactive index of the cladding \n", + "NA = 0.2; # Numerial aperture of optical fibre\n", + "\n", + "#Calculations\n", + "mu1 = sqrt(NA**2+mu2**2); # Refractive index of core\n", + "mu0 = 1.33; # Refactive index of fibre in water\n", + "NA = sqrt(mu1**2-mu2**2)/mu0; # Numerial aperture of optical fibre in water\n", + "theta_a = degrees(asin(NA)); # Acceptance angle for the fibre in water\n", + "\n", + "#Result\n", + "print \"The acceptance angle for the optical fibre in water = %3.1f degrees\"%theta_a\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The acceptance angle for the optical fibre in water = 8.6 degrees\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.4, Page 464" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu0 = 1; # Refractive index of air\n", + "mu1 = 1.50; # Refractive index of glass core`\n", + "delta = 0.005; # Fractional change in refractive index\n", + "\n", + "#Calculations&Results\n", + "mu2 = mu1*(1-delta); # Refractive index of cladding\n", + "print \"The refractive index of cladding =%6.4f\"%mu2\n", + "theta_c = degrees(asin(mu2/mu1)); # Critical angle, degrees\n", + "print \"The critical angle = %5.2f degrees\"%theta_c\n", + "theta_a = degrees(asin(sqrt(mu1**2-mu2**2)/mu0)); # Acceptance angle, degrees\n", + "print \"The value of acceptance angle is = %4.2f degrees\"%theta_a\n", + "NA = mu1*sqrt(2*delta); # Numerical aperture of optical fibre\n", + "print \"The NA of the optical fibre = %4.2f\"%NA #incorrect answer in the textbook\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The refractive index of cladding =1.4925\n", + "The critical angle = 84.27 degrees\n", + "The value of acceptance angle is = 8.62 degrees\n", + "The NA of the optical fibre = 0.15\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.5, Page 465" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "NA = 0.22; # Numerical aperture of the optical fibre\n", + "delta = 0.012; # Fractional difference between the refractive index of core and cladding\n", + "\n", + "#Calculations\n", + "mu1 = NA/sqrt(2*delta); # The refractive index of core of optical fibre\n", + "print \"The refractive index of core = %4.2f\"%mu1\n", + "mu2 = mu1*(1-delta); # The refractive index of cladding of optical fibre\n", + "\n", + "#Result\n", + "print \"The refractive index of cladding = %4.2f\"%mu2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The refractive index of core = 1.42\n", + "The refractive index of cladding = 1.40\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.6, Page 466" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu1 = 1.466; # Refractive index of core\n", + "mu2 = 1.460; # Refractive index of cladding\n", + "v = 2.4; # Cut-off parameter of the optical fibre\n", + "lamda = 0.8e-006; # Operating wavelength, m\n", + "\n", + "#Calculations&Results\n", + "NA = sqrt(mu1**2-mu2**2);\n", + "print \"The NA of optical fibre = %4.2f\"%NA\n", + "# Asthe cut-off parameter v of the optical fibre, v = 2*%pi*a*sqrt(mu1^2-mu2^2)/lambda, solving for a\n", + "a = lamda*v/(2*pi*sqrt(mu1**2-mu2**2));\n", + "print \"The core radius of the optical fibre = %4.2f micrometer\"%(a/1e-006)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The NA of optical fibre = 0.13\n", + "The core radius of the optical fibre = 2.31 micrometer\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.7, Page 466" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu1 = 1.54; # The refractive index of core\n", + "mu2 = 1.50; # The refractive index of cladding\n", + "lamda = 1.3e-006; # Operating wavelength of optical fibre, m\n", + "a = 25e-006; # Radius of fibre core, m\n", + "\n", + "#Calculations\n", + "v = 2*pi*a*sqrt(mu1**2-mu2**2)/lamda; # V-number of optical fibre \n", + "print \"The cut-off parameter of the optical fibre = %5.2f\"%v\n", + "n = v**2/2; # The number of modes supported by the fibre \n", + "\n", + "#Result\n", + "print \"The number of modes supported by the fibre = %3d\"%(ceil(n))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The cut-off parameter of the optical fibre = 42.14\n", + "The number of modes supported by the fibre = 888\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.8, Page 466" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu1 = 1.54; # Refractive index of core\n", + "v = 2.405; # Cut-off parameter of optical fibre\n", + "lamda = 1.3e-006; # Operating wavelength of optical fibre, m\n", + "a = 1e-006; # Radius of the core,\n", + "\n", + "#Calculations\n", + "NA = v*lamda/(2*pi*a); # Numerical aperture of optical fibre\n", + "delta = 1./2*(NA/mu1)**2; # Fractional change in refractive index of core and cladding\n", + "print \"The fractional difference of refractive indices of core and cladding = %7.5e\"%delta\n", + "mu2 = mu1*(1-delta); # Maximum value of refractive index of cladding\n", + "print \"The maximum refractive index of cladding = %5.3f\"%mu2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The fractional difference of refractive indices of core and cladding = 5.22018e-02\n", + "The maximum refractive index of cladding = 1.460\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.9, Page 467" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu1 = 1.45; # Index of refraction of core\n", + "NA = 0.16; # Numerical aperture of step index fibre\n", + "a = 3e-006; # Radius of the core, m\n", + "lamda = 0.9e-006; # Operating wavelength of optical fibre, m\n", + "\n", + "#Calculations\n", + "v = 2*pi*a*NA/lamda; # The normalized frequency or v-number of optical fibre\n", + "\n", + "#Result\n", + "print \"The normalized frequency of the optical fibre = %5.2f\"%v\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The normalized frequency of the optical fibre = 3.35\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.10, Page 467" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "mu1 = 1.52; # Refractive index of core\n", + "a = 14.5e-006; # Radius of the fibre core, m\n", + "delta = 0.0007; # Fractional index difference\n", + "lamda = 1.3e-006; # Operating wavelength of optical fibre, m\n", + "\n", + "#Calculations&Results\n", + "mu2 = mu1*(1-delta); # Refractive index of cladding\n", + "v = 2*pi*a*sqrt(mu1**2-mu2**2)/lamda; # Cut-off parameter v of the optical fibre\n", + "print \"The cut-off parameter of the optical fibre = %5.3f\"%v\n", + "#The is number of modes supported by the fibre given by,\n", + "n = v**2/2;\n", + "print \"The number of modes supported by the fibre = %d\"%(ceil(n))\n", + "#Incorrect answer in the textbook for mu2. Hence the difference in answers" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The cut-off parameter of the optical fibre = 3.985\n", + "The number of modes supported by the fibre = 8\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.11, Page 468" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "alpha = 3.5; # Attenuation of the optical fibre, dB/km\n", + "Pi = 0.5; # Input power of optical fibre, mW\n", + "L = 4; # Distance through the optical wave transmits through the fibre, km\n", + "\n", + "#Calculations\n", + "# As alpha = 10/L*log10(Pi/Po), solving for Po\n", + "Po = Pi/exp(alpha*L*2.3026/10); # Output power of optical fibre, mW\n", + "\n", + "#Result\n", + "print \"The output power of optical fibre = %4.1f micro-watt\"%(Po/1e-003)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The output power of optical fibre = 19.9 micro-watt\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.12, Page 468" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "Pi =1; # Input power of optical fibre, mW\n", + "Po = 0.85; # Outptu power of optical fibre, mW\n", + "L = 0.5; #The distance through the optical wave transmits through the fibre, km \n", + "\n", + "#Calculations\n", + "alpha = (10/L)*log10(Pi/Po); # The attenuation of power through the optical fibre\n", + "\n", + "#Result\n", + "print \"The attenuation of power through the optical fibre = %5.3f dB/km\"%alpha\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The attenuation of power through the optical fibre = 1.412 dB/km\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.13, Page 469" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "#Variable declaration\n", + "C = 0.8; # Connector loss per km, dB\n", + "F = 1.5; # Fibre loss per km, dB\n", + "alpha = C + F; # Attenuation of power the optical fibre, dB/km\n", + "Po = 0.3e-006; # Output power of optical fibre, W\n", + "L = 15; # The distance through the optical wave transmits through the fibre, km\n", + "\n", + "#Calculations\n", + "#As the attenuation, alpha = 10/L*log(Pi/Po), solving for Pi\n", + "Pi = Po*exp(2.3026*alpha*L/10); # Input power of optical fibre, mW\n", + "\n", + "#Result\n", + "print \"The minimum input power to optical fibre = %5.3f mW\"%(Pi/1e-003)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The minimum input power to optical fibre = 0.846 mW\n" + ] + } + ], + "prompt_number": 27 + } + ], + "metadata": {} + } + ] +}
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