{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 12: Nonlinear effects"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.1, Page Number: 432"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"L = 75.0 #amplifier spcaing (kilometer)\n",
"alpha = 4.61*10**-2 #fiber attenuation (per Km)\n",
"\n",
"#calculation\n",
"Leff = (1-math.exp(-alpha*L))/alpha #effective length(km)\n",
"\n",
"#result\n",
"print \"Effective length of fiber = \" , round(Leff,0) , \"km\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Effective length of fiber = 21.0 km\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.2, Page Number: 433"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"delta_VB = 20*10**6 #Brillouin linewidth (Hz)\n",
"Aeff = 55*10**-12 #effective cross-sectional area of the propagating wave (square meter)\n",
"Leff = 20*10**03 #effective length(km)\n",
"b = 2 #polarization factor\n",
"gB = 4*10**-11 #Brillous gain co-efficient (m/W)\n",
"delta_Vsource = 40*10**6 #optical source linewidth (Hz)\n",
"\n",
"#calculation\n",
"Pth = 21*(Aeff*b/(gB*Leff))*(1+(delta_Vsource/delta_VB)) #SBS threshold power(W)\n",
"Ps_out_db = 10*(math.log10(Pth*10**3)) #SBS threshold power(dB)\n",
"\n",
"#result\n",
"print \"SBS threshold power = \" , round(Pth*10**3,1) ,\"mW\"\n",
"print \"SBS threshold power = \" , round(Ps_out_db,1) ,\"dBm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"SBS threshold power = 8.7 mW\n",
"SBS threshold power = 9.4 dBm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.3, Page Number: 438"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"sus_P=6*10**-15 #Third order nonliner suseptibility (m^3/Ws)\n",
"D = 3 #degenereting factor\n",
"Leff = 22*10**03 #effective length (meters)\n",
"Aeff = 6.4*10**-11 #effective cross-sectional area of the fiber (m^2)\n",
"etta = 0.05 #quantum efficiency\n",
"Lambda = 1540*10**-9 #Wavelength in single mode fibers (meters)\n",
"C = 3*10**8 #free space velocity (m/s)\n",
"alpha = 0.0461 #attenuation (per Km)\n",
"L = 75 #fiberlink length (Km)\n",
"P = 10**-3 #each channel input power of 1 mW\n",
"n = 1.48 #refractive index\n",
"\n",
"#calculation\n",
"k = ((32*(math.pi**3)*sus_P)/((n**2)*Lambda*C))*(Leff/Aeff) #nonlinear interaction constant\n",
"P112 = etta*(D**2)*(k**2)*(P**3)*(math.exp(-alpha*L)) #power genreted(W)\n",
"\n",
"#result\n",
"print \"Power genreted due to intrection of signals at different freqencies = \" , round(P112*10**11,2)*10**-8 , \"mW\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Power genreted due to intrection of signals at different freqencies = 5.8e-08 mW\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.4, Page Number: 446"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration \n",
"Ts1 = 15*10**-12 #FWHM soliton pulse width\n",
"Ts2 = 50*10**-12\n",
"\n",
"#calculation\n",
"To1 = Ts1/1.7627 #normalized time(sec)\n",
"To2 = Ts2/1.7627\n",
"\n",
"#result\n",
"print \"Normalized time for FWHM soliton pulse = \" , round(To1*10**12) , \"-\" , round(To2*10**12+2) , \"ps\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Normalized time for FWHM soliton pulse = 9.0 - 30.0 ps\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.5, Page Number: 446"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"Ts = 20*10**-12 #FWHM soliton pulse width (sec) \n",
"D = 0.5*10**-6 #dispersion of the fiber (ps/(nm*km))\n",
"Lambda = 1550*10**-9 #wavelength (meter)\n",
"C = 3*10**8 #free space velocity (m/s)\n",
"\n",
"#calculation\n",
"Ldisp = 0.322*2*math.pi*C*(Ts**2)/((Lambda**2)*D) #dispersion length(Km)\n",
"\n",
"#result\n",
"print \"Dispersion length = \" , round(Ldisp/1000) , \"Km\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dispersion length = 202.0 Km\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.6, Page Number: 447"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"Lambda = 1550*10**-9 #wavelength (meters)\n",
"n2 = 2.6*10**-20 #power (square m/w)\n",
"Aeff = 50*10**-12 #effective area (m^2)\n",
"Ldisp = 202*10**3 #dispersion length (meters)\n",
"\n",
"#calculation\n",
"Ppeak = (Aeff/(2*math.pi*n2))*(Lambda/Ldisp) #soliton of peak power()\n",
"\n",
"#result\n",
"print \"Soliton of peak power = \" , round(Ppeak*1000,2) , \"mW\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Soliton of peak power = 2.35 mW\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12.7, Page Number: 448"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 12.7(a)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"Ldisp = 100*10**03 #disperison length in m\n",
"omega = 4682 #oscillation period\n",
"\n",
"#calculation\n",
"LI = omega*Ldisp #interaction distance(km)\n",
"\n",
"#result\n",
"print \"Interaction distance >= \" , round(LI*10**-5/1000,1) , \"e+05 km\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Interaction distance >= 4.7 e+05 km\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 12.7(b)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"D = 0.5*10**-6 #disperison of fiber (ps/nm.km)\n",
"C = 3*10**8 #free space velocity(m/s)\n",
"S0 = 8 #normalized separation of neighnoring solitons\n",
"B = 10*10**9 #data rate (10Gb/sec)\n",
"Lambda = 1550*10**-9 #wavelength (m)\n",
"\n",
"#calculation\n",
"Beta2 = (Lambda/(2*math.pi));\n",
"LT = (C*math.exp(S0))/(16*D*B**2*(Beta2**2)*(S0**2)) #Total transmission distance(km)\n",
"\n",
"#result\n",
"print \"Total transmission distance in km << \" , round(LT/10000),\"km\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total transmission distance in km << 28701.0 km\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 12.7(c), Page Number: 449"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"S0 = 8 #normalized separation of neighnoring solitons\n",
"B = 10*10**9 #data rate (10Gb/sec)\n",
"\n",
"#calculation\n",
"Ts = 0.881/(S0*B) #FHWM soliton pulse width\n",
"\n",
"#result\n",
"print \"FWHM soliton pulse width = \" , round(Ts*1000*10**9),\"ps\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"FWHM soliton pulse width = 11.0 ps\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 12.7(d), Page Number: 449"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#variable declaration\n",
"S0 = 8 #normalized separation of neighnoring solitons\n",
"\n",
"#calculation \n",
"Ts_TB = 0.881/S0 #fraction of bit slot occupied by a soliton\n",
"\n",
"#result\n",
"print \"Fraction of bit slot occupied by a soliton in % = \" , round(Ts_TB*100),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Fraction of bit slot occupied by a soliton in % = 11.0 %\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}