Lecture6-228a

Lecture6-228a - Lecture 6 Propagation in Optical Fibers and...

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ECE 228A Fall 2011 Daniel J. Blumenthal 6.1 Lecture 6 - Propagation in Optical Fibers and Dispersion
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ECE 228A Fall 2011 Daniel J. Blumenthal 6.2 Non-Linear Schrodinger Equation A(z,t) is the complex-envelope of the optical ±eld The resulting optical power is P(z,t)=| A(z,t) | 2 A A j t A t A j A z A 2 3 3 3 2 2 2 6 1 2 1 γ β α + = Attenuation Chromatic Dispersion Nonlinear Effects Both linear (dispersive) and nonlinear effects must be taken into account for pulse propagation in the ±ber The propagation of a signal in a single mode ±ber is set (to a very high level of accuracy) by the following equation, called the nonlinear Schrodinger equation:
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ECE 228A Fall 2011 Daniel J. Blumenthal 6.3 Pulse Broadening Assuming a Gaussian shaped input pulse and frst order dispersion dominates ( β 2 0) t Optical intensity L T 0 t T(z) Single Mode Fiber T ( z ) T 0 = 1 + C β 2 z T 0 2 " # $ % & ' 2 + 2 z T 0 2 " # $ % & ' 2 ( ) * + , - Defne Dispersion Length An unchirped pulse (C=0) will broaden by a ±actor o± 2 at z = L D
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ECE 228A Fall 2011 Daniel J. Blumenthal 6.4 Pulse Compression If β 2 C < 0, the pulse will initially decrease! This will happen if the (a) the initial pulse is positively chirped and propagates in the anomolous dispersion regime of the ±ber OR (b) if the pulse is initially negatively chirped and propagates in the normal dispersion regime of the ±ber t Optical intensity T 0 t T(z) Single Mode Fiber T min z min = C 1 + C 2 ! " # $ L D T min = T 0 1 + C 2 ( ) z min
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ECE 228A Fall 2011 Daniel J. Blumenthal 6.5 Chromatic Dispersion The two terms β 2 and 3 of the previous equation are the derivative of the mode propagation constant ( ω ) The meaning of is clear when considering a single pulse propagation It turns out that, considering
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Lecture6-228a - Lecture 6 Propagation in Optical Fibers and...

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