ece228 lecture 6 s10

# ece228 lecture 6 s10 - Bowers ECE 228A Dispersion...

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Bowers ECE 228A Dispersion Compensation Lecture #6 John Bowers ECE 228A Read Chapter 2. Also, Agrawal: Nonlinear Fiber Optics (on reserve)

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Bowers ECE 228A Non-Linear Schrodinger Equation ñ Both linear (dispersive) and nonlinear effects must be taken into account for pulse propagation in the fiber ñ The propagation of a signal in a single mode fiber is set (to a very high level of accuracy) by the following equation, called the nonlinear Schrodinger equation: A A j t A t A j A z A 2 3 3 3 2 2 2 6 1 2 1 (z t) the complex nvelope of the optical field Attenuation Chromatic Dispersion Nonlinear Effects ECE 228A A(z,t) is the complex-envelope of the optical field • The resulting optical power is P(z,t)=| A(z,t) | 2
Bowers ECE 228A Chromatic Dispersion The two terms and are the derivative of the mode propagation constant    g 3 3 2 2 1 0 1 1 ) ( ) ( n p 0 0 0 0 ) ( 6 2 n c c p 1 1 0 1 d d g ECE 228A

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Bowers ECE 228A Group Velocity Dispersion (GVD) Group velocity (GVD) is frequency-dependent Any communication signal (pulse) has a given bandwidth Different frequencies in pulse => Different group delays => Leads to pulse distortion A more quantitative analysis can be carried out by considering that the fiber acts as a filter with the following transfer function: z j e A z A 3 3 2 2 2 2 ) , 0 ( ) , ( This equation is obtained after some mathematical manipulation that “extracts” the absolute group delay he coefficient nd re evaluated on the pulse central frequency/wavelength The coefficient 2 and 3 are evaluated on the pulse central frequency/wavelength 0 ECE 228A
Bowers ECE 228A Dispersion parameters: 2 and D ± 2 is called the “group velocity dispersion” GVD parameter – It is expressed in units of ps 2 /km pp From a mathematical point of view, it is easier to handle equations dealing with 2 and optical frequency is also convenient to specify dispersion in terms of optical It is also convenient to specify dispersion in terms of optical wavelength The “D” parameter is 2 2 ) ( 1  n c d d D g D is called the “Dispersion parameter”, and it is expressed in units of ps/nm-km ECE 228A

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Bowers ECE 228A The Dispersion Parameter D he relation bet een the t o parameters is gi en b The relation between the two parameters is given by: D = –2 C/ 2 2 [ps/nm-km] Physical meaning: given two wavelengths separated by  , their different group velocities give rise to a (group) delay between the two components given by D L The gaussian pulse spread, in terms of D , is given by: delay =D L where is the spectral width of the gaussian pulse D L T ECE 228A
Bowers ECE 228A Laser Frequency Chirping The complex refractive index of a gain medium can be used to derive the Henry

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## This note was uploaded on 05/18/2010 for the course ECE 228a taught by Professor Bowers,j during the Spring '08 term at UCSB.

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ece228 lecture 6 s10 - Bowers ECE 228A Dispersion...

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