ece228 lecture 5 s10

ece228 lecture 5 s10 - Bowers ECE 228A Chirp and Dispersion...

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Bowers ECE 228A Chirp and Dispersion Lecture #5 John Bowers ECE 228A Read Chapter 2. Also, Agrawal: Nonlinear Fiber Optics (on reserve)
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Bowers ECE 228A Values for Sellmeier equation in silica • The index of refraction of bulk silica can be approximated using the Sellmeier equation with experimentally measured parameters. A 2 3 1.4695 index of refraction vs. wavelength n 2 ( ) 1 i i 2   i 2 i 1 0 401040; 1.468 1.4685 1.469 A 1 = 0.401040; 1 = 0.064270; A 2 = 0.521885; = 0 129408; .466 1.4665 1.467 1.4675 n 2 0.129408; A 3 = 0.904048; 3 = 9.425478; 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.4645 1.465 1.4655 1.466 ECE 228A wavelength (microns)
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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
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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
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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]
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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 5 s10 - Bowers ECE 228A Chirp and Dispersion...

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