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Lecture8-228a

# Lecture8-228a - Lecture 8 Chirp and Dispersion Compensation...

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ECE 228A Fall 2011 Daniel J. Blumenthal 8.1 Lecture 8 - Chirp and Dispersion Compensation

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ECE 228A Fall 2011 Daniel J. Blumenthal 8.2 Laser Chirp Another important parameter is the laser frequency chirp (frequency shift) Chirp will limit the bit-rate-distance product that a link can support Chirp occurs when directly driving a laser, the change in carrier density changes the effective index of refraction, and thus the oscillation optical frequency This can be interpreted as a bit-synchronous phase or frequency modulation Optical Intensity (field envelope) Actual Optical Field t Example of increasing frequency
ECE 228A Fall 2011 Daniel J. Blumenthal 8.3 Laser Frequency Chirping Coupled to carrier density modulation ( n 1 ( ω m ) ) via Kramers-Kronig, is frequency modulation via phase modulation. We define time varying frequency (modulation) as Chirp Solving the frequency domain rate equations for n 1 ( ω m ) including gain suppression and converting back to the time domain (by replacing i ω m with d/dt) and defining N(t) = N 0 + Δ N(t) n 1 ω m ( ) = i ω m + ε P 0 τ p \$ % & ' ( ) Γ AP 0 p 1 ω m ( ) Δ N ( t ) = 1 Γ A 1 P 0 dP 0 dt + ε τ p Δ P ( t ) \$ % & ' ( )

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ECE 228A Fall 2011 Daniel J. Blumenthal 8.4 Laser Frequency Chirping The complex refractive index of a gain medium can be used to derive the Henry α -factor and the resulting change in phase Δ n 0 resulting from a carrier density change Δ N(t) n 0 ( t ) = ! n 0 ( t ) i !! n 0 ( t ) Δ !! n 0 = ! n 0 4 πν A Δ N ( t ) α = Δ ! n 0 Δ !! n 0 = dn dN dg dN Δ ! n 0 = α ! n 0 A 4 πν Δ N ( t ) The change in index via carrier density modulation causes the laser frequency to change from its unperturbed value Δ ν ν = Δ \$ n 0 \$ n 0 Γ a = α Γ a A 4 πν Δ N ( t ) Δ ν ( t ) = α 4 π 1 P 0 dP dt + ε τ p Δ P ( t ) * + , - . /
ECE 228A Fall 2011 Daniel J. Blumenthal 8.5 SC Laser direct modulation As the laser current is changed between the low and high states, the laser carrier density changes and there is a resulting time dependent phase change.

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