Mar 12 2015
Contents Two-port model Rate equation and damping Small signal response Conclusion
Two Port Model I:Current V:Voltage P: Optical Power ν: Optical frequency shift Model summarize parasitic effects and overall response This model are valid in single frequency DFB lasers
Two Port Model P: Optical Power Δν: Optical frequency shift 3 sections of laser model 1. package or mount parasitic Bonding wire inductance, capacitance between input terminal 2. semiconductor chip parasitic parasitic capacitance, resistance with semiconductor material 3. Intrinsic laser(active layer & cavity)
Two Port Model Signal response of semiconductor laser IM p( j) I ( j) A ( j) FM I ( j) A Parasitic: Lower high frequency of signal response Intrinsic Laser: Resonance peak
Parasitic Chip cross section
Parasitic Circuit model of parasitic L p : bondwire inductuce R p : Small loss resistance C p : Pad capacitance C s : Shunt capacitance R s : Series resistance I L : Leakage current
Rate Equations and Damping Single mode rate equation dn I A N g 0( N N 0g )(1 S ) S dt qv act n ds 1 N g0( N N0g )(1 S) S dt p n N: electron density S: photon density Γ: optical confinement factor τ p : photon lifetime τ n : electron lifetime V act : Volume of active layer β: Fraction of spontaneous emission coupled into the laser mode ε: gain compression characteristic absorption Spontaneous emission Stimulated emission N,S are assumed constant across active layer
Rate Equations and Damping Cause of damping in the modulation response Spontaneous emission coupled into the lasing mode Spatial hole burning combined with carrier diffusion Nonlinear due to spectral hole burning Nonlinear absorption
Small Signal Response Intensity Modulation M( j) p( j) i ( j) A 2 M( j) B0 M (0) ' 1 ' S ( j) j S ( g ) B 2 0 2 0 0 0 S0 n p ns0 n p I ' qv th act gs 2 0 0 0 p h M (0) 2q Damping term With some approximation M( j) 1 M 2 (0) j j 1 0 m
Small Signal Response Damping of resonance Damping term: ' 1 S0( g0 ) S 0 n p Damping term peak, ω p ω 0 Damping term peak, ω p ω 0 Low S 0 (Low output power) Spontaneous emission term dominate Large S 0 (Large output power) gain compression damping term(ε)
High Frequency limitations Recall Then M( j) 1 2 M (0) j j 1 0 m 2 2 4 p 0 1 0 m m 2 m 2 2 4 4 3 p p db 0 m m m m 2 1 M p 2 4 0 1 0 m 4 m
High Frequency limitations ω 0 proportional to output power ω p ω 0 at low output power(ω 0 /ω m <<1) ω p /ω m max at ω 0 /ω m =1, zero at ω 0 /ω m = 2 ω 3dB /ω m max at ω 0 /ω m = 2 M p =0(no peak) at ω 0 /ω m = 2 Second order Butterworth
Design for Wide-Band Laser ω 3dB /ω m max at ω 0 /ω m = 2 Make large ω 0 (up to 2) for large bandwidth gs 2 0 0 0 p 1.Increse S 0 Decrease the width of the optical field distribution Design low threshhold current 2. Increase g 0 Decrease temperature 3. Reduce photon lifetime Reduce cavity length
Small Signal Response Frequency Modulation g0n 4 ( j) F( j) i ( j) A jm 1 2 F( j) 0 F(0) j j 0 m 2 ( ) 1
Small Signal Response IM FM Difference between IM,FM FM has much larger peak IM slope decade -40dB FM slope decade-20db
Conclusion Semiconductor Laser response modeling was described Bandwidth of direct modulator can control by small signal model