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Special Topics in Optical Engineering II(15/1) Yunsu Sung

Yunsu Sung

Mar 12 2015

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Contents

• Two-port model
• Rate equation and damping
• Small signal response
• Conclusion

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Two Port Model

• Model summarize parasitic effects and overall response
• This model are valid in single frequency DFB lasers
• I:Current
• V:Voltage
• P: Optical Power
• ∆ν: Optical frequency shift

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Two Port Model

• 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)

P: Optical Power Δν: Optical frequency shift

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Two Port Model

• Signal response of semiconductor laser
• Parasitic: Lower high frequency of signal response
• Intrinsic Laser: Resonance peak

( ) IM ( ) ( ) FM ( )

A A

p j I j j I j        

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Parasitic

• Chip cross section

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Parasitic

• Circuit model of parasitic
• Lp: bondwire inductuce
• Rp: Small loss resistance
• Cp: Pad capacitance
• Cs: Shunt capacitance
• Rs: Series resistance
• IL: Leakage current

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Rate Equations and Damping

• Single mode rate equation
• N,S are assumed constant across active layer

( )(1 ) 1 ( )(1 )

A g act n g p n

I dN N g N N S S dt qV dS N g N N S S dt                            

• N: electron density
• S: photon density
• Γ: optical confinement factor
• τp: photon lifetime
• τn: electron lifetime
• Vact: Volume of active layer
• β: Fraction of spontaneous emission

coupled into the laser mode

• ε: gain compression characteristic

absorption Spontaneous emission Stimulated emission

Special Topics in Optical Engineering II(15/1) Yunsu Sung

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

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Small Signal Response

• Intensity Modulation

With some approximation

2 2 2

( ) ( ) ( ) ( ) (0) ' 1 ' ( ) ( )

A n p n n p

p j M j i j B M j M S j j S g B S S                                      

2

' (0) 2

th act p

I qV g S h M q          

Damping term

2

( ) 1 (0) 1

m

M j M j j                    

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Small Signal Response

• Damping of resonance

Damping term: Damping term↓  peak↑, ωp ≈ ω0 Damping term↑  peak↓, ωp ≠ ω0 Low S0(Low output power)  Spontaneous emission term dominate Large S0(Large output power)  gain compression damping term(ε)

' 1 ( )

n p

S g S       

Special Topics in Optical Engineering II(15/1) Yunsu Sung

High Frequency limitations

• Recall
• Then

2

( ) 1 (0) 1

m

M j M j j                    

2 2 4 2 2 4 4 3 2 2 4

1 2 1 1 4

p m m m p p dB m m m m p m m

M                                                                               

Special Topics in Optical Engineering II(15/1) Yunsu Sung

High Frequency limitations

• ω0 proportional to output power
• ωp ≈ ω0 at low output power(ω0/ωm<<1)
• ωp/ωm max at ω0/ωm=1, zero at

ω0/ωm=√2

• ω3dB/ωm max at ω0/ωm=√2
• Mp=0(no peak) at ω0/ωm=√2

– Second order Butterworth

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Design for Wide-Band Laser

• ω3dB/ωm max at ω0/ωm=√2
• Make large ω0(up to √2) for large bandwidth
• 1.Increse S0

– Decrease the width of the optical field distribution – Design low threshhold current

• 2. Increase g0

– Decrease temperature

• 3. Reduce photon lifetime

– Reduce cavity length

2 p

g S   

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Small Signal Response

• Frequency Modulation

2 2

4 ( ) ( ) ( ) 1 ( ) (0) ( ) 1

A m m

g N j F j i j j F j F j j                             

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Small Signal Response

• Difference between IM,FM

– FM has much larger peak – IM slope decade -40dB – FM slope decade-20dB

IM FM

Special Topics in Optical Engineering II(15/1) Yunsu Sung

Conclusion

• Semiconductor Laser response modeling was described
• Bandwidth of direct modulator can control by small signal

model