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8. Optical Modulation. Modulation Techniques. Direct modulation of laser diode Vary the current supply to the laser diode Directly modulates the output power of the laser External modulation Change the transmission characteristics Change the power of a continuous wave laser. - PowerPoint PPT Presentation
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8. Optical Modulation
Modulation Techniques
• Direct modulation of laser diode
– Vary the current supply to the laser diode
– Directly modulates the output power of the laser
• External modulation
– Change the transmission characteristics
– Change the power of a continuous wave laser
Rate Equations of Laser Diodes
• The semiconductor laser is essentially a two-level laser
• Light emission based on two coupled rate equations
– The carrier density of excited electrons (N)
– The photon density (Nph)
Carrier Density Rate Equation
vg: group velocity L: confinement factor
a: gain constant g: gain suppression coef.
emission stimulated
emissionsspontaneou
2
ionrecombinatvenonradiati
injectioncurrent
ratecarrier
phgnr
NNgvNBN
dq
tJ
dt
dN
oNNaNg phg
o
N
aa
1
Photon Density Rate Equation
sp: percentage of spontaneous emission coherent and in phase with stimulated emission (~10E-5)
sp: photon decay constant
tot: total cavity loss
emission stimulatedemission
sspontaneou
2
photonsof lossrate Photon
phgspph
phph NNgvNBN
dt
dN
totgsp v 1
Steady State Solution
• Steady state requires the carrier density and the photon density to b constant
• The photon density rate equation yields
• Nph must be positive which requires
0dt
dN
dt
dN ph
NgvNB
Ngph
spph
1
2
phg Ngv 1
Threshold Condition
• The carrier threshold condition is where
• Since the gain is also given by
• Resulting in a threshold carrier density of
• The photon density then becomes
phthg Ngv 1
aNN tototh
othth NNaNg
gph
th vNg
1
NNav
NBN
thg
spph
2
Steady State
• This means that in steady state Nth>N
• High photon flux occurs when N~Nth
• With N~Nth
• Resulting in
• The total power is
ph
phth
nr
thN
NBN
qdJ
2
thphph JJ
dqN
thnrthth NBNdqJ 1
thtot
IIRmL
P
1
24.1
2
DC Laser Diode Response
Initial Photon Density
• Rate of increase of photon density (dNph/dt) is essentially zero when Nph is small
– It will not become significant until the net gain is positive
– This is equivalent to
– When the laser diode is initially turned on the photon density stays essentially zero until N reached Nth
Ng
thNN
phgspph
phph NNgvNBN
dt
dN 2
Initial Carrier Density
• Rate of increase of N (dN/dt) is positive when Nph is small
– Causing an increase in the carrier density
2BNN
dq
J
dt
dN
nr
Exceeding Threshold
• When N>Nth
– Optical gain becomes positive
– Photon density increases rapidly
– Exceeds the steady state value
• The increase in Nph causes
– decrease in the dN/dt because of the stimulated emission term is negative
• When Nph reaches a certain value dN/dt becomes negative
– N starts to decrease
phg NNgv
Relaxation Oscillations
• When N drops below Nth
– N starts increasing again
– The process repeats itself as a damped oscillation
• N stays very close to Nth
Final Pulse Response
• When the laser turns off
– N decreases
– When N<Nth the photon density drops to essentially zero