8. optical modulation. modulation techniques direct modulation of laser diode –vary the current...
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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