Transcript Optical Sources - EE562 Schedule

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
dN J t 


dt
qd


carrier
rate
current
injection
N

nr
 
B N 2   vg g N  N ph


nonradiative
recombination
g N   a N  N o 
vg: group velocity
a: gain constant
spontaneous
emission
a
stimulated
emission
ao
1  hg N ph
L: confinement factor
hg: gain suppression coef.
Photon Density Rate Equation
dN ph
dt

Photon rate

N ph

ph

loss of
photons
 b sp B N 2   v g g N  N ph


 

spontaneous
emission
stimulatedemission
bsp: percentage of spontaneous emission coherent and in phase with
stimulated emission (~10E-5)
sp: photon decay constant
1  sp  vg atot
atot: total cavity loss
Steady State Solution
• Steady state requires the carrier density and the photon density to b
constant
dN ph dN

0
dt
dt
• The photon density rate equation yields
N ph 
b sp B N 2
1  ph   vg g N 
• Nph must be positive which requires
 vg g N   1  ph
Threshold Condition
• The carrier threshold condition is where
 vg g Nth   1  ph
1
g N th  
 ph  vg
• Since the gain is also given by
g Nth   a Nth  No 
• Resulting in a threshold carrier density of
N th  N o 
atot
a
• The photon density then becomes
N ph 
b sp B N 2
 vg a N th  N 
Steady State
• This means that in steady state Nth>N
• High photon flux occurs when N~Nth
• With N~Nth
 N th
N ph 
2
J  qd 
 B N th 



ph 
 nr

• Resulting in
 ph
J  J th 
qd
J th  q d Nth 1  nr  B Nth 
N ph 
• The total power is
P
 1.24 

 1  R I  I th 
2 atot L   m 

DC Laser Diode Response
Initial Photon Density
• Rate of increase of photon density (dNph/dt) is essentially zero when
Nph is small
dN ph
dt

N ph
 ph
 b sp B N 2   vg g N  N ph
– It will not become significant until the net gain is positive
a
g N  

– This is equivalent to N  Nth
– When the laser diode is initially turned on the photon density stays
essentially zero until N reached Nth
Initial Carrier Density
• Rate of increase of N (dN/dt) is positive when Nph is small
dN
J
N


 BN 2
dt q d  nr
– Causing an increase in the carrier density
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
  vg g N  N ph
• When Nph reaches a certain value
dN/dt becomes negative
– N starts to decrease
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