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