Lecture 6

Polarization splitter based Filters

Acoustooptic Tunable Filters

Electrooptic Tunable Filters

Tunable Add-Drop Filters

Phase matched

AOTF : changing f for tuningEOTF: changing V for tuning.

1x zn n

Laser Diodes

Laser DiodesDirect modulation: easy to implement but

causing spectral broadening which can reduce bandwidth for long distance transmission.

External modulation: Overcoming excess spectral broadening, at cost of increased transmitter cost of complexity.

Laser DiodesTwo key features of laser operation

Gain: stimulated emission of light.Oscillation: resonant cavity.

Fabry-Perot model of laser

Fabry-Perot model of laserAfter one round trip

After N round trips

.

amplitude loss factor

round trip phase shift

is sE E E R e e

0

.

0 :

0 :

Nn

sn

i

E E a

a R e e

loss

gain

Fabry-Perot model of laserN : steady state

0

22 2

2

2 2

2 2

1; 1

1

; where 1

(1 . cos . sin )

(1 . cos ) ( . sin )

1 2 cos

n

n

si

a aa

EP E D a

D

D R e jR e

D R e R e

D R e R e

Fabry-Perot model of laser

2

2 4

is max. for 2 where N = 1,2,...

(1 . )

for . 1 : Threshold condition

is min. for (2 1) where N = 1,2,...

Let 1 ; 0 < 1

Let 2

cos 1 ...2 4!

i

i

i

P N

D R e

P R e

P N

Ke

N

Fabry-Perot model of laser2

2

2 2

2 2

2

1 (1 ) 2(1 ) 12

(1 )

For = 0, as 0

sout

s s

out

D

D

P e RP

P E

P

Fabry-Perot model of laserRelate Δ to spectral characteristic

4

2 ; where M = 1,2,...

4( )

( )

.

( )

nL

cM

Ln

cn n n

dnn

ddn

n nd

Fabry-Perot model of laserRecall N = group refractive index

2, 2

( )

4

dN c

dn

cd n n

N c nd

NL

c

Fabry-Perot model of laser

2 for longitude mode spacing

2

2

LM

LM

c

NL

Fabry-Perot model of laser

at 50% power points

LMFWHM

Fabry-Perot model of laserHow does total output power in a mode

depend on ?

2 2

22

total power (area under curve)

( )

2

( )

2

2

LM

LM

LM

dI

d

dI

Fabry-Perot model of laser

Output power in mode varies as 1/.

2 2

2Let

2

2

LM

LM

LM

X

dXI

X

I

Fabry-Perot model of laser

e 1 for lasing.

e gain for light passing through gain region ( < 0)

1Total power out LM

R

P

Example 1What is the longitudinal mode spacing in

Angstroms and Hz, for an InGaAsP Fabry-Perot laser emitting at a wavelength of 1.53 μm, with N = 4 and L = 300 μm?

Example 2From previous example, what is the total

spectral width of the laser emission, in Angstroms and Hz, if the laser emission contains seven longitudinal modes?

Laser Rate Equations

N = number of carriers (e-h pairs) in active region. S = number of photons in cavity in lasing mode. J = current for pumping diode. e = electronic charge = 1.6 x 10-19 C. sp = spontaneous lifetime of carriers.

N0 = number of carriers for transparency = fraction of spontaneous emission coupled into lasing mode. ph = photon lifetime in cavity. g = gain coefficient.

0

0

sp

sp ph

dN J Ng N N S

dt e

dS N Sg N N S

dt

Laser Rate EquationsSteady state:

For small current (S 0)

0

0

0

sp

sp ph

dN dS

dt dtJ N

g N N Se

N Sg N N S

sp

sp

J N

e

JN

e

Laser Rate Equations

Lasing threshold:

0

0

1

1

ph sp

sp ph

NS g N N

NS g N N

0

-

1( )

compare e 1 for Fabry Perot mode

ph

g N N

R

Laser Rate Equations

Above threshold:

0

0

1th

ph

th th

sp

thth

N Ng

J N

e

J Jg N N S

e

Laser Rate Equations

Example 3Parameters for a semiconductor laser are:

What is the photon lifetime?What is the number of carriers at lasing threshold?

8 -20

2.5 ns, = 300 m, R = 0.12, N = 4,

28 mA, = 2.1x10 m , 0.828 m

sp

th

L

I N

Laser Rate EquationsHow long does a photon stay in cavity?

0

0

1

0

Let loss per unit distance due to mirror reflectance

Propagation distance of photon over which

energy decays by 1/e.

1

1

ln ; = cavity length

L

L

L

e e

L

eR

L R L

Laser Rate Equations

0

; = group refractive index

ln

g ph

g

gph

v L

cv N

Nn L

c R

Example 4What is the power gain coefficient in cm-1 in a

semiconductor FP laser operating above threshold with a cavity length of 250 μm and facet reflectances of R1=R2 = 1%. In both cases assume that the gain is a constant within the cavity.