Lecture 6
Polarization splitter based
Filters
Acoustooptic Tunable Filters
Electrooptic Tunable Filters
Tunable Add-Drop Filters
 Phase matched
nx  nz

 AOTF : changing f for tuning
 EOTF: changing V for tuning.
1


Laser Diodes
Laser Diodes
 Direct 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 Diodes
 Two key features of laser operation
 Gain: stimulated emission of light.
 Oscillation: resonant cavity.
Fabry-Perot model of laser
Fabry-Perot model of laser
 After one round trip
E  Es  Es R.e ei
  amplitude loss factor
  round trip phase shift
 After N round trips
N
E  Es  a n
n0
a  R.e  ei
  0 : loss
  0 : gain
Fabry-Perot model of laser
 N  : steady state

1
a 
; a 1

1 a
n0
n
2
Pi  E 
Es
2
; where D  1  a
2
D
D  (1  R.e  cos   jR.e  sin  ) 2
D  (1  R.e  cos  ) 2  ( R.e  sin  ) 2
D  1  R 2 e 2  2 R cos  e 
Fabry-Perot model of laser
Pi is max. for   2 N  where N = 1,2,...
D  (1  R.e ) 2
Pi   for R.e   1 : Threshold condition
Pi is min. for   (2 N  1) where N = 1,2,...
Let Ke   1   ; 0 <  1
Let     2 N 
 2  4
cos   1 

 ...
2
4!
Fabry-Perot model of laser
  2 
D  1  (1   )  2(1   ) 1 

2


D  2   2
2
Ps e  (1  R )
Pout  2
   2
Ps  Es
2
For  = 0, Pout   as   0
Fabry-Perot model of laser
 Relate Δ to spectral characteristic
4 nL

c
    2 M  ; where M = 1,2,...
4 L
 
 (n )
c
(n )  n  n
dn
n 
.
d
dn 

(n )   n  


d 

Fabry-Perot model of laser
 Recall N = group refractive index
d
d
2 n

,   2
c
d   (n )
n
N c

 n 
d


4 NL
 

c
N c
Fabry-Perot model of laser
  2 for longitude mode spacing
c
 LM 
2 NL

  2
 LM
Fabry-Perot model of laser
    at 50% power points
 FWHM
 LM


Fabry-Perot model of laser
 How does total output power in a mode depend on ?

I
d
  2   2  total power (area under curve)


d ( )
 2  2  2
 
   
  LM 
 LM
I
2

d ( )
   LM 
 2  


Fabry-Perot model of laser
Let X 
2
 LM
 LM
I
2
I

dX
  2  X 2
 LM
2
 Output power in mode varies as 1/.
Fabry-Perot model of laser
R e  1 for lasing.
e  gain for light passing through gain region ( < 0)
Total power   Pout  LM 
1

Example 1
 What 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 2
 From 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
dN J N
 
 g  N  N0  S
dt
e  sp
dS
N S
 g  N  N0  S 

dt
 sp  ph









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.
Laser Rate Equations
 Steady state:
dN dS

0
dt
dt
J
N

 g  N  N0  S
e  sp
g  N  N0  S 
 For small current (S  0)
J
N

e  sp
N
J sp
e
N
S

 sp  ph
Laser Rate Equations
 1
 N
S
 g  N  N 0  
  ph
  sp
N
S
 sp
 1

 g  N  N0 

  ph

 Lasing threshold:
g ( N  N0 ) 
1
 ph
compare Re-  1 for Fabry Perot mode
Laser Rate Equations
N th  N 0 
1
g ph
J th N th

e
 sp
 Above threshold:
J  J th
 g  N th  N 0  S
e
Laser Rate Equations
Example 3
 Parameters for a semiconductor laser are:
 sp  2.5 ns, L = 300  m, R = 0.12, N = 4,
I th  28 mA, N 0 = 2.1x108 m-2 ,   0.828 m
 What is the photon lifetime?
 What is the number of carriers at lasing threshold?
Laser Rate Equations
 How long does a photon stay in cavity?
Let   loss per unit distance due to mirror reflectance
L0  Propagation distance of photon over which
energy decays by 1/e.
e  L0  e 1
 L0  1
1
R
 L   ln R ; L = cavity length
e  L 
Laser Rate Equations
vg ph  L0
c
vg  ; N = group refractive index
N
 ng L
 ph 
c ln R
Example 4
 What 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.