Transcript Chapter 4 Photonic Sources

Chapter 4
Photonic Sources
Contents
• Review of Semiconductor Physics
• Light Emitting Diode (LED)
- Structure, Material,Quantum efficiency, LED Power,
Modulation
• Laser Diodes
- structure, Modes, Rate Equation,Quantum efficiency,
Resonant frequencies, Radiation pattern
• Single-Mode Lasers
- DFB (Distributed-FeedBack) laser, Distributed-Bragg
Reflector, Modulation
• Light-source Linearity
• Noise in Lasers
Review of Semiconductor Physics
k B  1.38 1023 JK -1
a) Energy level diagrams showing the excitation of an electron from the valence band to the conduction band.
The resultant free electron can freely move under the application of electric field.
b) Equal electron & hole concentrations in an intrinsic semiconductor created by the thermal excitation of
electrons across the band gap
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
n-Type Semiconductor
a)
b)
Donor level in an n-type semiconductor.
The ionization of donor impurities creates an increased electron concentration distribution.
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
p-Type Semiconductor
a)
Acceptor level in an p-type semiconductor.
b)
The ionization of acceptor impurities creates an increased hole concentration distribution
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Intrinsic & Extrinsic Materials
• Intrinsic material: A perfect material with no impurities.
n  p  ni  exp( 
Eg
2 k BT
)
[4-1]
n & p & ni are the electron, hole & intrinsic concentrat ions respective ly.
E g is the gap energy, T is Temperatur e.
• Extrinsic material: donor or acceptor type semiconductors.
pn  ni
2
[4-2]
• Majority carriers: electrons in n-type or holes in p-type.
• Minority carriers: holes in n-type or electrons in p-type.
• The operation of semiconductor devices is essentially based on
the injection and extraction of minority carriers.
The pn Junction
Electron diffusion across a pn junction
creates a barrier potential (electric field)
in the depletion region.
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Reverse-biased pn Junction
A reverse bias widens the depletion region, but allows minority carriers to move freely with the applied field.
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Forward-biased pn Junction
Lowering the barrier potential with a forward bias allows majority carriers to diffuse across the junction.
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Direct Band Gap Semiconductors
Indirect Band Gap Semiconductors
E
E
E
CB
Direct Bandgap
Ec
Eg
Indirect Bandgap, Eg
CB
Photon
Ev
kcb
VB
–k
k
(a) GaAs
–k
VB kvb
(b) Si
Ec
CB
Er
Ev
k
–k
Ec
Phonon
Ev
VB
k
(c) Si with a recombination center
(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs is
therefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced from
the maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination of
an electron and a hole in Si involves a recombination center .
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Semiconductor Device Fabrication
• Device fabrication requires a critical study of the crystal structure of
the different materials
• Crystal structure is the periodic arrangement of atoms (Si or Ge) or
group of atoms (GaAs or NaCl etc.)
• The spacing between the atoms or group of atoms is called lattice
spacing or lattice constant
• To create a semiconductor device we need a crystalline base/
substrate for mechanical strength and electric contacts
• Thin layers of semiconductor materials are grown on the substrate
which should have the same lattice structure as that of the substrate
• Lattice matching is required, means lattice constant should be the
same
• Lattice matching is important as we want to avoid temperature
dependent stresses or strain
• This is known as epitaxial growth (we can change the impurity level
in the adjacent layers)
LED Structure
For use in the fiber transmission applications an LED must have
• High radiance output
Radiance is a measure , in watts, of the optical power radiated
into a unit solid angle per unit area of the emitting surface. High
radiances are necessary to couple sufficiently high optical
power levels into a fiber.
• Fast emission response time
The emission response time is the time delay between the
application of a current pulse and the onset of optical emission.
Time delay is responsible for limiting the band width with which
the source is modulated.
• High quantum efficiency
Quantum efficiency is related to the fraction of injected
electron-hole pairs that recombine radiatively
continued
To achieve high radiance and high quantum efficiency, the LED
structure must provide a means to confine the charge carriers and
the stimulated optical emission to the active region of the pn-junction
where radiative recombination can take place
Carrier Confinement:
It is important to achieve the high level of radiative recombination in
the active region of the device which yields a high quantum
efficiency.
Optical Confinement:
It is important for preventing absorption of the emitted radiations in
the surroundings.
Cross-section drawing of a typical
GaAlAs double heterostructure light
emitter. In this structure, x>y to provide
for both carrier confinement and optical
guiding.
b) Energy-band diagram showing the
active region, the electron & hole
barriers which confine the charge carriers
to the active layer.
c) Variations in the refractive index; the
lower refractive index of the material in
regions 1 and 5 creates an optical barrier
around the waveguide because of the higher
band-gap energy of this material.
 ( m) 
1.240
Eg (eV)
[4-3]
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Surface-Emitting LED
• Active region is etched circular
well.
• The circular active area have
diameter 50μm and up to 2.5 μm
thick.
• The emission pattern is almost
isotropic with a 120o half-power
beam width
• This pattern is called Lambertian
Pattern i.e., the source is equally
bright when viewed from any
direction
but
the
power
diminishes as cosθ where θ is the
angle between the viewing
direction and the normal to the
surface
• The power is half when θ = 60o so
half power beam width is 120o
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Edge-Emitting LED
Consists of an active junction
region (source of incoherent
light and two guiding
layers).
• To match the core diameter,
the contact strip is 50-70 m
• Length of active region
range from 100 to 150 m
• The emission pattern is
more directional.
• In the plane parallel to the
junction, emitted beam is
Lambertian with half power
width 120o
• In the perpendicular plane
half power width decrease
to 25 – 35o
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Light source Materials
• Material used in the active region should be a direct band gap
material.
• In direct band gap material, radiative recombination is very high to
maintain adequate level of optical emission.
• Single element semiconductors are not direct band gap materials.
• III (e.g., Al, Ga, In)-V (e.g., P, As, Sb) compounds are direct band
gap materials. Few ternary and quaternary combinations of the
binary compounds of III-V materials are also direct band gap
materials.
• For operation in 800 -900 nm spectrum, the material used is the
ternary alloy Ga1-x Alx As
• The ratio x will determine the band gap of the material or wavelength
of the peak emitted radiation. The value of x for active region is
chosen so that the emission spectrum should be 800 – 850nm
• For x = 0.8, peak is at 810nm
continued
•
•
•
•
At longer wavelengths, the quarternary alloy In1-x Gax Asy P1-y is
one of the premier candidate.
By varying x and y I the active area, LED’s with peak power at
any wavelength between 1.0 – 1.7μm
E = h= hc/
The peak emission wavelength can be expressed as a function
of band gap energy Eg in eV by the equation
 (μm) = 1.240/ Eg (eV)
Semiconductor Material
Bandgap energy (eV)
Silicon
1.12
GaAs
1.43
Germanium Ge
0.67
InP
1.35
Ga0.93Al0.03As
1.51
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Spectral width of LED types
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Rate equations, Quantum Efficiency & Power of
LEDs
• When there is no external carrier injection, the excess density
decays exponentially due to electron-hole recombination.
n(t )  n0 e t /
• n is the excess carrier density,
n0 : initial injected excess electron density
 : carrier lifetime.
• Bulk recombination rate R:
dn n
R

dt 
• Bulk recombination rate (R)=Radiative recombination rate +
nonradiative recombination rate
bulk recombinat ion rate ( R  1/τ ) 
radiative recombinat ion rate ( Rr  1/τ r )  nonradiati ve recombinat ion rate( Rnr  1/τ nr )
With an external supplied current density of J the rate equation for the electron-hole
recombination is:
dn(t ) J n


dt
qd 
q : charge of the electron; d : thickness of recombinat ion region
In equilibrium condition: dn/dt=0
J
n
qd
n is the steady state electron density in the active region when a constant
Current is flowing through it.
Internal Quantum Efficiency
The internal quantum efficiency in the active region is the fraction of electron-hole
pairs that recombines radiatively
int
 nr
Rr




Rr  Rnr  r   nr  r
Where Rr and Rnr are the radiative and non radiative recombination rates
and nr = n / Rnr is the non radiative life time
int : internal quantum efficiency in the active region
Where  is the bulk recombination life time and given as
1


1
r

1
 nr
Optical Power
In general r and nr are comparable for direct band gap materials so for
simple homojunction LED quantum efficiency would b ½. However double
heterostructures can have 60-80% efficiency
If the total current injected is I, then the total number of recombinations
per second is Rr + Rnr = I/q, substituting this equation in quantum efficiency
eq. we get
Rr = int I / q
Where Rr is the total number of photons generated per second and has energy h
Optical power generated internally in the active region in the LED is:
I
hcI
Pint  int h  int
q
q
Pint : Internal optical power,
I : Injected current to active region
External Quantum Eficiency
ext 
# of photons emitted from LED
# of LED internally generated photons
[4-10]
• In order to calculate the external quantum efficiency, we need to
consider the reflection effects at the surface of the LED. If we
consider the LED structure as a simple 2D slab waveguide, only
light falling within a cone defined by critical angle will be emitted
from an LED.
ext
c
1

T ( )(2 sin  )d

4 0
4n1n2
T ( ) : Fresnel Transmissi on Coefficien t  T (0) 
(n1  n2 ) 2
If n2  1  ext 
1
n1 (n1  1) 2
Pint
LED emitted optical powr, P  ext Pint 
n1 (n1  1) 2
Modulation of LED
• The frequency response of an LED depends on:
1- Doping level in the active region
2- Injected carrier lifetime in the recombination region, .
i
3- Parasitic capacitance of the LED
• If the drive current of an LED is modulated at a frequency of
the output optical power of the device will vary as:
P ( ) 

P0
[4-15]
1  ( i ) 2
• Electrical current is directly proportional to the optical power,
thus we can define electrical bandwidth and optical bandwidth,
separately.
 p() 
 I() 
Electrical BW  10log 

20
log

 I (0) 
p
(
0
)




p : electrical power, I : electrical current
[4-16]
 P( ) 
 I ( ) 
Optical BW  10 log 
 10 log 


P
(
0
)
I
(
0
)




Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
[4-17]
Some LED and Laser Diode Material Mixtures and
their Characteristics
LASER
Light Amplification by the
Stimulated Emission of
Radiation
Advantages:
Ideal laser light is single-wavelength only. This is not
exactly true for communication lasers.
Lasers can be modulated (controlled) very precisely.
Lasers can produce relatively high power. Indeed some
types of laser can produce kilowatts of power. In
communication applications, semiconductor lasers of
power up to about 20 mW are available
Because laser light is produced in parallel beams, a high
percentage (50% to 80%) can be transferred into the
fiber.
Disadvantages:
Lasers have been quite expensive by comparison with
LEDs.
Reason: Temperature control and output power control is
needed.
The wavelength that a laser produces is a characteristic
of the material used to build it and of its physical
construction. Lasers have to be individually designed for
each wavelength they are going to use.
Amplitude modulation using an analog signal is difficult
with most lasers because laser output signal power is
generally non-linear with input signal power
An Ideal Beam of LASER Radiation
Properties of LASER
LASER has three main characteristics:

Monochromatic

Coherent

Collimated
Properties of LASER
Monochromatic
Radiation which occurs at a single wavelength or
color.
Properties of LASER
Coherent
It means all waves vibrate in step, there by
constructively reinforcing each adjacent
wave.
A.
=
Coherent light
B.
Constructive interference
=
Incoherent light
Destructive interference
OPTICAL INTERFERENCE
Properties of LASER
Collimated
It means rays are travelling in the same
direction on parallel paths.
Collimating lens
Source
Source
Target area
A
B
LASER
(Light Amplification by the Stimulated Emission of Radiation)
• Laser is an optical oscillator. It comprises a resonant optical
amplifier whose output is fed back into its input with matching
phase. Any oscillator contains:
1- An amplifier with a gain-saturated mechanism
2- A feedback system
3- A frequency selection mechanism
4- An output coupling scheme
• In laser the amplifier is the pumped active medium, such as
biased semiconductor region, feedback can be obtained by
placing active medium in an optical resonator, such as FabryPerot structure, two mirrors separated by a prescribed distance.
Frequency selection is achieved by resonant amplifier and by
the resonators, which admits certain modes. Output coupling is
accomplished by making one of the resonator mirrors partially
transmitting.
Pumped active medium
• Three main process for laser action:
1- Photon absorption
2- Spontaneous emission
3- Stimulated emission
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Lasing in a pumped active medium
• In thermal equilibrium the stimulated emission is essentially
negligible, since the density of electrons in the excited state is
very small, and optical emission is mainly because of the
spontaneous emission. Stimulated emission will exceed
absorption only if the population of the excited states is greater
than that of the ground state. This condition is known as
Population Inversion. Population inversion is achieved by
various pumping techniques.
• In a semiconductor laser, population inversion is accomplished
by injecting electrons into the material to fill the lower energy
states of the conduction band.
Fabry-Perot Resonator
M1
A
M2
m=1
Relative intensity
f
1
R ~ 0.8
R ~ 0.4
m=2
 m
B
L
(a)
m=8
m - 1
(b)
m
m + 1

(c)
Resonant modes : kL  m m  1,2,3,..
Schematic illustration of the Fabry-Perot optical cavity and its properties. (a) Reflected
waves interfere. (b) Only standing EM waves, modes, of certain wavelengths are allowed
in the cavity. (c) Intensity vs. frequency for various modes.R is mirror reflectance and
lower R means higher loss from the cavity.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
(1  R) 2
I trans  I inc
(1  R) 2  4 R sin 2 (kL)
R: reflectance of the optical intensity, k: optical wavenumber
[4-18]
Laser Diode
•
Laser diode is an improved LED, in the sense that uses stimulated
emission in semiconductor from optical transitions between distribution
energy states of the valence and conduction bands with optical
resonator structure such as Fabry-Perot resonator with both optical
and carrier confinements.
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Laser Diode Characteristics
•
•
•
•
Nanosecond & even picosecond response time (GHz BW)
Spectral width of the order of nm or less
High output power (tens of mW)
Narrow beam (good coupling to single mode fibers)
• Laser diodes have three distinct radiation modes namely,
longitudinal, lateral and transverse modes.
• In laser diodes, end mirrors provide strong optical feedback in
longitudinal direction, so by roughening the edges and cleaving
the facets, the radiation can be achieved in longitudinal direction
rather than lateral direction.
DFB(Distributed FeedBack) Lasers
•
In DFB lasers, the optical resonator structure is due to the incorporation
of Bragg grating or periodic variations of the refractive index into
multilayer structure along the length of the diode.
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Laser Operation & Lasing Condition
• To determine the lasing condition and resonant frequencies, we
should focus on the optical wave propagation along the
longitudinal direction, z-axis. The optical field intensity, I, can be
written as:
I ( z, t )  I ( z )e j (t  z )
[1]
• Lasing is the condition at which light amplification becomes
possible by virtue of population inversion. Then, stimulated
emission rate into a given EM mode is proportional to the
intensity of the optical radiation in that mode. In this case, the
loss and gain of the optical field in the optical path determine the
lasing condition. The radiation intensity of a photon at energy h
varies exponentially with a distance z amplified by factor g, and
attenuated by factor  according to the following relationship:
I ( z)  I (0) expg (h )   (h )z 
n1
R1
Z=0
R2
n2
Z=L
I (2L)  I (0) R1R2 expg (h )   (h )(2L)
[2]
 : Optical confinemen t factor, g : gain coefficien t
 n1  n2 

α : effective absorption coefficien t, R  
 n1  n2 
Lasing Conditions:
I ( 2 L )  I ( 0)
exp(  j 2 L)  1
2
[3]
[4]
Continued
Previous eq. gives us the information related to the
resonant frequencies of Fabry-Perot cavity.
Condition for Threshold:
The condition to just reach the lasing threshold is the
point at which the optical gain is equal to the total loss αt,
in the cavity.
Using the condition for threshold and eqs. [2] and [3] we
will get the relation for threshold gain
Threshold gain & current density
1  1 

g th   t   
ln 
2 L  R1 R2 
g th     end
[4-23]
Where αend is the mirror loss in the lasing cavity. Thus
Laser starts to " lase" iff : g  gth
For laser structure with strong carrier confinement, the threshold current
Density for stimulated emission can be well approximated by:
gth  J th
 : constant depends on specific device constructi on
[4-24]
Optical output vs. drive current
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Semiconductor laser rate equations
•
Rate equations relate the optical output power, or # of photons per unit
volume,  , to the diode drive current or # of injected electrons per
unit volume, n. For active (carrier confinement) region of depth d, the
rate equations are:
d

 Cn  Rsp 
dt
 ph
Photonratestimulated emission  spontaneous emission  photon loss
[4-25]
dn
J
n


 Cn
dt qd  sp
electron rate  injection  spontaneous recombination  stimulated emission
C : Coefficien t expressing the intensityof the opticalemission & absorptionprocess
Rsp : rate of spontaneous emission into the lasingmode
 ph : photonlife time
J : Injectioncurrent density
Threshold current Density & excess electron density
•
At the threshold of lasing:
  0, d / dt  0, Rsp  0
from eq. [4 - 25]  Cn   /  ph  0  n 
•
1
C ph
 nth
[4-26]
The threshold current needed to maintain a steady state threshold
concentration of the excess electron, is found from electron rate
equation under steady state condition dn/dt=0 when the laser is just
about to lase:
J th nth
nth
0

 J th  qd
qd  sp
 sp
[4-27]
Laser operation beyond the threshold
J  J th
• The solution of the rate equations [4-25] gives the steady state
photon density, resulting from stimulated emission and
spontaneous emission as follows:
s 
 ph
qd
( J  J th )   ph Rsp
[4-28]
External quantum efficiency
• Number of photons emitted per radiative electron-hole pair
recombination above threshold, gives us the external quantum
efficiency.
ext 
i ( g th   )
g th
q dP
dP (mW )

 0.8065[ m]
E g dI
dI (mA )
• Note that:
i  60%  70%;
ext  15%  40%
[4-29]
Laser Resonant Frequencies
• Lasing condition, namely eq. [4-22]:
exp(  j 2 L)  1 
• Assuming
mode is:

mc
m 
2 Ln
2n

2 L  2m , m  1,2,3,...
the resonant frequency of the mth
m  1,2,3,...
c
2
   m   m1 
  
2 Ln
2 Ln
[4-30]
[4-31]
Spectrum from a laser Diode
 (  0 ) 
g ( )  g (0) exp 
 : spectral width
2

2 

[4-32]
Laser Diode Structure & Radiation Pattern
• Efficient operation of a laser diode requires reducing the # of
lateral modes, stabilizing the gain for lateral modes as well as
lowering the threshold current. These are met by structures that
confine the optical wave, carrier concentration and current flow
in the lateral direction. The important types of laser diodes are:
gain-induced, positive index guided, and negative index
guided.
(a) gain-induced guide
(b)positive-index waveguide
(c)negative-index waveguide
Laser Diode with buried heterostructure (BH)
Single Mode Laser
• Single mode laser is mostly based on the indexguided structure that supports only the fundamental
transverse mode and the fundamental longitudinal
mode. In order to make single mode laser we have
four options:
1- Reducing the length of the cavity to the point
where the frequency separation given in eq[4-31] of
the adjacent modes is larger than the laser transition
line width. This is hard to handle for fabrication and
results in low output power.
2- Vertical-Cavity Surface Emitting laser (VCSEL)
3- Structures with built-in frequency selective grating
4- tunable laser diodes
.
VCSEL
Frequency-Selective laser Diodes:
Distributed Feedback (DFB) laser
2ne 
B 
k
[4-33]
Frequency-Selective laser Diodes:
Distributed Feedback Reflector (DBR) laser
B 2
1
  B 
(m  )
2ne Le
2
[4-35]
Output spectrum symmetrically distributed around Bragg wavelength in an idealized DFB laser diode
Frequency-Selective laser Diodes:
Distributed Reflector (DR) laser
Modulation of Laser Diodes
• Internal Modulation: Simple but suffers from non-linear effects.
• External Modulation: for rates greater than 2 Gb/s, more
complex, higher performance.
• Most fundamental limit for the modulation rate is set by the
photon life time in the laser cavity:
1
 ph
c
1
1  c
  g th
   ln
n
2L R1 R2  n
[4-36]
• Another fundamental limit on modulation frequency is the
relaxation oscillation frequency given by:
1
f 
2
1
 sp ph
 I


 1
 I th

1/ 2
[4-37]
Relaxation oscillation peak
Pulse Modulated laser
• In a pulse modulated laser, if the laser is completely turned off
after each pulse, after onset of the current pulse, a time
t d delay,
given by:


Ip
t d   ln 

 I p  ( I B  I th ) 
 : carrier life time
I B : Bias current
I p : Current pulse amplitude
[4-38]
Temperature variation of the threshold
current
I th (T )  I z e
T / T0
Linearity of Laser
Information carrying
electrical signal s(t)
LED or Laser diode
modulator
Optical putput power:
P(t)=P[1+ms(t)]
Nonlinearity
x(t)
Nonlinear function y=f(x)
y(t)
x(t )  A cos t
y (t )  A0  A1 cos t  A2 cos 2t  ...
Nth order harmonic distortion:
 An 
20 log  
 A1 
Intermodulation Distortion
x(t )  A1 cos 1t  A2 cos  2 t 
y (t )   Bmn cos( m1  n 2 )t
m,n  0,1,2,...
m,n
Harmonics:
n1 , m 2
Intermodulated Terms:
1   2 ,21   2 ,1  2 2 ,...
Laser Noise
• Modal (speckel) Noise: Fluctuations in the distribution of
energy among various modes.
• Mode partition Noise: Intensity fluctuations in the longitudinal
modes of a laser diode, main source of noise in single mode
fiber systems.
• Reflection Noise: Light output gets reflected back from the fiber
joints into the laser, couples with lasing modes, changing their
phase, and generate noise peaks. Isolators & index matching
fluids can eliminate these reflections.