PART II:-

OPTICAL FIBRE SOURCES AND

DETECTORS

• Materials

• Construction

• Working

• Efficiencies and response time

• Modulation

• Drawbacks and Limitations

• Power Launching Efficiencies

• Coupling to fibre

• Photo-detector noises

OPTICAL FIBER

COMMUNICATION

FIBER OPTIC SOURCE

CHARACTRISTIC LED LASER

Coherence Non-Coherent Coherent

Chromaticity Many wavelengths Highly Monochromatic

Spectral Width 36 to 40nm 2nm

Divergence Cosine power distribution Narrow pencil beam

Output Power Low (pW) High

Modes Feeds MM Fiber Only Can feed MM and SM

Bit Rate < 100-200Mbps > 2Gbps

Cost Less expensive More expensive

Construction Simple- pn junction Complex–Laser cavity

Emission Spontaneous Stimulated

CHOICE OF SOURCE

Parameters for choice – geometry of fiber,

attenuation, group velocity, group delay distortion,

modal characteristics.

LED – Low power, Multimode, Less precision

requirement.

LASER – High power, Single/Multimode, High

precision, Fiber with high attenuation, Longer

distance application etc.

P-N JUNCTION

• If proper material chosen, recombination energy release is light.

• p-side lightly doped and n-side highly doped.

• Major recombination in p-side.

SPONTANEOUS EMISSION

• h- Plank’s constant = 6.625 x 10-34 Js

Frequency of radiation

IN- DIRECT BAND GAP MATERIALS

DIRECT BAND GAP MATERIALS

MATERIAL FOR LED

Spontaneous Emission:

Electron is excited from valance band to conduction

band using external bias.

Electron stays there for carrier lifetime and then falls

back to valance band, emitting energy equal to band-

gap energy.

In p-n junction in forward bias, electrons and holes

cross junction and recombine to emit energy equal to

band-gap energy.

MATERIAL FOR LED

In-Direct band-gap materials: Momentum of

electrons in valance band and conduction band are not

same. (Higher/lower)

Electrons in conduction band have to search for

Phonon(high energy lattice vibration) to balance

momentum to convert to photon.

This requires generation of phonon and photon

simultaneously for every recombination.(Highly unlikely)

This results in non-radiative recombination. Si, Ge

Direct band-gap materials: Momentum of electrons

in valance band and conduction band are same.

This does not require generation of phonon and photon

simultaneously for every recombination.

This results in most recombinations radiative.

CHOICE OF MATERIAL No pure semiconductor is direct band gap material.

Binary, Ternary and quaternary combination of band

III and band V materials can give direct band gap

material.

Can give almost all recombination radiative.

Band III – Al, Ga, In

Band V – P, As, Sb

GaAs, GaAlAs, InGaAsP

CHOICE OF MATERIAL

Alloy Ga1-xAlxAs has ratio x of Aluminum Arsenide and

Gallium Arsenide.

With x = 0.08, peak wavelength is 810nm.

CARRIER LIFETIME At positive biased p-n junction, carrier injection occurs.

Excess electrons and holes created in p and n- type material

(minority carriers).

Δn = Δp, as carriers form and recombine in pairs.

When injection stops, carrier return to equilibrium value.

Excess carrier density decays exponentially with time.

• Δno initial injected excess electron density.

• Time constant τ is carrier lifetime or bulk

recombination life time, time between creation and

recombination.

DIFFUSION LENGTH

Distance moved by carrier after diffusion and before

recombination.

Can be defined for electrons and holes as Le and Lh.

Le and Lh are electron and hole diffusion coefficients.

τ is carrier lifetime.

Electric current due to electrons and holes is result of

non uniform carrier distribution in material.

Flows even in absence of electric field.

INTERNAL QUANTUM EFFICIENCY In radiative recombination, photon of energy hν is released.

Non radiative recombination releases energy as heat(lattice

vibration).

IQE in active region is fraction of electron-hole pairs which

recombine radiatively.

Rr and Rnr are radiative and non radiative recombination

rate per unit volume.

Bu

t

an

d

LED STRUCTURE - HOMOJUNCTION

n+

p

n+ substrate

n+

Dielectric SiO2

Ohmic Contact

p

LED STRUCTURE - HOMOJUNCTION p-n junction formed by diffusion or epitaxial

technique.

Specially designed to enable most radiative recombination at junction side nearer to surface.

Done when major current flow carried by carriers injected into surface layer.

By making n-side heavily doped.

Major junction crossing is due to electrons to p-side.

Light in p-region radiated out.

Light in n-region may be absorbed.

Both p and n-type semiconductor are made of same base material. (e.g. GaAs).

Called Homo Junction.

HETERO JUNCTION

n-side made of n-type GaAs on n-type GaAlAs.

GaAs – Smaller and direct band gap – Larger electron affinity.

GaAlAs – Larger and direct band gap – Smaller electron affinity.

Electrons flows into GaAs layer.

GaAs becomes collection layer of electrons.

N-GaAlAs - Depletes.

Reduces diffusion length and carrier life time.

Increases bandwidth.

P GaAlAs

N GaAlAs

n GaAs

DOUBLE HETERO JUNCTION

Lower band gap GaAs sandwiched between two larger

band gap GaAlAs layers.

Central GaAs layer becomes active layer.

Placed closest to surface.

Gives carrier confinement and light confinement.

P GaAlAs

N GaAlAs

n or p GaAs

p GaAs

n GaAs

Contact layer

Contact layer

Confining layer

Confining layer

Active layer

DOUBLE HETERO JUNCTION

5 layer structure.

n-N and p-P on two sides.

Ohmic resistive element

Gives good ohmic contact of active layer to conduction layer.

Narrow band gap material at device contact.

Low resistance at device terminal.

Central layers make active layer p or n-type GaAs

sandwiched between N-GaAlAs and P-GaAlAs.

CARRIER

CONFINEMENT

At n-N, electrons flow from N to n higher band gap to

lower band gap.

n-GaAs becomes collection region of electrons.

These electrons do not enter P-GaAlAs as higher BG

even in forward bias.

In forward bias, holes from P-GaAlAs come to active

region.

All recombination take place in active layer.

Gives narrow output.

Flow of electrons from higher BG to lower BG more

efficient than same BG.

P GaAlAs

N GaAlAs

n GaAs

OPTICAL

CONFINEMENT

Refractive Index inversely proportional to BG energy.

GaAs – Higher RI

GaAlAs – Lower RI

Higher RI layer sandwiched between two lower RI.

Acts as slab wave guide.

Light generated inside active region remains guided

through total internal reflection.

Optical confinement.

Required for preventing absorption of emitted

radiation by material around p-n junction.

High efficiency, high radiance.

P GaAlAs

N GaAlAs

n GaAs

N-type

Ga1-

xAlxAs

n-type

GaAs

P-type

Ga1-

xAlxAs

DOUBLE

HETERO

JUNCTION

SURFACE EMITTING LED

BURRUS/FRONT EMITTER

LED

SURFACE EMITTING LED Plane of active light emitting

region perpendicular to axis of fiber.

Fiber cemented into well.

Active region approximately 50μm dia and 2.5 μ.m thick.

Emission pattern isotropic with 120⁰ half power beam width.

Lambertian pattern.

Power decreases as cosine of θ.

Source is equally bright when viewed from any direction.

As projected area decreases as cosθ.

Coupling not good.

Highly divergent.

EDGE EMITTING LED

EDGE EMITTING LED Active region RI greater than side

layers.

Forms waveguide channel that directs

optical radiation towards side into fiber.

Active region 50-70μm wide, 100-150μm

long.

Emission pattern-

Lambertian 120⁰ horizontally.

With proper choice of waveguide thickness, it

can be 25⁰ to 35⁰ vertically.

Better than Surface Emitter.

RADIANCE AND EMISSION RESPONSE TIME

Radiance – (Brightness)

Measure in watts, of the optical power radiated into

a unit solid angle per unit area of the emitting

surface.

High radiance necessary to couple sufficiently high

power levels into a fiber.

Emission response time –

Time delay between application of current pulse and

the onset of optical emission.

OPTICAL OUTPUT

Highly divergent, high power Less divergent, low power

MODULATION CAPABILITY OF LED

Light output from LED can be modulated by wideband

information signal.

Response time > 1µs.

Sufficient for common applications.

Not suitable for communication application as

response time required < 1ns.

Modulation capability restricted by –

Diffusion capacitance

Parasitic diode space charge capacitance

DIFFUSION CAPACITANCE

During forward bias storage of charge carriers in

active region cause diffusion capacitance.

Cdiff = dQ/dV

dQ is change in number of minority carriers stored

outside the depletion region when a change in voltage

across the diode dV is applied.

Delays storage of injected carriers.

Shows how fast change in charge takes place for a

particular change in voltage.

Very large in F.B.(8000pf to 20µf )

PARASITIC DIODE SPACE CHARGE CAPACITANCE

Delays charge injection process itself.

It determines emission response time.

C = εA/d

Emission response time due to this Capacitance can be

made negligible by applying a small constant forward

bias.

Varies more slowly with current that Diff Capacitance.

Considered constant.

Typical value – 350 to 1000pf.

FREQUENCY RESPONSE OF LED Then Frequency Response is entirely determined by

Diffusion Capacitance.

Drive current is modulated by frequency ω, output

optical intensity is -

• Io is intensity emitted at zero modulation frequency.

• τeff is effective carrier life time.

OPTICAL OUTPUT BANDWIDTH

3DB ELECTRICAL VS OPTICAL BANDWIDTH For electrical bandwidth, we feed Iin and receive Iout.

We plot electrical Pout /Pin α (Iout / Iin)2.

Electrical 3dB bandwidth is when output current falls to 70.7% of peak value.

For optical bandwidth, again we feed Iin and receive Iout.

We plot optical Pout /Pin α (Iout / Iin) .

Electrical 3dB bandwidth is when output power falls to 50% of peak value.

Fictitiously gives Optical BW > Electrical BW.

Both BWs are normally mentioned to avoid confusion.

ELECTRICAL BANDWIDTH OF LED

It is frequency band over which –

P(ω) = P(0)/2

I2(ω) = I2(0)/2

Using I(ω) and ω = Δω

Δω = 1/τeff

Higher BW if τeff is lower.

Effective carrier lifetime can be reduced by

increasing doping level in active region.

Controlling injected carrier density.

TRANSIENT RESPONSE

Square pulse when applied to LED gives rise time and fall time due to Diffusion capacitance.

Junction space charge capacitance

To avoid the above current peaking is achieved using peaking coil in parallel to LED.

TRANSIENT RESPONSE

A current 2I is fed.

At t=0, current through coil =0.

Double current through LED enhances injection and recombination rate, reducing rise time.

Current gradually distributed in L and D.

At t=t1, I=0, coil tries to flow current in same direction ½ LI2.

Negative current I through diode brings injected carriers to equilibrium faster, reducing fall time.

TEMPERATURE DEPENDENCE

TEMPERATURE DEPENDENCE

Internal quantum efficiency of LED decreases

exponentially with increasing temperature.

Light emitted decreases.

Edge emitting LED has lower output power than

surface emitting LED.

Edge emitting LED are more temperature dependent.

EXTERNAL QUANTUM EFFICIENCY

Fresnel Reflection – When light strikes boundary between two homogeneous media

with different refractive indices, a portion reflects back and rest transmits further

through refraction. It is not total internal reflection.

EXTERNAL QUANTUM EFFICIENCY

Ratio of the number of photons finally emitted to

number of carriers crossing junction.

• Not same as Internal Quantum Efficiency. as – 1. Only light emitted in the direction of the semiconductor air surface

is useful.

2. Out of light in 1, only light striking emitting surface at angle less

than critical angle will be transmitted through.

3. Some of this light in 2, will be reflected back at semiconductor-air

surface due to Fresnel reflection.

4. There is absorption of light along the path till emitting surface.

ɳext < ɳint

LED POWER AND EFFICIENCY

Excess minority carrier Δn = Δnoe-t/τ

Equilibrium established at constant current flow into junction.

Total carrier generation rate

= externally supplied + thermally generated rate

Current density in ampere/sq m = J

Electrons injected across p-n junction per cubic meter per second = J/qd

q = charge on electron

d = thickness of recombination region.( cubic meter hence include d)

Rate equation for carrier recombination in LED is –

d(Δn)/dt = J/qd - Δn/τ m-3s-1

At equilibrium d(Δn)/dt = 0

Δn = J τ /qd (steady state electron density at constant current into

junction.)

LED POWER AND EFFICIENCY

Total R = Δn/τ = J /qd = Rr + Rnr

Total number of recombination per second R = i/q

i = Forward bias current into device.

(All excess carriers recombine either radiatively or non-

radiatively)

ɳint = Rr/R

Rr = ɳint i/q

= Photons generated/second

Total optical power generated = Rr hν

Pint = ɳint hν i/q watts

Pint = ɳint hc i/qλ watts

LED POWER AND EFFICIENCY

External power efficiency =

• Optical power emitted externally Pe / Electrical power

provided

Pe /P x 100%

Optical power emitted Pe into medium of low RI n from

the face of planer LED fabricated from material of RI

nx is appox

Pe = (Pint F n2)/ 4 nx 2

F is transmission factor of semiconductor – external interface.

(Due to Fresnel reflection, all power will not transmit outside)

LASER

LIGHT AMPLIFICATION BY STIMULATED EMISSION OF

RADIATION

• h- Plank’s constant = 6.625 x 10-34 Js

Frequency of radiation

STIMULATED EMMISSION

Electron at higher excited energy level E2, is impinged

with external stimulation = photon energy = hν12

Electron is forced to come down to stable state E1,

radiating energy hν12

Electron can be stimulated mush before its natural

spontaneous transition time.

Emitted photon by stimulation emission has same

frequency, phase and polarization as the incident

photon.

POPULATION INVERSION

In thermal equilibrium, density of electrons in non-excited lower level E1 is much more than excited level E2.

Most photons emitted will be absorbed. Stimulated emission negligible.

Stimulated emission will exceed absorption only if population of excited stage is greater than that of ground state.

Called Population Inversion.

Inverted population is not an equilibrium condition.

Hence requires pumping techniques.

In semiconductor LASER, it is achieved by injecting electrons into material at device contact to fill lower energy state of conduction band.

In pn junction diode, forward bias applied to inject e into conduction band of p-region or holed are injected into valance band of n-region.

POPULATION INVERSION

Boltzmann Distribution-

Thermal Equilibrium Non equilibrium Distribution-

Population Inversion

LASING ACTION

Two processes:-

Stage one:-

FB applied to active layer and confining layer forming pn

junction.

Hole-electron pair created , recombine after carrier lifetime

to emit spontaneous emission.

FB is gradually increased causing more pairs and more

emission.

Some of these photons are re-absorbed to create more pairs

and some will stimulate pairs to recombine before

spontaneous carrier lifetime emitting stimulated emission.

Stimulated emissions increases with current.

Current at which stimulated emission completely takes over

spontaneous emission is called Threshold current.

THRESHOLD CONDITION

LASING ACTION

Stage two:-

Tries for sustaining the oscillations to act as source.

Light generated remains guided in GaAs active layer of three

layer hetero-structure acting as slab waveguide.

Two sides of waveguide cleaved perpendicular to axis.

Act as two parallel mirror facets.

One side completely reflective and other partially

transparent to emit light out.

Part of light in direction of transparent facets will emit out.

Light towards reflective facet will reflect back towards

output suffering absorption all along.

Only those wavelengths sustain for which round trip phase

of reflected light is same as forward light.

Rest will decay.

LASING ACTION

LASING ACTION

Length of cavity l chosen to give ‘gain’ to chosen wavelength.

All other wavelengths have ‘loss’.

Desired power suffers absorption and power loss as it travels.

For overall gain, total gain > total loss.

Constructive oscillations for desired wavelength.

Light increases due to stimulated emission.

Emitted photon in phase with incident photon stimulating the emission.

LASING ACTION

Optical power P varies exponentially with distance z.

Solving dP/dz :

• Beam is supplemented due to stimulated emission as it traverses

causing gain.

Solving dP/dz :

Combining both:

For round trip Z = 2L

LASING ACTION

For oscillations to sustain --

Solving for limiting condition :

RELATION BETWEEN THRESHOLD CURRENT AND

THRESHOLD GAIN COEFFICIENT GTH:

Threshold current density Jth for stimulated emission is proportional to threshold

gain coefficient gth.

REFLECTIVITY FOR NORMAL INCIDENT OF A PLANE WAVE ON

SEMICONDUCTOR – AIR LAYER INTERFACE CAN BE OBTAINED USING

FRESNEL LAW AS:

Threshold current Ith = Jth X area of optical cavity.

EXTERNAL DIFFERENTIAL QUANTUM EFFICIENCY

• Can be expressed in many ways.

• Number of photons emitted per radiative electron-hole pair

recombination above threshold.

Substituting gth and α

ɳext

EXTERNAL DIFFERENTIAL QUANTUM EFFICIENCY

• Experimentally, ɳext can be calculated from straight portion of curve for

emitted power P Vs Current I :

• Eg is bandgap energy hf on electron volt.

• q is charge on electron, (used for eV)

TOTAL EFFICIENCY

• P is directly proportional to I where I > Ith,

ɳT = ɳext { (I – Ith) / I}

= ɳext { 1 – Ith/I}

If I » Ith , ɳT = ɳext .

EXTERNAL POWER EFFICIENCY OR DEVICE EFFICIENCY

• Conversion of electrical input to optical output.

• ɳep = P / IV X100%

• From Total efficiency -

• ɳep = ɳT (Eg/ V) X100%

FEBRY PERROT LASER DIODE

RESONANT FREQUENCY

At lasing threshold, steady state oscillations occur inside cavity.

Magnitude and phase of returned wave must be equal to those of original wave.

P(2L) = P(0)

e-jβ2L = 1 β is propagation constant inside medium.

2 βL = 2πm …… m = 1,2,3, …integer

As

Also m = 2L/λm as wavelength inside medium λm = λ/n

RESONANT FREQUENCY

Cavity resonates and creates standing wave patterns when

integer number m of half lengths between mirrors.

Gain is a function of frequency /wavelength as the condition

satisfies for a number of wavelengths.

Each of these frequencies corresponds to a mode of

oscillation of LASER.

By changing structure, laser can be made SM or MM.

Relation between gain and frequency is similar to Gaussian

with λo as wavelength at center of spectrum, σ spectral

width of gain and maximum gain g(0) proportional to

population inversion.

RESONANT FREQUENCY

SPACING BETWEEN MODES OF MM LASER

For each longitudinal mode, there will be many transverse modes

due to reflection from sides.

Considering two successive longitudinal modes fm-1 and fm for

integer m-1 and m.

and

Subtracting the two

SPACING BETWEEN MODES OF MM LASER

Also with

• Hence number of modes, their heights and their spacing

depends on laser construction.

STRIPE GEOMETRY DH laser can provide optical confinement in vertical

direction but lasing takes place across whole width.

Broad emission area creates problems like

Difficult heat sinking

Unsuitable light output geometry for efficient

coupling to cylindrical fibers

Can be eliminated by stripe geometry to provide

optical confinement in horizontal plane.

Stripe acts as guiding mechanism.

Provides single transverse mode in horizontal

direction.

Called gain guided lasers.

STRIPE GEOMETRY

Series of wavelength peaks for several longitudinal modes.

Spacing of modes depends on optical cavity length.

Each corresponds to integral number of lengths.

Broadening of longitudinal mode peaks due to higher order

horizontal transverse modes.

Due to unrestricted width of active region.

Stripe geometry limits width of optical cavity.

Allows only single transverse mode

Gives good multimode laser.

SINGLE MODE LASER

Single longitudinal and single transverse mode.

By reducing length L of cavity until frequency separation

is larger than laser transition line width.

Rigid control of parameters required to provide and

maintain single mode operation.

Can be achieved by gain guided and index guided lasers.

GAIN GUIDED

LASERS- PROTON

ISOLATED STRIPE

Active GaAs bounded by p-type GaAlAs region on both

side.

Resistive region formed by proton bombardment.

Gives better current confinement.

Superior thermal properties due to absence of SiO2

layer.

GAIN GUIDED LASERS-

P-N JUNCTION

ISOLATED STRIPE

Selective diffusion through n-type surface region.

Both types gives pure multimode characteristics.

Highly efficient coupling into MM fibers.

Low coupling efficiency into SM fibers.

INDEX GUIDED LASERS-

Narrow current confining stripe.

Weak index guiding for light.

INDEX GUIDED

LASERS-

Transverse mode control.

Buried hetero-structure where active region is completely

buried in material of wider BG and lower RI.

Optical field well confined in both transverse and lateral

direction.

Good carrier confinement and index guiding.

MM and SM operation.

MODULATION OF LASERS

Pulse modulation

Analog modulation

Major limitations on modulation rate are…

LIMITATIONS OF MODULATION

Spontaneous carrier life time ζsp—

Life of carrier before it combines spontaneously.

It is function of semiconductor band structure and

carrier concentration.

Also called Radiative life time.

At room temperature, ζsp= ζr =1ns in GaAs based

material for dopant concentration of the order of

1019/cm3.

LIMITATIONS OF MODULATION

Stimulated carrier life time ζst—

Depends on optical density in the lasing cavity.

Of the order of 10ps.

LIMITATIONS OF MODULATION

Photon life time ζph—

Average time that the photon resides in the lasing

cavity before being lost either by absorption or by

emission through faces.

ζ-1ph is rate of transmission of photon.

For Febry Perrot Cavity..

ζ-1ph = (c/n) gth

For gth =50/cm, n=3.5, ζph = ? This sets upper limit to modulation capability of

laser.

LIMITATIONS OF MODULATION

Pulse modulation—

Easy as photon life time is small.

During ‘0’ laser is off. ζsp limits the modulation rate.

Time required to achieved population inversion to

provide gain to overcome losses in cavity is td.

td = ζ ln [ Ip/(Ip + ( IB – Ith))]

Ip is current pulse amplitude.

IB is bias current.

ζ is average life time of carrier when Ip + IB = Ith

LIMITATIONS OF MODULATION

Pulse modulation—

Delay time can be eliminated by dc-biasing the

diode at lasing threshold current.

Pulse modulation by modulating laser only in region

above threshold.

Life time is now a function of stimulated emission

life time only.

ζst <<ζsp

ζph is very small.

High modulation rates are possible.

LIMITATIONS OF MODULATION

Analog modulation—

Drive current above threshold proportional to

modulating signal.

Requires linear relation between light output and

carrier input.

Linearity better than LED.

Due to non-linearity inter-modulation and cross-

modulation effects exists.

TEMPERATURE EFFECT

TEMPERATURE EFFECT

Threshold current temperature dependent.

Approximate relation is given as –

Ith(T) = Iz exp(T/To)

Iz is a constant.

To is a measure of relative temperature insensitivity.

For typical stripe geometry GaAlAs laser diode, To is

120° to 165 ° C.

Using feedback mechanism, laser output can be

maintained constant.

Give a typical circuit for maintaining output constant.

POWER LAUNCHING AND COUPLING Parameter under consideration are

numerical aperture, Core size, Refractive index profile,

Core-cladding refractive index difference of fiber

Size, radiance and angular power distribution of optical

source.

Coupling efficiency ɳ is measure of amount of optical power

emitted from source that can be coupled into a fiber.

ɳ = PF / PS (Power coupled/ power from source)

Efficiency depends on type of fiber and coupling process –

lensed etc..

Flylead or pigtail attached to source at manufacturer’s

premise.

Power launching limits thus to fiber misalignment, different

core sizes, numerical apertures and refractive index profiles.

SOURCE TO FIBER POWER LAUNCHING

Radiance is optical power radiated into a unit solid angle per unit emitting surface area.

Watts per square centimeter per steradian.

Optical power which can be coupled into fiber depends on spatial distribution of optical power i.e. radiance.

Radiance function of θ and ɸ, varying from point to point.

Uniform emission across source area assumed for simplicity.

LAMBARTIAN PATTERN OF

SOURCE SURFACE EMITTING LED

Source equally bright when viewed from any direction.

Projected area of emitting surface varies as cosθ with viewing direction.

Hence power delivered at an angle θ normal to emitting surface varies as cosθ

EMISSION PATTERN OF SOURCE EDGE EMITTING LED AND LASER DIODE

Different radiance B(θ,0⁰) and B(θ,90⁰) in plane

parallel and normal.

Integer T and L transverse and lateral power

distribution coefficient s.

For edge emitters, L = 1(Lambertian with 120⁰ half

power distribution) and T is larger.

For laser diodes L can be over 100.

Much narrower output from Laser.

POWER COUPLING TO FIBER

COUPLED POWER --STEP INDEX

Symmetrical source of radiance B(As,Ωs) from an

individual radiating point source.

function of area and solid emission angle of source.

Fiber kept as close and centered as possible for

maximum coupling.

Total power is radiance integrated over entire emitting

surface area for entire solid angle.

COUPLED POWER --STEP INDEX

Radiance B(As,Ωs) is first integrated over solid

acceptance angle of fiber.

θo,max is maximum acceptance angle of fiber.

Power thus obtained is summed up for each point

source on LED emitting surface area (circular).

Calculated for source radius more than and less than

core radius both.

COUPLED POWER --STEP INDEX

SOURCE RADIUS RS < FIBER CORE RADIUS A

rm = rs

B(θ,ɸ) = Bocosθ

COUPLED POWER --STEP INDEX

In step index fiber NA in independent of position θs

and r on fiber end face.

For rs < a

TOTAL OPTICAL POWER PS EMITTED FROM

SOURCE OF AREA AS INTO A HEMISPHERE

As Φ = 2π

θ = 0 to π/2

θ

TOTAL OPTICAL POWER EMITTED FROM SOURCE OF

AREA AS INTO HEMISPHERE (2Π SR)

COUPLED POWER --STEP INDEX

SOURCE RADIUS RS > FIBER CORE RADIUS A

Calculate total coupled power if Source radius rs > fiber core radius a.

Compare it with power radiated into a hemisphere.

COUPLED POWER --GRADED INDEX

NA depends on distance r from fiber axis.

For source radius rs < fiber core radius a.

EQUILIBRIUM NUMERICAL APERTURE

All modes enter the fiber.

Non-propagating modes scatter out of fiber and die out

at few tens of meters. (Say 50m)

Equilibrium condition reached. Power Peq.

Gives Power loss.

Equilibrium numerical aperture is launch numerical

aperture giving same power Peq at 50m without any

non-propagating modes.

EQUILIBRIUM NUMERICAL APERTURE

Determines excess power loss.

More important for surface emitting LEDs, which

launches power in all modes in fiber.

Fiber coupled lasers are less prone as it excites fewer

non-propagating fiber modes.

LENSING SCHEMES

LENSING SCHEMES

If Source radius rs > fiber core radius a, power coupled

will not be less (with some power spilled), but all

modes will be equally excited.

If Source radius rs < fiber core radius a, power coupled

will be full , but all modes will not be excited.

For best coupling efficiency, rs = a

Miniature lenses can be used to achieve the same.

Micro lens magnifies emitting area of source to match

exactly the core area of fiber.

Solid acceptance angle increases by factor M if

emitting area is increased by same factor.

Creates fabrication and handling difficulties as size too

small.

NON-IMAGING MICROSPHERE

Small spherical lens used if LED area is less than core area.

For collimated output, source should be at focal point of lens.

Focal length can be found from Gaussian lens formula.

s and q are object and image distances from lens surface.

n and n’ are refractive indices of LED and coupling media respectively.

r is radius of curvature of lens.

SIGN CONVENTIONS USED…

Light travels from left to right.

Object distances are measured as positive to the left of

vertex and negative to the right.

Image distances are measured as positive to the right

of vertex and negative to the left.

All convex surfaces encountered by the light have a

positive radius of curvature and concave surfaces

negative radius.

NON-IMAGING MICROSPHERE

NON-IMAGING MICROSPHERE

For example- To collimate, q is infinite, source should be at focus.

Let n = 2, n’ = 1, r = -RL(from B) , Focal point = ?

s from B = f = 2RL

Thus Focal point is located at A.

Magnification given by lens, is ratio of cross sectional area of the lens to the emitting area.

Magnification and power coupled are .

With magnification

COUPLING EFFICIENCY

• Coupling efficiency is determined by size of fiber.

• For fiber of radius a and numerical aperture NA,

maximum coupling efficiency is -

• If radius of emitting area > fiber radius, no

improvement in coupling efficiency with lens.

LASER DIODE TO FIBER COUPLING

LASER has FWHM of 30° to 50° in transverse

direction.

LASER has FWHM of 5° to 10° in plane parallel to

junction.

Laser emitting area smaller than fiber core.

Spherical or cylindrical lenses or optical fiber tapers

can be used to increase efficiency.

PHOTODETECTORS

PHOTO DETECTORS - CHARACTERISTICS

REQUIRED..

Capability to sense light power and convert to

corresponding varying current.

Very high efficiency required to convert all of weak

input power to desired signal.

High response or sensitivity in desired wavelength.

Minimum noise.

Fast response speed and high bandwidth.

Insensitive to temperature variation.

Physically compatible dimension of optical fiber.

Low cost and long life.

PHOTO DETECTORS - TYPES

Photomultipliers –

Photocathode and electron multiplier in vacuum tube.

High gain, low noise.

Large size and high voltage required.

Pyro-electric crystals –

Photon to heat conversion.

Variation in dielectric constant gives change in

capacitance.

Cooling arrangements required.

Semiconductor photo detectors –

Size is large.

Photodiodes.

PHOTO DETECTORS - ADVANTAGES

Small size

Suitable material

High sensitivity

Fast response time.

Types of photo diodes –

PiN diode

Avalanche Photodiode APD

PIN PHOTO DETECTOR

p and n region sandwiching very lightly n-doped i-region.

Very large reverse bias depletes the i-region completely.

Photon with energy equal or greater than band gap energy,

excites an electron into conduction band.

Energy absorbed creates one electron-hole pair called

photocarriers.

PIN PHOTO DETECTOR

Reverse bias collects the photo carriers and result

proportional current through load resistor, called

photocurrent.

i-region larger than p and n region to ensure

generation of photo carriers in i-region only.

ENERGY BAND DIAGRAM

PIN PHOTO DETECTOR

As carriers flow, some Electron-hole pair will recombine after traversing distance Le and Lh for carrier life time τe and τh respectively.

• Po is incident optical power level and P(x) is optical

power absorbed at distance x.

LIGHT

ABSORPTION

COEFFICIENT

PIN PHOTO DETECTOR

Absorption coefficient depends on wavelength.

A photodiode can be used for a particular wavelength region only.

Lower wavelength – very high absorption coefficient.

Most photons absorbed at surface to give e-h pairs.

At surface, carriers loosely bound, recombination much faster.

Photocurrent very low.

Higher wavelength – absorption too low.

Low photocurrent.

Upper wavelength cutoff depends on minimum band gap energy.

PHOTOCURRENT

Depletion region width is w.

Power absorbed at distance w is:

• Entrance face reflectivity if is Rf,

• Po is incident power.

• hν is photon energy.

•q is charge on electron.

QUANTUM EFFICIENCY

Number of electron-hole pair generated per incident photon.

Practically ɳ varies from 30 to 95

Depends on thickness of depletion layer and wavelength.

If thickness too small, less e-h pair but have to travel less.

If thickness too large, more e-h pair but have to travel more

and recombination chances more.

Less response speed in both cases.

Compromise to be struck.

RESPONSIVITY

Photon current generated per unit optical power.

Typically 0.65μA/ μW for Silicon at 900nm, 0.45μA/

μW for Germanium at 1.3μm, 0.6μA/ μW for GaAlAs at

1.3μm.

AVALANCHE PHOTO DIODE

AVALANCHE PHOTO DIODE

APD multiplies primary photocurrent before giving out as output.

Increases sensitivity as multiplication is done before noise producing amplification.

n+ and p+ are thin heavily dopes n and p regions.

p is normally doped and i is nearly intrinsic.

Reverse bias will result in equal number of uncovered atoms on two sides of junction.

Depletion will reach deeper into p and i-region till reach through to p+ region.

Result in very high positive electric field in n+ at junction.

It will give large velocity to electrons generated and cause avalanche effect.

Large photocurrent through electron multiplication.

AVALANCHE PHOTO DIODE

Ionization rate is average number of e-h pair created

by an electron per unit distance travelled.

Low noise and large gain-bandwidth product as only

one type of carrier dominated impact ionization.

Average Multiplication factor M = IM/IP

Im and IP are multiplied and primary photocurrents.

Responsivity of APD is -

PHOTO-DETECTOR NOISE

To detect weakest received signal, photo detector and

amplifier must be optimized to give desired S/N.

To achieve desired S/N,

Photo detector must have high quantum efficiency to

generate a large signal power.

Photo detector and amplifier noises must be as low as

possible.

PHOTO-DETECTOR NOISE

Noise current decides the minimum optical power

levels that can be detected.

Sensitivity or minimum detectable optical power is

the power necessary to produce a photocurrent of same

magnitude as the root mean square of the total noise

current.

Or S/N = 1.

It is necessary to know various noise sources in photo

detector, to design a receiver.

MODEL OF PHOTO DETECTOR RECEIVER

PHOTO DETECTOR RECEIVER EQUIVALENT

CIRCUIT

Photodiode has series resistance Rs, bias resistor RL and total capacitance Cd comprising of junction and packaging capacitance.

Amplifier has input resistance and capacitance of Ra and Ca.

Rs much smaller than RL is neglected.

NOISE SOURCES

Modulated signal power P(t) falls on detector, primary

photocurrent generated iph(t) is:

• Primary current contains average photocurrent due to

dc signal power, Ip and signal current ip(t).

• For pin photo diode, mean square signal current <is2>

is:

• For avalanche photo detectors with multiplication

factor M:

NOISE SOURCES

For sinusoidally varying input signal of modulation

index m, signal component <ip2> is:

SHOT NOISE OR QUANTUM NOISE

Arises due to Statistical nature of production and collection of photo carriers after photons are incident on photo detector.

Follow Poison’s distribution.

Fundamental property of photo detection.

Sets a lower limit on receiver sensitivity when all conditions are optimized.

Quantum noise current has a mean square value in BW B, proportional to average value of Photocurrent Ip.

Mean square quantum or shot noise current for pin photodiode is = <iq

2> = 2qIpB

Mean square quantum or shot noise current for avalanche photodiode is = <iq

2> = 2qIpBM2F(M)

F(M) is noise figure due to random nature of avalanche process.

M is multiplication factor for APD

PHOTODIODE DARK CURRENT

Current that continues to flow without any incident

light.

Bulk Dark Current : Due to thermally generated

electrons and holes.

For pin diode, Bulk dark current = <iDB2> = 2qIDB

For avalanche diode, Bulk dark current = <iDB2> =

2qIDBM2F(M)

ID is Primary detector bulk dark current, proportional to

active area.

PHOTODIODE DARK CURRENT

Surface Dark Current : Depends on surface defects,

cleanliness, bias voltage and surface area.

Results due to recombination defects at surface.

For pin and avalanche diode both , Surface dark current

= <iDS2> = 2qILB

IL is surface leakage current.

Can be reduced by a guard ring which shunts leakage

current away from load resistor.

It is not a bulk phenomena, but a surface phenomena.

Hence multiplication factor does not effect leakage

current

THERMAL NOISE

Assuming Zin of amplifier much greater than load resistor ZL.

Photo detector contributes major thermal noise.

• KB is Boltzmann constant.

• T is absolute temperature.

TOTAL PHOTO DETECTOR NOISE CURRENT

Dark current and signal currents are uncorrelated.

Total mean square noise current is:

+

+

SIGNAL TO NOISE RATIO

For pin diode, dominant noise current is thermal noise.

For APD, dominant noise current is due to photo detector noise.

Signal current and bulk dark current are multiplied by M2.

Surface dark current is independent of M2.

F(M) also increases with M.

There exists an optimum value for M which gives maximum S/N.

For sinusoidal modulation, m=1, F(M) ≈ Mx -

DETECTOR RESPONSE TIME

DETECTOR RESPONSE TIME Major photons absorbed, photo carriers created in depletion

layer.

They drift across the depletion region giving drift current density Jdr.

Some photons absorbed and photo carriers created outside the depletion layer, in bulk of semiconductor.

They diffuse into depletion giving diffusion current density Jdiff.

Under steady state condition total current density is:

Where A is photo diode area and Φo is incident photon flux per unit area.

DETECTOR RESPONSE TIME

Lp is diffusion length.

Pno is equilibrium hole density.

Dp is diffusion coefficient for hole.

DETECTOR RESPONSE TIME

Response time depends on:-

1. Transit time of carriers in depletion region = td = w/vd

vd is carrier drift velocity and w is width of depletion region.

Field so high that vd is maximum. td = 1ns

2. Diffusion time of photo carriers generated outside depletion region.

3. RC time constant of photodiode and its associated circuit.

Diffusion is very slow process w.r.t. drift process.

Diffusion time can be made small if most carriers generated in depletion region.

Otherwise, output will take longer to follow.

Will result in rise time and fall time.

RISE AND FALL TIME

In fully depleted photodiode, rise time and fall time are equal.

Are different at low bias levels.

RESPONSE OF PHOTODIODE WHICH IS NOT FULLY

DEPLETED

TYPICAL RESPONSES OF PHOTODIODE

For high quantum efficiency, depletion layer width w should be very large w.r.t. inverse of absorption coefficient.

JUNCTION CAPACITANCE

RC time constant limits response time.

If RT is combination of load and amplifier input

resistance and CT is photodiode and amplifier

capacitance, pass band of detector (filter) is --

PHOTODIODE MATERIAL - CRITERIA

Absorption coefficient αs reduces with increase in

wavelength.

If w>> 1/ αs is satisfied for longest wavelength, it will

work for all other frequencies too.

Best responsivity and highest quantum efficiency are

obtained if band gap energy of material is slightly less

than energy of photon at longest wavelength.

It will give low dark current as thermally generated e-h

pair will be less due to large Eg.

PHOTODIODE MATERIAL

For 800-900nm, Si, Ge, GaAs, InGaAs, InGaAsP etc..

Most widely used Si has lowest avalanche

multiplication noise, highest receiver sensitivity, and

highly developed technology.

For wavelength above 1μm- Responsivity of Si is too slow

as photons energy < Silicon band gap Eg of 1.17eV.

Hence for range 1μm – 1.6μm, material used are Ge,

InP, InGaAsP, GaSb, GaAlSb, HgCdTe, InGaAs.

Most widely used InGaAs has good absorption

coefficient, good responsivity.