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Optical Devices for High Speed Communication Systems

Lecture Notes

Optoelectronic Devices & Communication Networks

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Optoelectronic Devices for Communication Networks

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Optoelectronic Devices for Communication Networks

• Requirements to understand the concepts of Optoelectronic Devices:

1. We need to study concepts of light properties

2. Some concepts of solid state materials in particular semiconductors.

3. Light + Solid State Materials

Light Properties

• Wave/Particle Duality Nature of Light

• Reflection• Snell’s Law and Total Internal Reflection (TIR)• Reflection & Transmission Coefficients• Fresnel’s Equations• Intensity, Reflectance and Transmittance

• Refraction• - Refractive Index

• Interference• - Multiple Interference and Optical Resonators

• Diffraction• Fraunhofer Diffraction• Diffraction Grating

Light Properties

• Dispersion

• Polarization of Light• Elliptical and Circular Polarization• Birefringent Optical Devices• Electro-Optic Effects• Magneto-Optic Effects

Some Concepts of Solid State MaterialsContents

The Semiconductors in EquilibriumNonequilibrium Condition

Generation-RecombinationGeneration-Recombination rates

Photoluminescence & ElectroluminescencePhoton Absorption

Photon Emission in SemiconductorsBasic Transitions

RadiativeNonradiative

Spontaneous EmissionStimulated Emission

Luminescence EfficiencyInternal Quantum EfficiencyExternal Quantum Efficiency

Photon AbsorptionFresnel Loss

Critical Angle LossEnergy Band Structures of Semiconductors

PN junctionsHomojunctions, Heterojunctions

MaterialsIII-V semiconductors

Ternary SemiconductorsQuaternary SemiconductorsII-VI SemiconductorsIV-VI Semiconductors

Light

• The nature of light

Wave/Particle Duality Nature of Light

--Particle nature of light (photon) is used to explain the concepts of solid state optical sources (LASER, LED), optical detectors, amplifiers,…--The wave nature of light is used to explain refraction, diffraction, polarization,… used to explain the concepts of light transmission in fiber optics, WDM, add/drop/ modulators,…

λλν hpmcEchhE ==== 2

The wave nature of Light


• Polarization• Reflection• Refraction• Diffraction• Interference

To explain these concepts light can be treated as rays (geometrical optics) or as an electromagnetic wave (wave optics, studies related to Maxwell Equations).

An electromagnetic wave consist of two fields:• Electric Field• Magnetic Field

Ex

z

Direction of Propagation

By

z

x

y

k

An electromagnetic wave is a travelling wave which has timevarying electric and magnetic fields which are perpendicular to eachother and the direction of propagation, z.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

An electromagnetic wave consist of two components; electrical field and magnetic field components.

k is the wave vector, and its magnitude is 2π/λ

Light can treated as an EM wave, Ex and By are propagating through space in such a way that they are always perpendicular to each other and to the direction of propagation z.


We can treat light as an EM wave with time varying electric and magnetic fields.

Ex and BY which are propagating through space in such a way that they are always perpendicular to each other and to the direction of propagation z.

( )00 .cos),( φω +−= rktEtrE

z

Ex = Eosin(ωt–kz)Ex

z

Propagation

E

B

k

E and B have constant phasein this xy plane; a wavefront

E

A plane EM wave travelling along z, has the same Ex (or By) at any point in agiven xy plane. All electric field vectors in a given xy plane are therefore in phase.The xy planes are of infinite extent in the x and y directions.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)


( ) ( )00 cos, φω +−= krtEtrE

tconskzt tan0 =+−= φωφ

νλω===

ΔΔ

=kdt

dztzV πνω 2=Phase velocity

]Re[),( )(0

0 kztjjx eeEtzE −= ωφ

During a time interval Δt, a constant phase moves a distance Δz,

λπφ zzk Δ

=Δ=Δ2

y

z

kDirection of propagation

r

O

θ

E(r,t)r′

A travelling plane EM wave along a direction k© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

k

Wave fronts

rE

k

Wave fronts(constant phase surfaces)

z

λλ

λ

Wave fronts

PO

P

A perfect spherical waveA perfect plane wave A divergent beam

(a) (b) (c)

Examples of possible EM waves


( )krtrAE −= ωcos Spherical wave

( ) ( )00 cos, φω +−= krtEtrE Plane wave

tEE 2

22

∂∂

=∇ εμ Maxwell’s Wave Equations

Electric field component of EM wave:

These are the solutions of Maxwell’s equation

y

x

Wave fronts

z Beam axis

r

Intensity

(a)

(b)

(c)

2wo

θ

O

Gaussian

2w

(a) Wavefronts of a Gaussian light beam. (b) Light intensity across beam crosssection. (c) Light irradiance (intensity) vs. radial distance r from beam axis (z).© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Wo is called waist radius and 2Wo is called spot size

)2(42

0wπλθ = Is called beam divergence

Refractive Index

cV ==00

1με

0

1εμ

=V

0εεε r=

Phase velocity

Speed of light

rvcn ε== k(medium) = nk

λ(medium)= λ/n

Isotropic and anisotropic materials?

δω

ω

ω + δω

ω – δω

δkEmax Emax

Wave packet

Two slightly different wavelength waves travelling in the samedirection result in a wave packet that has an amplitude variationwhich travels at the group velocity.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

dz/dt = δω/δk or Vg = dω/dk group velocity

Refractive index n and the group index Ng of pureSiO2 (silica) glass as a function of wavelength.

Ng

n

500 700 900 1100 1300 1500 1700 19001.44

1.45

1.46

1.47

1.48

1.49

Wavelength (nm)


gg N

c

ddnn

cdkdmediumv =

−==

λλ

ω)(

⎥⎦⎤

⎢⎣⎡⎥⎦

⎤⎢⎣

⎡==

λπ

λω 2

)(ncvk

z

Propagation direction

E

B

k

Area A

vΔt

A plane EM wave travelling along k crosses an area A at right angles to thedirection of propagation. In time Δt, the energy in the cylindrical volume AvΔt(shown dashed) flows through A .


In EM wave a magnetic field is always accompanying electric field, Faraday’s Law. In an isotropic dielectric medium Ex = vBy = c/n (By),where v is the phase velocity and n is index of refraction of the medium.

n

y

n2 n1

Cladding

Core z

y

rφ

Fiber axis

The step index optical fiber. The central region, the core, has greater refractiveindex than the outer region, the cladding. The fiber has cylindrical symmetry. Weuse the coordinates r, φ, z to represent any point in the fiber. Cladding isnormally much thicker than shown.


Structure of Fiber Optics

n 2

n 2

z2a

y

A

1

2 1

B

θθ

θA′

B′

Cπ−2θ 2θ−π/2

k1E

xn 1

Two arbitrary waves 1 and 2 that are initially in phase must remain in phaseafter reflections. Otherwise the two will interfere destructively and cancel eachother.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

n2

z

a y

A

1

2

θθ

A′

C

kE

x

y

a−y

Guide center

π−2θ

Interference of waves such as 1 and 2 leads to a standing wave pattern along the y-direction which propagates along z.


n2

Light

n2

n1

y

E(y)

E(y,z,t) = E(y)cos(ωt – β0z)

m = 0

Field of evanescent wave(exponential decay)

Field of guided wave

The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest θ. It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.


( ) ( )ztyEtzyE mm βω −= cos)(2,,1

( ) ⎟⎠⎞

⎜⎝⎛ ++−⎟

⎠⎞

⎜⎝⎛ += mmmmm ykztykEtzyE φβωφ

21cos

21cos2,, 01

y

E(y)m = 0 m = 1 m = 2

Cladding

Cladding

Core 2an1

n2

n2

The electric field patterns of the first three modes (m = 0, 1, 2)traveling wave along the guide. Notice different extents of fieldpenetration into the cladding.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Low order modeHigh order mode

Cladding

Core

Light pulse

t0 t

Spread, Δτ

Broadenedlight pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes which then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.


n2z

y

O

θi

n1

Ai

λ λ

θrθi

Incident Light BiAr

Br

θt θt

λt

Refracted Light

Reflected Light

kt

At

Bt

B′A

B

A′

A′′θr

ki

kr

A light wave travelling in a medium with a greater refractive index ( n1 > n2) suffersreflection and refraction at the boundary.


Snell’s Law and Total Internal Reflection (TIR)

1

2

sinsin

nn

VV

t

i

t

i ==θθ

1

2

sinsin

nn

VV

r

i

r

i ==θθ

Vi = Vr , therefore θi = θr

When θt reaches 90 degree, θi = θc called critical angle

1

2sinnn

c =θ , We have total internal reflection (TIR)

n 2

θi

n 1 > n2θi

Incidentlight

θt

Transmitted(refracted) light

Reflectedlight

k t

θi>θcθc

TIRθc

Evanescent wave

k i k r

(a) (b) (c)

Light wave travelling in a more dense medium strikes a less dense medium. Depending onthe incidence angle with respect to θc, which is determined by the ratio of the refractiveindices, the wave may be transmitted (refracted) or reflected. (a) θi < θc (b) θi = θc (c) θi> θc and total internal reflection (TIR).


00

1μεε r

v =rv

cn ε==

Isotropic and

anisotropic materials

( ) ( )zktjEezyxE iziy

t −= −⊥ ωα exp,, 0,

221

22

2

122 1sin2

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛= in

nnθ

λπ

α

α2 is the attenuation coefficient and 1/ α2 is called penetration depth

k i

n2

n1 > n 2

θt=90°Evanescent wave

Reflectedwave

Incidentwave

θi θr

Er,//

Er,⊥Ei,⊥

Ei,//

Et,⊥

(b) θi > θc then the incident wavesuffers total internal reflection.However, there is an evanescentwave at the surface of the medium.

z

y

x into paper θi θr

Incidentwave

θt

Transmitted wave

Ei,//

Ei,⊥ Er,//

Et,//

Et,⊥

Er,⊥

Reflectedwave

k t

k r

Light wave travelling in a more dense medium strikes a less dense medium. The plane ofincidence is the plane of the paper and is perpendicular to the flat interface between thetwo media. The electric field is normal to the direction of propagation . It can be resolvedinto perpendicular (⊥) and parallel (//) components

(a) θi < θc then some of the waveis transmitted into the less densemedium. Some of the wave isreflected.

Ei,⊥


Transverse electric field (TE)

Transverse magnetic Field (TM)

).(0

→→−= rktj

iiieEE ω

).(0

→→−= rktj

rrreEE ω

).(0

→→−= rktj

ttteEE ω

Fresnel’s Equations:

using Snell’s law, and applying boundary conditions:

[ ][ ]2122

21

22

,0

,0

sincos

sincos

ii

ii

i

r

n

nEE

rθθ

θθ

−+

−−==

⊥

⊥⊥ [ ]2

122,0

,0

sincos

cos2

ii

i

i

t

nEE

tθθ

θ

−+==

⊥

⊥⊥

[ ][ ] ii

ii

i

r

nn

nnEE

rθθ

θθ

cossin

cossin22

122

221

22

//,0

//,0//

+−

−−== [ ]2

1222//,0

//,0//

sincos

cos2

ii

i

i

t

nn

nEE

tθθ

θ

−+==

n = n2/n1

Internal reflection: (a) Magnitude of the reflection coefficients r// and r⊥vs. angle of incidence θi for n1 = 1.44 and n2 = 1.00. The critical angle is44°. (b) The corresponding phase changes φ// and φ⊥ vs. incidence angle.

φ//

φ⊥

(b)

60

120

180

Incidence angle, θi

00.10.20.30.40.50.60.70.80.9

1

0 10 20 30 40 50 60 70 80 90

| r// |

| r⊥ |

θc

θp


(a)

Magnitude of reflection coefficients Phase changes in degrees

0 10 20 30 40 50 60 70 80 90

θc

θp

TIR

0

−60

−120

−180


1

2tannn

p =θ

Polarization angle

[ ]i

i nθ

θθ

cossin

21tan

21

22 −=⎟

⎠⎞

⎜⎝⎛

⊥[ ]

i

i

nnθ

θπθ

cossin

21

21tan 2

21

22

//−

=⎟⎠⎞

⎜⎝⎛ +and

The reflection coefficients r// and r⊥ vs. angleof incidence θi for n1 = 1.00 and n2 = 1.44.

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0 10 20 30 40 50 60 70 80 90

θp r//

r⊥


External reflection


202

1or EVI εε=

22

,0

2

,0⊥

⊥

⊥⊥ == r

E

ER

i

r2//2

//,0

2

//,0// r

E

ER

i

r==

2

21

21// ⎟⎟

⎠

⎞⎜⎜⎝

⎛+−

=== ⊥ nnnnRRR

2

1

22

,0

2

,02⊥

⊥

⊥⊥ ⎟⎟

⎠

⎞⎜⎜⎝

⎛== t

nn

E

EnT

i

t2//

1

22

//,0

2

//,02// t

nn

E

EnT

i

t

⎟⎟⎠

⎞⎜⎜⎝

⎛==

( )221

21//

4nnnn

TTT+

=== ⊥

Light intensity

Reflectance

for normal incident

Transmittance

d

Semiconductor ofphotovoltaic device

Antireflectioncoating

Surface

Illustration of how an antireflection coating reduces thereflected light intensity

n1 n2 n3

AB


n1 n2

AB

n1 n2

C

Schematic illustration of the principle of the dielectric mirror with many low and highrefractive index layers and its reflectance.

Reflectance

λ (nm)0

1

330 550 770

1 2 21

λo

λ1/4 λ2/4


Lightn2

A planar dielectric waveguide has a central rectangular region ofhigher refractive index n1 than the surrounding region which hasa refractive index n2. It is assumed that the waveguide isinfinitely wide and the central region is of thickness 2a. It isilluminated at one end by a monochromatic light source.

n2

n1 > n2

Light

Light Ligh


n2

n2

d = 2a

θθk1

Light

A

B

C

λ

β

κ

E

θn1

A light ray travelling in the guide must interfere constructively with itself topropagate successfully. Otherwise destructive interference will destroy thewave.


z

y

x

( )πφθ

λπ man

mm =−⎥⎦⎤

⎢⎣⎡ cos22 1

mmmnk θλπ

θβ sin2sin 11 ⎟

⎠⎞

⎜⎝⎛==

mmmnkk θλπ

θ cos2cos 11 ⎟

⎠⎞

⎜⎝⎛==

ΔΦ (AC) = k1(AB + BC) - 2Φ = m(2π), k1 = kn1 = 2πn1/λ

m=0, 1, 2, …

Waveguide condition

n2

Light

n2

n1

y

E(y)

E(y,z,t) = E(y)cos(ωt – β0z)

m = 0

Field of evanescent wave(exponential decay)

Field of guided wave

The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest θ. It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.


( ) ( )ztyEtzyE mm βω −= cos)(2,,1

( ) ⎟⎠⎞

⎜⎝⎛ ++−⎟

⎠⎞

⎜⎝⎛ += mmmmm ykztykEtzyE φβωφ

21cos

21cos2,, 01

y

E(y)m = 0 m = 1 m = 2

Cladding

Cladding

Core 2an1

n2

n2

The electric field patterns of the first three modes (m = 0, 1, 2)traveling wave along the guide. Notice different extents of fieldpenetration into the cladding.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Low order modeHigh order mode

Cladding

Core

Light pulse

t0 t

Spread, Δτ

Broadenedlight pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes which then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.


Ey (m) is the field distribution along y axis and constitute a mode of propagation.

m is called mode number. Defines the number of modes traveling along the waveguide. For every value of m we have an angle θm satisfying the waveguide condition provided to satisfy the TIR as well. Considering these condition one can show that the number of modes should satisfy:

m = ≤ (2V – Φ)/π

V is called V-number ( )21

22

21

2 nnaV −=λπ

For V ≤ π/2, m= 0, it is the lowest mode of propagation referred to single mode waveguides.

The cut-off wavelength (frequency) is a free space wavelength for v = π/2

θθ

E⊥

By

Bz

z

y

O

θθ

B⊥

E// Ey

Ez

(b) TM mode(a) TE mode

B//

x (into paper)

Possible modes can be classified in terms of (a) transelectric field (TE)and (b) transmagnetic field (TM). Plane of incidence is the paper.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

y

E(y)

Cladding

Cladding

Core

λ2 > λ1λ1 > λc

ω2 < ω1ω1 < ωcut-off

vg1

y

vg2 > vg1

The electric field of TE0 mode extends more into thecladding as the wavelength increases. As more of the fieldis carried by the cladding, the group velocity increases.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

n

y

n2 n1

Cladding

Core z

y

rφ

Fiber axis

The step index optical fiber. The central region, the core, has greater refractiveindex than the outer region, the cladding. The fiber has cylindrical symmetry. Weuse the coordinates r, φ, z to represent any point in the fiber. Cladding isnormally much thicker than shown.


For the step index optical fiber Δ = (n1 – n2)/n1

is called normalized index difference

Fiber axis

12

34

5

Skew ray1

3

2

4

5

Fiber axis

1

2

3Meridional ray

1, 3

2

(a) A meridionaray alwayscrosses the fibeaxis.

(b) A skew raydoes not haveto cross thefiber axis. Itzigzags aroundthe fiber axis.

Illustration of the difference between a meridional ray and a skew ray.Numbers represent reflections of the ray.

Along the fiber

Ray path projectedon to a plane normalto fiber axis

Ray path along the fiber


E

r

E01

Core

Cladding

The electric field distribution of the fundamental modin the transverse plane to the fiber axis z. The lightintensity is greatest at the center of the fiber. Intensitypatterns in LP01, LP11 and LP21 modes.

(a) The electric fieldof the fundamentalmode

(b) The intensity inthe fundamentalmode LP01

(c) The intensityin LP11

(d) The intensityin LP21


( ) ( )ztjrEE lmlmLP βωϕ −= exp.

LPs (linearly polarized waves) propagating along the fiber have either TE or TM type represented by the propagation of an electric field distribution Elm(r,Φ) along z.

ELP is the field of the LP mode and βlm is its propagation constant along z.

V-number

( ) ( )21

121

22

21 222

Δ=−= nnannaVλπ

λπ

( ) 405.2221

22

21 =−=− nnaV

coffcut λ

π

( ) ( ) 21

22

21121 2// nnnnnn −≈−=Δ

Normalized index difference

For V = 2.405, the fiber is called single mode (only the fundamental mode propagate along the fiber). For V > 2.405 the number of mode increases according to approximately

2

2VM =

0 2 4 61 3 5V

b

1

0

0.8

0.6

0.4

0.2

LP01

LP11

LP21

LP02

2.405

Normalized propagation constant b vs. V-numberfor a step index fiber for various LP modes.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

( )22

21

22

2/nn

nKb−

−=

β

Cladding

Coreα < αmax

AB

θ < θc

A

B

θ> θc

α> αmax

n0 n1

n2

Lost

Propagates

Maximumacceptance angleαmax is that whichjust givestotal internal reflectionat thecore-claddinginterface, i.e.whenα=αmax thenθ=θc.Rays withα>αmax (e.g. rayB) become refractedandpenetrate the claddingandareeventuallylost.

Fiber axis

©1999S.O. Kasap, Optoelectronics (Prentice Hall)

( )0

21

22

21

maxsinn

nn −=α

2/122

21 )( nnNA −=

0maxsin

nNA

=α

NAaVλπ2

=

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