Chapter 1a

Chapter 1:

Introduction to Optics and optoelectronics

Light has many properties that make it very attractive for information processing

1. Immunity to electromagnetic interference– Can be transmitted without distortion due to electrical

storms etc

2. Non-interference of crossing light signals– Optical signals can cross each other without distortion

3. Promise of high parallelism– 2D information can be sent and received.

4. High speed/high bandwidth– Potential bandwidths for optical communication systems

exceed 1013 bits per second. (1250 GigaByte/second)

5. Signal (beam) steering– Free space connections allow versatile architecture for

information processing

6. Special function devices– Interference/diffraction of light can be used for special

applications

7. Ease of coupling with electronics– The best of electronics & photonics can be exploited by

optoelectronic devices

Radiation/Light Sources

Classification of radiation source by Flux Output

1. A point source• An LED or a small filament clear bulb with small emission

area2. An area source

• An electroluminescence panel or frosted light bulb with an emission area that is large

3. A collimated source• A searchlight with flux lines that are parallel

4. A coherent source• A laser which is either a point source or a collimated

source with one important difference: the wave in coherence source are all in phase

Radiation spectrum1. A continuous spectrum source

• Has a wavelength of emission that ranges from ultraviolet to infrared.

2. A line spectrum source• Has a distinct narrow bands of radiation throughout the

ultraviolet to infrared range.

3. A single wavelength source• Radiates only in a narrow band of wavelength

4. A monochromatic source• Radiates at a single wavelength/a very narrow band of

wavelength.

The nature of light

Light wave in a homogenous medium

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)

k

Wave fronts

rE

k

Wave fronts(constant phase surfaces)

z

Wave fronts

PO

P

A perfect spherical waveA perfect plane wave A divergent beam

(a) (b) (c)

Examples of possible EM waves


z

Ex = E

osin(wt–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.


Light as plane electromagnet (EM) wave

• We can treat light as an EM wave with time varying electric and magnetic fields Ex and By perpendicular to each other propagating in z

direction.

Ex (z, t) = Eo cos ( t – kz + o)Ex =electric field at position z at time t, k = 2/λ is the propagation constant, λ is the wavelengthand is the angular frequency, Eo is the amplitude of the wave and o is a phase

constant.

Ex (z, t) = Re[ Eo exp (jo) exp j(t – kz)]

Electromagnet (EM) wave

• We indicate the direction of propagation with a vector k, called the wave vector.– whose magnitude, k = 2/λ

• When EM wave is propagating along some arbitrary direction, k, then electric field at a point r isEx (r, t) = Eo cos (t – k ∙ r + o)– Dot product (k r)∙ is along the direction of propagation

similar to kz.– In general, k has components kx , ky & kz along x, y and z

directions: (k r)∙ = kx x + ky y + kz z

y

z

k

Direction of propagation

r

O

q

E(r,t)r¢

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

Maxwell’s Equation2 2 2 2

2 2 2 20x x x x

o o r

E E E E

x y z t

2

20xE

x

2

20xE

y

Given wave equation: Ex (z, t) = Eo cos ( t – kz + o)

22

2cos( )x

o o

Ek E t kz

z

22

2cos( )x

o o

EE t kz

t

2 2cos( ) cos( ) 0o o o o r o ok E t kz E t kz 2 2( ) cos( ) 0o o r o ok E t kz

Phase velocity

• During a time interval t, this constant phase moves a distance z. – The phase velocity of this wave is therefore z/t.

• Phase velocity,

f is the frequency ( = 2f )

f

kdt

dzv

Phase Velocity

2 2( ) cos( ) 0o o r o ok E t kz

2

2

1

o o rk

1/2

o o rv

f

kdt

dzv

Group Velocity

• There are no perfect monochromatic wave in practice– All the radiation source emit a group of waves differing slightly

in wavelength, which travel along the z-direction• When two perfectly harmonic waves of frequency w–dw & w+dw and wave vectors k–dk & k+dk interfere, they generate wave packet.

• Wave packet contains an oscillating field at the mean frequency w that is amplitude modulated by a slowly varying field of frequency dw.

• The maximum amplitude moves with a wavevector dk and the group velocity is given Vg = dw/dk

Group velocity

, cos cos

, 2 cos cos

, v

x o o

x o

g

E x t E t k k z E t k k z

E x t E t k z t kz

dz d

dt k dk

+

–

kEmaxEmax

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.


What is refractive index, (n) ?

Interaction between dielectric medium and EM wave

• When an EM wave is traveling in a dielectric medium, – the oscillating Electric Field (E-field) polarizes the molecules

of the medium at the frequency of the wave.• The field and the induced molecular dipoles become

coupled– The net effect: The polarization mechanism delays the

propagation of the EM wave.– The stronger the interaction, the slower the propagation of

the wave– r: relative permittivity (measures the ease with which the

medium becomes polarized).

Phase velocity in dielectric medium

• For EM wave traveling in a non-magnetic dielectric medium of r , the phase velocity,

• If the frequency is in the optical frequency range, – r will be due to electronic polarization as ionic polarization

will be too slow to respond to the field.• At the infrared frequencies or below,

– r also includes a significant contribution from ionic polarization and phase velocity is slower

oor 1

Definition of Refractive Index

• For an EM wave traveling in free space (r= 1)

velocity

(1)• The ratio of the speed of light in free space to its

speed in a medium is called refractive index n of the medium,

n= c/v = r (2)

181031 mscv

oo

Example: phase velocity

• Considering a light wave traveling in a pure silica glass medium. If the wavelength of light is 1mm and refractive index at this wavelength is 1.450, what is the phase velocity ?

The phase velocity is given byv= c/n = 3108ms–1/1.45 =2.069108ms–1

Refractive Index in Materials

• In free space, k is the wave vector (k=2 /) and is the wavelength

• In medium, kmedium=nk and medium = /n.– Light propagates more slowly in a denser medium

that has a higher refractive index– The frequency f remains the same– The refractive index of a medium is not necessarily

the same in all directions

Refractive Index in non-Crystal Materials

• In non-crystalline materials (glass & liquids), the material structure is the same in all directions– Refractive index, n, is isotropic and independent

on the direction

Refractive Index in Crystal Materials

• In crystals, the atomic arrangements and inter-atomic bonding are different along different directions

• In general, they have anisotropic properties except cubic crystals.– r is different along different crystal directions– n seen by a propagating EM wave in a crystal will

depend on the value of r along the direction of the oscillating E-field

Cubic crystal

hexagonal crystal

Refractive index and phase velocity

• For example: a wave traveling along the z-direction in a particular crystal with its E-field oscillating along the x-direction– Given the relative permittivity along this x-direction is rx

then , – The wave will propagate with a phase velocity that is c/nx

• The variation of n with direction of propagation and the direction of the E-field depends on the particular crystal structure

rxxn

Technology

Chapter 1a