Physics II - Wydział Fizyki Politechniki Warszawskiejdanielb/?download=PhysicsII_part2_EM...These...

Electromagnetic waves

Daniel Budaszewski Ph.D. Eng.

Physics II

*


x

3

• particle (photon) - Isaac Newton (1642-1727)

• EM wave - Huygens (1629-1695)

Fresnel (1788-1827)

• dualism - wave-particle duality, De Broglie (1924)

Wave model - electromagnetic theory

Photon model - quantum electrodynamics

Light – electromagnetic wave or

particle?

The electromagnetic wave can be described by Maxwell equations:

„The time varying magnetic field acts as a source of

electric field, as well as time varying electric field

acts as a source of magnetic field”


•Visible light 400 to 700 nm – This is the only form of electromagnetic wave

visible to the human eye.

•Ultraviolet – these cause our skin to darken (tan) and can even damage our skin.

The ozone layer protects us from most UV radiation from the sun.

•X-rays – these EM waves pass through much matter. It doesn’t pass through dense

bone, so it is useful in determining whether a bone is broken or not.

•Gamma rays – these EM waves are very penetrating and can severely damage cells.

•Infrared – these waves are responsible for the heat we feel. Heat seeking missiles

detect infrared sources such as tanks or aircraft.

•Microwaves – these waves are used obviously to heat food. As these waves pass

through food, it causes the particles to vibrate resulting in the heating of the food.

Microwaves are also used in communication.

•Radio waves – these waves include both TV and radio waves. Signals are transmitted

and devices with antennas can receive the signals.


• In 1865 James Clerk Maxwell created a

mathematical theory that joined electricity

and magnetism,

• It explained existing experiments with

electromagnetism,

• …and made new predictions.

Electromagnetic waves - beginings

4 equations written in integral form or differential form.

Gauss’s Law (E)

Gauss’s Law (B)

Ampere’s law

Faraday’s law

Electromagnetic waves - beginings

Maxwell’s equations can be used to derive the wave equation for electromagnetic

waves.

The wave speed is the speed of light c.

This means that if the a charged particle is

accelerating, then EM waves are radiating

outward from it.


• Electric field lines of a point charge oscilating in simple harmonic motion (during

one period T)

• The arrow shows one kink in the lines of electric field as it propagates outwards

from the point charge.

• Their magnetic field (not shown in figure) comprises circles that lie in planes

perpendicular to these figures and concentric with the axis of oscilation,


• Also known as Gauss’s flux theorem,

• Formulated by Carl Friedrich Gauss in 1835,

• Relates the distribution of electric charge to the resulting electric field,

The electric flux through any closed surface is proportional

to the enclosed electric charge.

A surface integral

denoting the electric

flux through a closed

surface S

total charge enclosed

by S divided by the

electric constant.

εₒ= 8.854...×10−12 F/m

Maxwell’s equations – Gauss law

in differential form:

Divergence of

electric field

ρ – charge density

ε0= 8.854×10−12 F/m

These two forms are correct for electric charges in vacuum


The contribution of medium can be expressed

using the electric induction.

Inside the material media, the electric field causes a dispacement of electric

charges, which results in generation of induced charges.

where ΦD,S is the flux of the electric displacement field D through S, and Qfree is

the free charge contained in V.

The divergence of the electric displacement field is equal to the free electric

charge density ρfree


The magnetic field B has divergence equal to zero.

(magnetic monopoles does not exist – only magnetic dipoles)

For each volume element in space, there is exactly the same number of

"magnetic field lines" entering and exiting the volume. No total "magnetic

charge" can build up in any point in space.

the net flux of the

magnetic field out

of the surface


for magnetism

• Relates the integrated magnetic field around a closed loop to the electric

current passing through the loop,

• Corrected by Maxwell (by including the displacement current)

Displacement current

The magnetic field is generated by current and

electric field changes.

Maxwell’s equations – Ampere’s

law

A changing magnetic field creates an electric field

Due to existence of only partial time derivatives, this equations can be used when

the test charge is stationary in a time varying magnetic field.

When a charged particle moves in a magnetic field, it does not account for

electromagnetic induction.

One restriction:

Maxwell’s equations – Faraday’s

law of induction

Electric induction D can be expressed as sum of electric constant (ε0) × E and

polarization density (P),

Magnetic field intensity H can be expressed as difference of magnetic field density

B per magnetic constant and magnetization M

Two fields (E and H) are orthogonal to each other

and moves with the speed c

Maxwell’s equations – continuity

equations

• The EM waves predicted by Maxwell

were discovered by Heinrich Hertz in

1887.

• He used an LC circuit with an alternating

source.

• This discovery was exploited by Marconi

(Radio)

Electromagnetic waves - discovery

• Hertz’s basic LC circuit

• When the switch is closed, oscillations

occur in the current and in the charge

on the capacitor,

• When the capacitor is fully charged, the

total energy of the circuit is stored in the

electric field of the capacitor

– At this time, the current is zero and

no energy is stored in the inductor.


S

C L

Qmax

+

-

• As the capacitor discharges, the energy stored in the electric field decreases ,

• At the same time, the current increases and the energy stored in the magnetic

field increases,

• When the capacitor is fully discharged, there is no energy stored in its electric

field,

• The current is at a maximum and all the energy is stored in the magnetic field

in the inductor,

• The process repeats in the opposite direction,

• There is a continuous transfer of energy between the inductor and the

capacitor.


• An induction coil is connected to two large spheres forming a capacitor,

• Oscillations are initiated by short voltage pulses,

• The inductor and capacitor form the transmitter,

Hertz’s experimental setup

Input

Induction coil

Transmitter

Receiver

• When the resonance frequencies of the

transmitter and receiver matched,

energy transfer occurred between

them,

• Hertz hypothesized the energy transfer was in the form of waves

• These are now known to be electromagnetic waves

• Hertz confirmed Maxwell’s theory by showing the waves existed and had all

the properties of light waves

• They had different frequencies and wavelengths

• Hertz measured the speed of the waves from the transmitter

• He used the waves to form an interference pattern and calculated the wavelength,

From v = f λ, v was found (very close to speed of light)

• This provided evidence in support of Maxwell’s theory

Hertz’s conclusions

• When a charged particle undergoes an acceleration, it must radiate energy

• If currents in an ac circuit change rapidly, some energy is lost in the form of EM

waves

• EM waves are radiated by any circuit carrying alternating current

• An alternating voltage applied to the wires of an antenna forces the

electric charge in the antenna to oscillate.

EM waves emitted by antenna

• Because the oscillating charges in the rod

produce a current, there is also a

magnetic field generated

• As the current changes, the magnetic field

spreads out from the antenna

EM waves emitted by antenna

• Both the electric field and the magnetic field have energy.

• Waves transport energy.

• The EM wave transports energy at the speed of light!

• Let S be the rate of energy flow per unit area.

• – Energy per unit time per unit area.

• S is called the Poynting vector.

• The time-averaged value of S is the intensity.

Energy of EM waves

x

y

z

• EM waves carry momentum too,

• EM waves can exert a pressure on an object,

• The flow rate of momentum is a pressure,

Crooks radiometer

• also known as the light mill,

• consists of an airtight glass bulb, containing a partial vacuum.

• Inside are a set of vanes (white and black) which are mounted on a

spindle.

• The vanes rotate when exposed to light, with faster rotation for more

intense light,

• It gives possibility to measure the electromagnetic radiation intensity.

Energy of EM waves

STOP:

• The idea of work is not related to the pressure of light!

• The darker side of the vane is heated faster than the light one,

• The pressure difference causes the vane to move cold (light) side forward.

Energy of EM waves

• The retina contains two major types of

light-sensitive photoreceptor cells used

for vision: the rods and the cones.

Eyes – natural EM detectors

• Rods

• cannot distinguish colours,

• responsible for low-light, monochrome (black&white)

vision,

• they work well in dim light as they contain a pigment

(but saturates at higher intensities).

• Cones

– function best in relatively bright light,

– less sensitive to light than the rod cells,

– allow the perception of color.

– Are also able to perceive finer detail and more rapid

changes in images (response times to stimuli are faster

than those of rods),

– We have three kinds of cones with different response

curves and thus respond to variation in color in different

ways (trichromatic vision).


Wavelength [nm]

Norm

alis

ed

inte

nsity [

a.u

.]


• The frequency of light is very high,

• There is no such detector to measure the electric field changes,

• We are able only to measure the mean value of the square root of the electric

field,

• our eyes can detect only intensity of light, not phase.

Energy of EM waves

If two monochromatic waves described as:

will overlap in some plane x=const, then:

Responsible for interference

Interference

For : > 0 constructive interference

= 0

destructive interference < 0

The same phases The oposite phases

Constructive interference Destructive interference

-2,5

-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

2,5

0 2 4 6 8 10

-1,5

-1

-0,5

0

0,5

1

1,5

0 2 4 6 8 10

Interference

Christian Huygens

1629-1695

All points in a wavefront serve as point

sources of spherical secondary waves.

After a time t, the new wavefront will be

the tangent to all the resulting spherical

waves.

Huyghens principle

For plane waves entering a single slit, the waves emerging from the slit start

spreading out, diffracting

Interference

For waves entering two slits, the emerging waves interfere and form an

interference (diffraction) pattern

Young experiment in 1801:

light is a wave phenomenon

First plane wave through a small

slit yields coherent spherical

wave,

Then interposed two slits:

interference of two spherical

waves on a screen,

Young’s double slit experiment

• Phase difference between two waves can change for paths of different lengths

• Each point on the screen is determined by the path length difference DL of the

rays reaching that point

Path Length Difference: sinL d D

Interference

If sin integer bright fringeL d D

Maxima-bright fringes:

sin for 0,1,2,d m m

Minima-dark fringes: 12

sin for 0,1,2,d m m

1 1.51 dark fringe at: sinm

d

1 22 bright fringe at: sinm

d

Interference

• Two sources can produce an interference that is stable over time, if their light has a

phase relationship that does not change with time: E(t)=E0cos(wt+f).

• Coherent sources: Phase f must be well defined and constant

• Sunlight is coherent over a short length and time range

• Since laser light is produced by cooperative behavior of atoms, it is coherent of long

length and time ranges

• Incoherent sources: f jitters randomly in time, no stable interference occurs

Interference

Michelson’s

Mach-Zehnder’s

Ring

Interferometers

Central

maximum

Side or secondary

maxima

Light

Fresnel Bright Spot.

Bright

spot

Light

These patterns cannot

be explained using

geometrical optics!

Diffraction

When light goes through a

narrow slit, it spreads out to

form a diffraction pattern.

Single slit diffraction

X-band: =10cm

You are doing 137 mph on I-10 and you pass a little old lady doing 55mph when

a cop, Located 1km away fires his radar gun, which has a 10 cm opening. Can he

punish you for fast driving, if the gun Is X-band? What about Laser?

1m

1m

10 m 1000m

w 2L

a2 0.1m 1000m

0.1m 2000m w

2L

a2 0.000001m 1000m

0.1m 0.02m

Laser-band: =1m

Diffraction

The Rayleigh Resolution Criterion

says that the minimum separation to

separate two objects is to have the

diffraction peak of one at the

diffraction minimum of the other, i.e.,

D 1.22 /D.

Example: The Hubble Space Telescope

has a mirror diameter of 4 m, leading to

excellent resolution of close-lying objects.

For light with wavelength of 500 nm, the

angular resolution of the Hubble is D = 1.53 x 10-7 radians.

Diffraction

A spy satellite in a 200km low-Earth orbit is imaging the

Earth in the visible wavelength of 500nm.

How big a diameter telescope does it need to read a

newspaper over your shoulder from Outer Space?

Diffraction

R

Dx

D

Dx = RD = R(1.22/D) D = R(1.22/Dx) = (200x103m)(1.22x500x10–9m)/(10X10–3m) = 12.2m

Holography

• Holography is a method of producing a three-dimensional (3-D) image

of an object. (The three dimensions are height, width, and depth.)

• Later the object can be reconstructed.

• The hologram is actually a recording of the difference between two

beams of coherent light

• Can be used as optical store disk, in information processing,

Conventional:

• 2-d version of a 3-d scene

• Photograph lacks depth perception or parallax

• Film sensitive only to radiant energy

• Phase relation (i.e. interference) are lost

Holography vs. conventional photo

Light

Object

Reflected

wave

Photographic film:

The intensity is

recorded



Light

Hologram:

• Freezes the intricate wavefront of light that carries all the visual

information of the scene

• To view a hologram, the wavefront is reconstructed

• View what we would have seen if present at the original scene through

the window defined by the hologram

• Provides depth perception and parallax


• Converts phase information into amplitude information (in-phase -

maximum amplitude, out-of-phase – minimum amplitude)

• Interfere wavefront of light from a scene with a reference wave

• The hologram is a complex interference pattern of microscopically

spaced fringes


Reference wave

Photographic film.

Interference of reference and

reflected waves is recorded


• Film is developed,

• Hologram illuminated at same angle as reference beam during

original exposure to reveal holographic image,


)/2sin( txAEy

Vertically (y axis) polarized wave having an amplitude A, a wavelength of and an

angular velocity (frequency * 2) of , propagating along the x axis.

Polarization of EM waves

Vertical

Horizontal

)/2sin( txAEy

)/2sin( txAEz


• superposition of two waves that have the same amplitude and

wavelength,

• are polarized in two perpendicular planes and oscillate in the same

phase.

• Oscillating in the same phase means that the two waves reach their

peaks and cross the zero line in the same moments


Right circular

Left circular

)90/2sin( txAEy

)/2sin( txAEz

)90/2sin( txAEy

)/2sin( txAEz


• two circularly polarized waves can meet as well.

• In that case, the fields are added according to the rules of vector addition, just as

with plane-polarized waves.

• The superposition of two circularly polarized light beams can result in various

outcomes.

Any linearly polarized light wave can be obtained as a superposition of a left

circularly polarized and a right circularly polarized light wave, whose amplitude is

identical.


Different polarization of light get reflected and

refracted with different amplitudes (“birefringence”).

At one particular angle, the parallel polarization is

NOT reflected at all!

This is the “Brewster angle” B, and B + r = 90o.

(Absorption)

cos)90sin(sin 221 nnn o

1

2tann

n Polarizing Sunglasses


f2

max cosII Malus’s law, polarized light

passing through an analyzer

Malus’s law

• Opaque

• absorbs or reflects all light

• Transparent

• allows light to pass through completely

• Translucent

• allows some light to pass through

Light interaction in media

)/2sin( txAeE x

y

Material with an extinction

coefficient

The light gets weaker (its amplitude

drops)

In Out

The process by which EM radiant energy is absorbed by a molecule or particle

and converted to another form of energy

Absorption

In Out

• The intensity of light decreases

exponentially inside the shown piece of

material.

• After the light exits the medium, its field

vector rotates as before but its length is

lower than the original value.

Absorption

In Out

Material with an index of

refraction n

The light slows down inside the

material, therefore its wavelength

becomes shorter and its phase gets

shifted

)/2sin( tnxAEy

Refraction

In Out

Material having different

extinction coefficients for

right and left circularly

polarized lights: R and L

Plane-polarized light becomes

elliptically polar

)90/2sin()90/2sin(

txAetxAeExx

yLR

)/2sin()/2sin( txAetxAeExx

zLR

Circular dichroism

In Out


refraction indices for right

and left circularly polarized

lights: nR and nL

The plane of polarization of plane-

polarized light gets rotated

)90/2sin()90/2sin( LR txnAtxnAEy

)/2sin()/2sin( R txnAtxnAE Lz

Circular birefringence

In Out


extincion coefficients AND

refraction indices for right

and left circularly polarized

lights: R and L AND nR and

nL

Plane polarized light gets elliptically

polar, with the great axis of the ellipse

being rotated relative to the original

plane of polarization

)90/2sin()90/2sin( LR

txnAetxnAeExx

yLR

)/2sin()/2sin( LR txnAetxnAeExx

zLR

Circular dichroism and birefringence

• Rayleigh

• Mie

• Geometric

The process whereby EM radiation is absorbed and immediately

re-emitted by a particle or molecule – energy can be emitted in

multiple-directions

The type of scattering is controlled by the size of the wavelength relative

to the size of the particle

Light scattering

NOON

• less atmosphere

• less scattering

• blue sky, yellow sun

SUNSET

• more atmosphere

• more scattering

• orange-red sky & sun

• Molecules in atmosphere

scatter light rays.

• Shorter wavelengths (blue, violet) are

scattered more easily.

Light scattering

Blue sky and red sunset

• Wavelength of light is much larger than scattering particles,

• Blue light ~4000 Angstroms, scattering particles ~1 Angstrom (1A=10-10 m)

Rayleigh scattering

• Occurs when the wavelength ≅ particle size,

• Explains scattering around larger droplets such as Corona around the sun or

moon, Glory and similar phenomena.

• Occurs with particles that are actually 0.1 to 10 times the size of the

wavelength

• Primary Mie scatterers are dust particles, soot from smoke

• Mie scatterers are found lower in theTroposphere

Mie scattering

Rayleigh and Mie scattering

• The dependence of wave speed and index of

refraction on wavelength is called dispersion,

• The index of refraction depends on the frequency

of the light: the higher the frequency, the higher

the index of refraction,

• Because white light is a mixture of frequencies,

different wavelengths travel in different directions.

• Dispersion is the cause of chromatic aberration in

a simple lens:

• Different colours focus at different points,

• It’s a common defect of simple lenses,

• Sometimes you see a fringe of colours around an

image seen through a lens or a telescope,

• Chromatic aberration can be corrected by

combining two or more lenses.

Dispersion

• 1665-1666 – First experiment of Isaac Newton with dispersion,

experimentum crucis

• For this distribution of colours Newton coined the term spectrum,

• White light can be dispersed into different wavelengths,

• Dispersed ray (monochromatic) cannot be divided into other wavelengths

Dispersion

*

Slit Slit

• White light is a “Heterogeneous mixture of different refrangible Rays”

• Colours of the spectrum cannot be individually modified.

• Colours are “Original and connate properties, which in divers Rays

are divers. Some Rays are disposed to exhibit a red colour and no

other; some a yellow and no other, some a green and no other, and

so of the rest”.

Dispersion – Newton’s conclusions

*

• In the presence of dispersion, wave

velocity is no longer uniquely defined,

giving rise to the distinction of phase

velocity and group velocity.

• A well-known effect of phase

velocity dispersion is the color

dependence of light refraction that

can be observed in prisms and

rainbows.

• Dispersion may be caused either by

geometric boundary conditions

(waveguides, shallow water) or by

interaction of the waves with the

transmitting medium.

Dispersion

• is the phenomenon in which the phase velocity of a wave depends on its

frequency, or alternatively when the group velocity depends on the frequency.

• Media having such a property are termed dispersive media. Dispersion is

sometimes called chromatic dispersion to emphasize its wavelength-

dependent nature, or group-velocity dispersion (GVD) to emphasize the

role of the group velocity.

• Dispersion is called normal when the refractive index decreases with the

wavelength,

• For materials with selective absorption

the refractive index can increase in

some selective wavelength ranges…

• This kind of dispersion is called

anomalous.

Dispersion

Refr

active index

(n)

• A rainbow is caused by the dispersion of light in droplets of rain.

• When sunlight enters a drop,

it is separated into its coloured

components.

• The final direction of light is

quite opposite to its incident

direction.

• Violet light changes its

direction by 320°.

• Red light changes its direction

by 318°.

Dispersion

• In a range of absorption maximum, the

refractive index can be even <1,

• it means that for 0<n<1 the wave speed:

• There is no paradox in it.

• Phase velocity is the rate at which the

phase of the wave propagates,

• It this does not indicate any superluminal

information or energy transfer,

Phase velocity

Phase velocity

• The group velocity of a wave is the velocity with which the overall shape of

the wave's amplitudes — known as the modulation or envelope of the wave

— propagates through space.

• The group velocity is often thought of as the velocity at which energy or

information is conveyed along a wave.

• In most cases this is accurate, and the group velocity can be thought of as

the signal velocity of the waveform.

• However, if the wave is travelling through an absorptive medium, this does

not always hold.

Group velocity

• various experiments have verified that it is possible for the group velocity of laser light

pulses sent through specially prepared materials to significantly exceed the speed of

light in vacuum,

• However, superluminal communication is not possible in this case, since the signal

velocity remains less than the speed of light.

• It is also possible to reduce the group velocity to zero, stopping the pulse, or have

negative group velocity, making the pulse appear to propagate backwards.

• However, in all these cases, photons continue to propagate at the expected speed of

light in the medium

• 1999 Rowland Institute for Science, Cambridge,

• 2000 NEC Research Institute, Princton,

Group velocity (equal to an electron's speed) should not be confused with phase

velocity (equal to the product of the electron's frequency multiplied by its

wavelength).

Phase and group velocity

• In a dispersive medium, the phase velocity varies with frequency and is not

necessarily the same as the group velocity of the wave, which is the rate at

which changes in amplitude (known as the envelope of the wave) propagate.

• In some specific cases the phase velocity has a negative sign as group

velocity.

moves with the phase velocity,

moves with the group velocity

Phase and group velocity

• In such medium single light pulse will spread (dispersion)

• Due to the dispersion there are limits in signal transmission (ex. optical fiber

telecommunication)

• Are there such media in which signal will not change the shape?

Dispersive media

Spectrum broadening

Difference in group velocity

Wavelength

Gro

up

ve

loci

ty

Δλ

1

Time

1 0

Original signal

Time

Transmitter output

Time

Receiver input

Time

1 1 1

Regenerated signal

Wavelength

Optical spectrum

Δλ

Pulse broadening (Waveform distortion)

Optical fiber

*

Dispersive media

• a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that

maintains its shape while it travels at constant speed.

• Solitons are caused by a cancellation of nonlinear and dispersive effects in

the medium. (The term "dispersive effects" refers to a property of certain

systems where the speed of the waves varies according to frequency.)

• Single soliton behaves like a particle

• Travels with constant shape and velocity

Soliton

dispersion

dispersion + nonlinearity

Soliton

• 3 properties to solitons: o They are of permanent form;

o They are localised within a region;

o They can interact with other solitons, and emerge from the collision

unchanged, except for a phase shift.

Soliton

• The soliton phenomenon was first

described by John Scott Russell (1808–

1882)

• Observation in 1834 in canal near

Edinburgh

• He reproduced the phenomenon in a

wave tank and named it the "Wave of

Translation".

• Large “wave of translation” which did

not dissipate

“Happiest day of my life”

John Scott-Russell’s Soliton

John Scott-Russell’s Soliton

• When two solitary waves get closer, they gradually deform

• Finally merge into a single wave packet

• This packet soon splits into two solitary waves with the same shape and

velocity before "collision".

Two Solitons interaction

Two Solitons interaction

• LASER acronym Light Amplification by Stimulated Emission of Radiation

• They produce narrow beams of intense light,

• They often have pure colors,

• They are dangerous to eyes,

Laser

• Excited atoms normally emit light spontaneously

• Photons are uncorrelated and independent

• Incoherent light

Spontaneous emission

• Excited atoms can be stimulated into duplicating passing light

• Photons are correlated and identical

• Coherent light

Stimulated emission

• Stimulated emission can amplify light

• Laser medium contains excited atom-like systems

• Photons must have appropriate wavelength, polarization, and orientation to

be duplicated

• Duplication is perfect; photons are clones

Laser amplification

• Laser medium in a resonator produces oscillator

• A spontaneous photon is duplicated over and over

• Duplicated photons leak from semitransparent mirror

• Photons from oscillator are identical

Laser oscilation

• Coherent – identical photons

• Controllable wavelength/frequency – nice colors

• Controllable spatial structure – narrow beams

• Controllable temporal structure – short pulses

• Energy storage and retrieval – intense pulses

• Giant interference effects

• Apart from these issues, laser light is just light

Properties of laser light

• Gas (HeNe, CO2, Argon, Krypton)

• Powered by electricity

• Solid state (Ruby, Nd:YAG, Ti:Sapphire, Diode)

• Powered by electricity or light

• Liquid (Dye, Jello)

• Powered by light

• Chemical (HF)

• Nuclear

Types of lasers

• Many wavelengths

• Multidirectional

• Incoherent

• Monochromatic

• Directional

• Coherent

Incandescent light vs. Laser

1. Energy is applied to a medium raising electrons to an unstable energy level.

2. These atoms spontaneously decay to a relatively long-lived, lower energy, metastable state.

3. A population inversion is achieved when the majority of atoms have reached this metastable state.

4. Lasing action occurs when an electron spontaneously returns to its ground state and produces a photon.

5. If the energy from this photon is of the precise wavelength, it will stimulate the production of another photon of the same wavelength and resulting in a cascading effect.

6. The highly reflective mirror and partially reflective mirror continue the reaction by directing photons back through the medium along the long axis of the laser.

7. The partially reflective mirror allows the transmission of a small amount of coherent radiation that we observe as the “beam”.

8. Laser radiation will continue as long as energy is applied to the lasing medium.

Lasing action

En

erg

y I

ntr

od

ucti

on

Ground State

Excited State

Metastable State

Spontaneous

Energy Emission

Stimulated Emission

of Radiation

Lasing action

• Beyond some maximum incident angle the ray of light cannot pass

through the boundary of the two materials and the ray is completely

reflected.

• When the angle of incidence exceeds the maximum angle or Critical

Angle, we have Total Internal Reflection.

• Total Internal Reflection is the property that allows fiber optic

communication to occur.

n1

n2 n

1 > n

2

c

r

c =

r

Incident Wave Reflected Wave

Transition Boundary

1

2sinn

nC

Critical Angle

Optical fibers – Total internal

reflection

• Optical Fiber is a cylindrical waveguide made of a high purity fused silica.

• The core has a refractive index slightly higher than the cladding which allows

the propagation of light via total internal reflection.

• A single-mode core diameter is typically 5-10m.

• A multimode core diameter is typically over 100 m.

Cladding (n2)Core (n

1)

n1 > n

2Total Internal

Reflection

Optical fibers – Total internal

reflection

(Acrylic lacquer)

Optical fibers

• Multimode fiber has a larger core and allows several modes to

propagate while single mode only allows the first (or

fundamental) mode to propagate.

n2

n1 n

Dia

me

ter

n2

n1 n

Dia

me

ter

Single Mode Fiber

Multi-Mode Fiber

Optical fibers – single and multimode

:modesEH Hybrid

:modesHE Hybrid

:modesTM

:modes TE

lm

lm

lm

lmThe electric field vector lies in transverse plane.

The magnetic field vector lies in transverse plane.

TE component is larger than TM component.

TM component is larger than TE component.

l= # of variation cycles or zeros in direction.

m= # of variation cycles or zeros in r direction.

f

Linearly Polarized (LP) modes in weakly-guided fibers ( ) 121 nn

)HETMTE(LP),HE(LP 000110 mmmmmm

Fundamental Mode: )HE(LP 1101

Mode designation in Optical fibers

NA22 2

2

2

1

ann

aV

Mode propagation constant

ligthofwavelength

coreofradiusa

NAaV

:

:

/2

2.405

Definition: the wavelength below which multiple modes of light can be propagated

along a particular fiber, i.e., l>=lc, single mode, l<lc, multi-mode

NAa

c 405.2

2

Cut-off wavelength

In general, a linearly polarized mode is a combination of both of the

degenerate modes. As the modal wave travels along the fiber, the difference in

the refractive indices would change the phase difference between these two

components & thereby the state of the polarization of the mode. However after

certain length referred to as fiber beat length, the modal wave will produce its

original state of polarization. This length is simply given by:

f

pkB

L2

Fiber beat length

• To better describe some optical phenomena, it is important to

remember that light is actually a traveling electromagnetic wave.

• As light propagates through a fiber, it creates a “standing wave” across

the diameter of the fiber core. This is called waveguide propagation.

• A small portion of the power also penetrates into the cladding.

Cladding

Core

Propagating

Wavefronts

Mode propagation constant

850 940 1030 1120 1210 1300 1390 1480 1570 1660 17500

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Water Impurities

(OH-)IR Absorbtion

Rayleigh

Scattering

Wavelength (nm)

Att

en

ua

tio

n (

dB

/km

)

• Due to the characteristic attenuation curve of fiber, there are two regions typically used for communications.

Fiber attenuation

3 main types of Photonic Crystal Fibers

Isotropic with solid core Hollow-core Birefringent with solid core

• 2-dimmensional photonic crystals with deffect along the fiber length inside

the core region,

• made of one type of glass material with periodic matrix of air micro-holes

forming a structure of photonic crystal,

Photonic Crystal Fibers

D

d

Λ

•Pitch,

• Large hole diameter, D

• Small hole diameter, d

• Diameter of holey region

• Filling factor, d/

4.4 m

4.5 m

2.2 m

40 m

0.5

Commercially available birefringent PCF from NKTPhotonics

Parameters

Photonic Crystal Fibers

m-TIR (modified Total Internal Reflection) – characteristic for PCFs with solid

core,

PBG (Photonic Band Gap) – characteristic for „hollow-core” PCFs,

Propagation mechanisms in PCF

• Low sensivity for temperature influence,

• Birefringence is generated by introducing 2-fold the symmetry in the periodic structure of the PCF,

• Group and phase birefringence depends on wavelength,

• Group and phase birefringence may have different values, and even signs,

Blazephotonics 1550-01

Properties of PCFs

The highest level of tunability of propagation and

polarization properties by external fields

Thermal, external ac & dc

fields, optical field sensitivity

Variety of LC materials and LC

structures; influence of

molecular ordering

Advantages of both

mTIR and PBG phenomena

Variety of PCF structures

(birefringence, SM,

nonlinearity, etc.)

Liquid Crystal Photonic Crystal Fiber Liquid Crystals Photonic Fibers

Photonic Liquid Crystal Fibers

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