3. Statistical mechanics Lasers and Fiber Optics.pptx

7/24/2019 3. Statistical mechanics Lasers and Fiber Optics.pptx

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Statistical mechanicsIntroduction to MB, BE, FD distributions

Application of probability theory (largepopulations)hermodynamics as a natural result ofstatistics and mechanics (classical and!uantum) at the microscopic le"el

#hat is most li$ely to happen (no actualmotions or interactions )%"erall beha"ior of system properties ofparticles

&annot re"eal the history but can say for


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Statistical distributions

o determine the most probable ay in hich agi"en amount of energy Eis distributed among Nmembers of the system of particles in thermale!uilibrium at absolute temperature T

(no. of differentways in which

particles can be

arranged)

P W

Eg. Rolling two dices: Total 36 possibilities

To get 12: (6,6)

(12) 1 36P

=

( ) ( ) ( )To get !: (1, "), 2,3 , 3, 2 , ",1

(!) " 36P =


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eneral formula for WMost probable distribution is the one ha"ing ma*imum W

#$%ber of particles of energy

( ) ( ) ( )n g f

=

( ) & n$%ber of states of energy

& statistical weigth corresponding to energy

g

( ) & distrib$tion f$nction

& a'erage n$%ber of particles in each state of energy

& probability of occ$pancy of each state of energy

f

Three types of distrib$tion f$nctions eist

according to their properties of the particles


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Distribution function

Maxwell-Boltzmann

Bose-Einstein Fermi-Dirac

Applies tosystems of

Identical,distinguishableparticles

Identical,indistinguishableparticles that do not

obey +auli principle

Identical,indistinguishableparticles that obey

+auli principle

1

ep( )A kT

1

ep( ) 1)*F kT

1

ep( ) * 1)F kT +( )f

&ategoryof particles

&lassical Bosons Fermions

+ropertiesof particles

Any spin, particlesare far enoughapart so a"efunctions do not

o"erlap

Integral spin a"efunctions aresymmetric tointerchange of

particles

-alf.integral spina"e functions areantisymmetric tointerchange of

particlesE*amples

Molecules of a gas +hotos in a ca"ity,phonons in a solid,li!uid -e at lo

Free electrons in ametal, nucleons innucleus

+ropertiesofdistribution

/o limit to numberof particles perstate

/o limit to numberof particles perstate moreparticles per statethanf

MB

at lo

energies

/e"er more than 0particle per statefeer particles perstate than fMBat lo

energiesapproachesfMBat


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Fermi.Dirac distribution

( )

1( )

1FFD kT

fe

= +

( )

1+, ( )

1FF FD kT

T fe

= =

+

1

To appreciate the significance of the -er%i energy, let $s consider a syste%of fer%ions at T & + and in'estigate the occ$pancy of states whose energies

are less than Fand greater than F

1

1e=

+

1

+ 1=

+

1=

( )

1+, ( )

1FF FD kT

T fe

= = +2

1

1e=

+1

=

+=


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3ASE4 5 Basics

6ery nearlymonochromatic

-ighly coherent

Does not di"erge

E*tremely intense

Light Ampli7cation by Stimulated Emission ofRadiation


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approach

( )i j i ijN N B u v = j jiN A ( )j jiN B u v

( )*j i j ji jiN N A B u v = +.t e/$ilibri$%,

i j j iN N = ( ) ( )*i ij j ji jiN B u v N A B u v = +

0i'iding both sides by

and sol'ing for ( )

j jiN B

u v ( ) ( )ij jii

j ji ji

B AN

u v u vN B B

= +

( )

1

ji ji

iji

j ji

A Bu v

BN

N B

=

Njato%s

Niato%s

ti%$lated

absoption

pontaneo$s

e%ission

ti%$lated

e%ission

#o of ato%s that

absorb photons

oefficient of proportionality

Energy density


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Einstein9s approach (contd')

ep( ) ep( )i i j jN C E kT N C E kT = =

ato%s%olec$les in a gas follow 4 distrib$tion

ep ( ) *i i jj

NE E kT

N= ep( ) *j iE E kT= ep( )hv kT=

( )1

ji ji

iji

j ji

A B

u v BN

N B

=

ep( ) 1

ji ji

ij

ji

A B

Bhv kT

B

=

3

3

5

6lanc7 radiation law: ( ) ep( ) 1

h v dv

u v dv c hv kt

=

onsistency between abo'e two epressions de%and

4ij jiB=

3

3

5

and

ji

ji

A hv

B c

=

i i : i


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Einstein9s coe:cients

Stimulated emission does occur and itsprobability is e!ual to the probability forabsorption

he ratio beteen to probabilities "ariesith v3, so the relati"e li$elihood ofspontaneous emission increases rapidly

ith the energy di;erence beteen theto states

All e need to $no is one of theprobabilitiesAij, Bij, Bjito 7nd others

4ij ji

B=3

3

5and

ji

ji

A hv

B c

=

bl


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Metastable state< le"els are re!uired to achie"e population in"ersion

0 5 %rdinary e*cited state= 5 Metastable state< 5 Stable (ground) state

An atom can e*ist in a metastable state for alonger time before radiating than it can in anordinary energy le"el

+ i i l f < l l l


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+rinciple of


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4uby laser (


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Four le"el laser

ntinuous operation is possible

- li / l


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-elium./eon laser

f l


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ypes of lasersas lasers

&hemical lasers

E*cimer lasers

Solid.state lasers

Fiber.hosted lasers

+hotonic crystal lasers

Semiconductor lasers

Dyelasers

Free e.


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poer

&D>D6D 4># ti


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&D>D6D 5 4># operation

- l h


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-olography%rdinary photograph8 only intensity is recorded =D imageHologram8 Images are formed by interference,

ithout lenses

Interference of to beams allos the 7lm to recordboth intensity and relati"e phase

&oherency is crucial

- l h ( td )


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-olography (contd')After de"eloping such a 7lm and placing it in laser

light, e get a


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&ommunication "ia light

-uman e e


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-uman eye

he rods and cones ofthe eye pass opticalsignals

Fiberscope


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Fiberscope

Endoscope is a familiar e*ampleState.of.art 7berscope has 0?,???

7bers of bundle ith 0mm dia

&apable of resol"ing ob@ects ?m across

otal internal reection


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otal internal reection

1 1 2 2sin sin 8nell9s lawn n =

2 1-or total internal reflection, + , C = =

1 2sin Cn n =2

1

sin Cn

n = 1 2

1

sinC

n

n

=

he optical 7ber


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he optical 7ber

/umerical aperture


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/umerical aperture

2

1

-or total internal reflection, sin cos n

n = =

2

2 2

1

cos n

n

=

2

2 2

1sin 1

n

n

=

2

2

1sin 1

n

n

=

2 2

1 1 2sinn n n =

+ 1 +-or air;core interface, sin sin 8 1n i n n= =

2 2

1 2#$%erical apert$re sin mNA i n n = =

Some details


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Some details

/umber of Modes in a Fiber


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/umber of Modes in a Fiber

+.!

core dia%eter

operating wa'elength

n$%erical apert$re

m

D NAN

D

NA

=

ypes of 7bers


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ypes of 7bers

Ad"antages of Fiber %ptics


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Ad"antages of Fiber %pticsLess expensive. Se"eral miles of optical cable canbe made cheaper than e!ui"alent lengths of copper

ire' his sa"es your pro"ider (cable 6, Internet) andyou money'

Thinner. %ptical 7bers can be dran to smallerdiameters than copper ire'

Higher carring capacit. Because optical 7bers arethinner than copper ires, more 7bers can be bundledinto a gi"en.diameter cable than copper ires' hisallos more phone lines to go o"er the same cable or

more channels to come through the cable into yourcable 6 bo*'

Less signal !egra!ation. he loss of signal inoptical 7ber is less than in copper ire'

Light signals. nli$e electrical signals in copper


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(contd')

Low power. Because signals in optical 7bers degradeless, loer.poer transmitters can be used instead ofthe high."oltage electrical transmitters needed forcopper ires' Again, this sa"es your pro"ider and youmoney'

Digital signals. %ptical 7bers are ideally suited forcarrying digital information, hich is especially useful incomputer netor$s'

"on-#amma$le. Because no electricity is passedthrough optical 7bers, there is no 7re haard'

Lightweight. An optical cable eighs less than acomparable copper ire cable' Fiber.optic cables ta$eup less space in the ground'

Flexi$le


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Medium

E"olution of 7ber lin$s


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E"olution of 7ber lin$s

&urrent status


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&urrent status

State.of.the.art numbers8

E*perimental trial8 Simens demonstrated bi.directional bps'

/E& demonstrated 'G bps (G? o"er 0?H9s in ?.- spacing) o"er 0J $m

&ommercial systems can go up to =bps

Single H8 /ortel demonstrated J? transmission o"er GJ? $m

Se"eral abo"e.tera.bps lin$s are beinginstalled orldide

Future trend8 More than 0?? H9s ill

be used

4eferences


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4eferences

A' Beiser 5 KConcepts of Modern PhysicsL, Ed',ata Mcra.-ill (/e Delhi, =??

3. Statistical mechanics Lasers and Fiber Optics.pptx

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