Atomic model

MIT 2.71/2.710 Optics 10/20/04 wk7-b-21

Semi-classical view of atom excitations

Energy

Energy

Atom in ground state

Atom in excited state

Absorption

Spontaneous emission

Stimulated emission

E1

E2

• n1 - the number of electrons of energy E1

• n2 - the number of electrons of energy E2

2 2 1

1

( )exp

n E E

n kT

Boltzmann’s equation

example: T=3000 K E2-E1=2.0 eV

42

1

4.4 10n

n

Einstein’s theory of spontaneous and stimulated emission

Einstein’s coefficients

Probability of stimulated absorption R1-2

R1-2 = r (n) B1-2

Probability of stimulated and spontaneous emission :

R2-1 = r (n) B2-1 + A2-1

assumption: n1 atoms of energy e 1 and n2 atoms of energy e 2 are in

thermal equilibrium at temperature T with the radiation of spectral density r (n):

n1 R1-2 = n2 R2-1 n1r (n) B1-2 = n2 (r (n) B2-1 + A2-1)

2 1 2 1

1 1 2

2 2 1

/ =

1

A Bn Bn B

E1

E2

B1-2/B2-1 = 1

According to Boltzman statistics:

r (n) = =

12 1

2

exp( ) / exp( / )n

E E kT h kTn

1)exp(

/

12

21

1212

kT

h

B

BBA 1)/exp(

/8 33

kTh

ch

3

3

12

12 8

c

h

B

A

Planck’s law

The probability of spontaneous emission A2-1 /the probability of stimulated

emission B2-1r( )n :

1. Visible photons, energy: 1.6eV – 3.1eV.

2. kT at 300K ~ 0.025eV.

3. stimulated emission dominates solely when h n /kT <<1!(for microwaves: hn <0.0015eV) The frequency of emission acts to the absorption:

if h n /kT <<1.

1)/exp()(12

12

kThB

A

1

2

1

2

12

12

211

122122 ])(

1[)(

)(

n

n

n

n

B

A

Bn

BnAnx

x~ n2/n1

Population inversion

For lasing action

• Active medium• Pumping mechanism

– Optical– Electrical discharge– Chemical pumping

• Optical resonator Resonator

Laser characteristics

Carbon Di Oxide LASER Principle

The transition between the rotational and vibrational 　 energy levels lends to the construction of a molecular gas laser.　 Nitrogen atoms are 　 raised to the excited state which in turn deliver energy to the CO2 atoms whose

energy levels are close to it. Transition takes place between the energy levels of CO2 atoms and the laser beam is emitted.

Type : Molecular gas laser

Active Medium : Mixture of CO2, N2, He or H2O vapour

Active Centre : CO2

Pumping Method : Electric Discharge Method

Optical Resonator : Gold mirror or Si mirror coated with Al

Power Output : 10 kW

Nature of Output : Continuous or pulsed

Wavelength Emitted : 9.6 μm or 10.6 μm

Symmetric 100 C - stationaryO - vibrates simultaneously along molecular axis

Bending 010,020

C & O vibrate perpendicular to molecular axis

Asymmetric Stretching

001, 002

C & O atoms vibrate in opposite directions along molecular axis

Applications• Bloodless surgery• Open air

communication

• Military field

Nd (Neodymium) – YAG (Yttrium Aluminium Garnet) LASER Principle Characteristics

Doped Insulator laser refers to yttrium aluminium garnet doped with neodymium.

The Nd ion has many energy levels and due to

optical pumping these ions are raised to excited levels. During the transition from the metastable state to E1,

the laser beam of wavelength 1.064μm is

emitted

Type : Doped Insulator Laser

Active Medium : Yttrium Aluminium Garnet

Active Centre : Neodymium

Pumping Method

: Optical Pumping

Pumping Source

: Xenon Flash Pump

Optical Resonator

: Ends of rods silver coatedTwo mirrors partially and totally reflecting

Power Output : 20 kWatts

Nature of Output

: Pulsed

Wavelength Emitted

: 1.064 μm

Nd (Neodymium) – YAG (Yttrium Aluminium Garnet) LASER

Power Supply

Capacitor

Resistor

Laser Rod

Flash Tube

M1– 100% reflector mirror

M2 – partial reflector mirror

E1, E2, E3 – Energy levels of NdE4 – Meta Stable StateE0 – ground State Energy Level

ApplicationsTransmission of signals over large distancesLong haul communication systemEndoscopic applicationsRemaote sensing

Energy Level Diagram of Nd– YAG LASER

Non radiative decay

Laser1.064μm

Non radiative decay

E3

E2

E0

E1

E4

Nd

Principle• The electron in the

conduction band combines with a hole in the valence band and the recombination produces radiant energy. This photon induces another electron in the CB to combine with a hole in the VB and thereby stimulate the emission of another photon.

Type : Homojunction Semiconductor laser

Active Medium : P – N junction

Active Centre : Recombination of electrons and holes

Pumping Method

: Direct Pumping

Optical Resonator

: Polished junction of diode

Power Output : 1 mW

Nature of Output

: Continuous or pulsed

Wavelength Emitted

: 8400 – 8600 Angstrom Units

HOMOJUNCTION SEMICONDUCTOR LASER (Ga-As Laser)

P- and N-type Semiconductors

• In the compound GaAs, each gallium atom has three electrons in its outermost shell of electrons and each arsenic atom has five. When a trace of an impurity element with two outer electrons, such as zinc, is added to the crystal. The result is the shortage of one electron from one of the pairs, causing an imbalance in which there is a “hole” for an electron but there is no electron available. This forms a p-type semiconductor.

• When a trace of an impurity element with six outer electrons, such as selenium, is added to a crystal of GaAs, it provides on additional electron which is not needed for the bonding. This electron can be free to move through the crystal. Thus, it provides a mechanism for electrical conductivity. This type is called an n-type semiconductor.

Reverse-biased pn Junction

Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

A reverse bias widens the depletion region, but allows minority carriers to move freely with the applied field.

Forward-biased pn Junction


Lowering the barrier potential with a forward bias allows majority carriers to diffuse across the junction.

Applications• Compact & used in fibre optic communications• CD writer• Relieves pain• Laser printers

Excimer LASER

• Excited dimer– Short lived molecule formed from one or two

species, at least one of which is in an electronically excited state

– May not be stable in ground state• Excimer LASER:

– Electron pumped LASER– Dimer (excimer)/complex (exciplex) formation– LASER radiation: relaxation from excited state

dimer to ground state

ExcimerFunctionChemicalsCharacteristicapplications

Organic DyeChemicalsFunction Characteristicapplications

Excimer

e- + A → A*A* + B → AB* → AB + hν

ImmediatelyAB → A + B

Two important facts:1. The lower state does not exist!2. No rotational/vibrational bands



Excimer LASER



Energy states of an excimer

Excimer

• Excited Dimers– F2, Xe2 ect.

• Excited Complexes (Exciplex)– Combination of rare gas atoms and halogen

atoms– Ar, Kr, Xe– F, Cl, Br



Excimer LASER



Excimer Wavelength

Ar2 126 nm

Kr2 146 nm

F2 157 nm

Xe2 172 and 175

ArF 193 nm

CaF2 193 nm

KrCl 222 nm

KrF 248 nm

Cl2 259 nm

XeBr 282 nm

XeCl 309 nm

N2 337 nm

XeF 351 nm

•Many wavelength possibilities

• Depends upon the excited dimer

•Repetition rate from 0.05 Hz to 20 kHz

•High power:

• several 10-200 W

Excimer LASER

• Micromaching– Ink jet cartidges (drilling the nozzles)

• Radiation for changing the structure and properties of materials– Active matrix LCD monitors– Fiber bragg gratings– High temperature superconducting films

• “Short wavelength light bulb” in optical litography– Computer chips



1. Introduction

Magnetostatic “wiggler” field

Relativistic electron beam

EM radiationN

S N

S N

S N

S N

S

The Free Electron Laser (FEL) consists of a relativistic beam of electrons (v≈c)

moving through a spatially periodic magnetic field (wiggler).

Principal attraction of the FEL is tunability :- FELs currently produce coherent light from microwaves through visible to UV- X-ray production via Self- Amplified Spontaneous Emission (SASE) (LCLS – 1.5Å)

(wavelength lw)

l lw /g2 << lw

PrincipleTwo beams (object beam and reference beam) are superimposed on a

holographic plate to form an image called a hologram.

PrincipleA beam of light

(reading beam) having the same wavelength as that of the reference beam used for constructing the hologram, is made to fall over the hologram, which in turn gives rise to a 3-D image in the field of view.

Extra slides

Review of Semiconductor Physics

a) Energy level diagrams showing the excitation of an electron from the valence band to the conduction band.The resultant free electron can freely move under the application of electric field.b) Equal electron & hole concentrations in an intrinsic semiconductor created by the thermal excitation of electrons across the band gap

-123 JK 1038.1 Bk


n-Type Semiconductor

a) Donor level in an n-type semiconductor. b) The ionization of donor impurities creates an increased electron concentration distribution.


p-Type Semiconductor

a) Acceptor level in an p-type semiconductor.

b) The ionization of acceptor impurities creates an increased hole concentration distribution


The pn Junction


Electron diffusion across a pn junction creates a barrier potential (electric field) in the depletion region.

Atomic model

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