Overall Ingle and Crouch, Spectrochemical Analysis.

OverallOverall

iijjjijjii nn

d

dn

UB nUB A t

iijjjijjii nn

d

dn

UB nUB A t

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

For an ideal black body, the rate of absorption For an ideal black body, the rate of absorption and emission must be balanced:and emission must be balanced:

BBijijUUnnii = A = Ajijinnjj + B + BjijiUUnnjj

Rearrange:Rearrange:

UB A

UB

n

n

i

j

jiji

ij

UB A

UB

n

n

i

j

jiji

ij

Population of Energy StatesPopulation of Energy States

Classical Boltzmann Population:Classical Boltzmann Population:

nnii = n = n00ee--ii/kT/kT

The higher the energy state of interest, the greater the value The higher the energy state of interest, the greater the value of of ii, and the fewer atoms there will be in that state., and the fewer atoms there will be in that state.

To find the ratio of populations between two states:To find the ratio of populations between two states:

nnjj = n = niiee-(E-(Ejj-E-E

ii)/kT)/kT = n = niiee-h-h

jiji/kT/kT

Thus, we can predict the excited state population that is Thus, we can predict the excited state population that is eligible for emission.eligible for emission.

Are you getting the concept?Are you getting the concept?

Determine the population ratio for atoms/molecules in two Determine the population ratio for atoms/molecules in two energy states spaced by 1 eV at T = 300 K:energy states spaced by 1 eV at T = 300 K:

Recall: h = 6.63 x 10-34 Js k = 1.38 x 10-23 J/K 1 eV = 1.6 x 10-19 J

nj

ni

We know:We know:

Set equal and solve for USet equal and solve for Uvv::

UB A

UB

n

n

i

j

jiji

ij

UB A

UB

n

n

i

j

jiji

ij

kTe /h-

i

j ji n

n kTe /h-

i

j ji n

n

1 - e

1

c

8 U

/kTh3

3b

h

1 - e

1

c

8 U

/kTh3

3b

h

1 - e

1 U

/kThb

ij

ji

B

A 1 - e

1 U

/kThb

ij

ji

B

A

Looks similar to Planck’s Radiation Law:Looks similar to Planck’s Radiation Law:

3

3h8

cB

A

ij

ji 3

3h8

cB

A

ij

ji

Spectral Energy DensitySpectral Energy Density

Population InversionPopulation Inversion

Goal: More atoms or molecules in the upper energy level Goal: More atoms or molecules in the upper energy level than the lower energy level.than the lower energy level.

Heating the lasing medium will not work:Heating the lasing medium will not work:

nnjj = n = niiee-(E-(Ejj-E-E

ii)/kT)/kT

Must selectively excite atoms/molecules to particular energy Must selectively excite atoms/molecules to particular energy levels. Most common approaches:levels. Most common approaches:

*light*light*electricity*electricity

Optical PumpingOptical Pumping

Intense light source at hIntense light source at h(e.g. flash lamp)(e.g. flash lamp)

Excites to a metastable state to achieve population inversionExcites to a metastable state to achieve population inversion

With fast flashing, initial photons start chain reactionWith fast flashing, initial photons start chain reaction

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Electrical DischargeElectrical Discharge

Accelerated eAccelerated e-- and ions excite atoms/molecules and ions excite atoms/molecules into higher energy statesinto higher energy states

Common in gas lasersCommon in gas lasers


Three - Level SystemThree - Level System

No saturationNo saturation

Not very efficientNot very efficient

Better for pulsed mode operationBetter for pulsed mode operation


The ruby laser is a The ruby laser is a three – level laserthree – level laser


Commercial ruby laserCommercial ruby laseroperates with efficiency ~ 1%operates with efficiency ~ 1%

Four - Level SystemFour - Level System

More efficient than 3-levelMore efficient than 3-level

Laser transition does not involve Laser transition does not involve ground state or most highly ground state or most highly excited stateexcited state

Easier to achieve population Easier to achieve population inversioninversion



The He – Ne laser is a The He – Ne laser is a four – level laserfour – level laser

He* + Ne → He + Ne* + ΔE

Resonance Cavity and GainResonance Cavity and Gain


Gain = degree ofamplification basedon positive feedback

GainGain

Gain (G) = eGain (G) = e(n(njj-n-n

ii)b)b

= transition cross-section= transition cross-sectionb = length of active mediumb = length of active medium

Oscillation begins when:Oscillation begins when:

gain in medium = losses of systemgain in medium = losses of system

1122GG22 = 1 = 1

Threshold population inversion:Threshold population inversion:


bnn thij

2

)/1ln()( 21

bnn thij

2

)/1ln()( 21


Light Amplification in Light Amplification in Resonance CavityResonance Cavity

Highly collimated beamHighly collimated beam

Typically ~mm beam width, Typically ~mm beam width, ~mrad divergence~mrad divergence

A typical photon travels A typical photon travels about 50 times forward and about 50 times forward and backward within the cavitybackward within the cavity

Mirror ArrangementsMirror Arrangements




Knowing that the purpose of the resonance cavity is to direct Knowing that the purpose of the resonance cavity is to direct the majority of the photons back through the active medium, the majority of the photons back through the active medium, what cavity characteristics will be most important?what cavity characteristics will be most important?

Achieving ResonanceAchieving Resonance

Stimulated emission is coherent (all light waves in phase)Stimulated emission is coherent (all light waves in phase)

If the cavity is an integer multiple of the wavelength, each If the cavity is an integer multiple of the wavelength, each wave will be at the same phase when it reflects from one of wave will be at the same phase when it reflects from one of the cavity mirrors (recall that a photon make many round the cavity mirrors (recall that a photon make many round trips in a laser cavity before it is emitted).trips in a laser cavity before it is emitted).

This allows constructive interference between all photons.This allows constructive interference between all photons.

Want: mWant: m = 2nL = 2nL

Other wavelengths will not be strongly amplified, and thus, Other wavelengths will not be strongly amplified, and thus, will die out.will die out.

In practice, laser transitions have gain over a range of In practice, laser transitions have gain over a range of wavelengths – the gain bandwidth… so that resonance wavelengths – the gain bandwidth… so that resonance cavity lengths are not impossible to achieve.cavity lengths are not impossible to achieve.

Achieving ResonanceAchieving Resonance

Goal: Laser cavity where L = mGoal: Laser cavity where L = m/2/2

This condition is not as strict as it sounds because:This condition is not as strict as it sounds because:

1.1. Laser transitions have gain over a range of wavelengthsLaser transitions have gain over a range of wavelengths

2.2. Any integer multiple (longitudinal mode) of Any integer multiple (longitudinal mode) of will work will work

http://micro.magnet.fsu.edu/primer/java/lasers/gainbandwidth/index.html

Amp = (1+Gain)L

Estimate amplification factor:

http://micro.magnet.fsu.edu/primer/java/lasers/gainbandwidth/index.html

Longitudinal ModesLongitudinal Modes

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, , Addison-Wesley, Reading, MA, 1998.Reading, MA, 1998.

L 2n

m

L 2n

m

2nL

mc 2nL

mc

2nL

c m1m 2nL

c m1m

Actual Actual is the convolution of the is the convolution of the transition bandwidth and the transition bandwidth and the of of the longitudinal modes.the longitudinal modes.

Transverse ModesTransverse Modes

www.wikipedia.org and and www.lexellaser.com

Transverse modes determine the pattern of intensity distribution across Transverse modes determine the pattern of intensity distribution across the width of the beam.the width of the beam.

TEMTEM0000 has a Gaussian distribution and is the most commonly used. has a Gaussian distribution and is the most commonly used.

The resonator geometry of many commercial lasers is designed to The resonator geometry of many commercial lasers is designed to obtain “single transverse mode” operation.obtain “single transverse mode” operation.

22 /22d

2P (r) dreI

22 /22d

2P (r) dreI

http://www.wikipedia.org/

http://www.lexellaser.com/

CoherenceCoherence

Factors that compromise coherence:Factors that compromise coherence:1. thermal fluctuations1. thermal fluctuations2. vibrational fluctuations2. vibrational fluctuations3. emission of multiple wavelengths3. emission of multiple wavelengths4. multiple longitudinal modes4. multiple longitudinal modes

Temporal Coherence – How long do the light waves remainTemporal Coherence – How long do the light waves remainin phase as they travel?in phase as they travel?

Coherence Length = Coherence Length = 22/n/n

www.wikipedia.org

CoherenceCoherence

Spatial Coherence – Over what area does the light remainSpatial Coherence – Over what area does the light remainin phase?in phase?

www.wikipedia.org

Are you getting the conceptAre you getting the concept

Calculate the coherence length for the sources belowCalculate the coherence length for the sources belowusing nusing nairair = 1.00: = 1.00:

(a)(a)light bulb emitting from 400-1000 nmlight bulb emitting from 400-1000 nm(b)(b)semiconductor laser emitting from 799.5 – 800.5 nmsemiconductor laser emitting from 799.5 – 800.5 nm(c)(c)He-Ne laser emitting from 632.799 – 632.801 nmHe-Ne laser emitting from 632.799 – 632.801 nm

Laser WavelengthsLaser Wavelengths

Factors influencing monochromaticity of laser light:Factors influencing monochromaticity of laser light:1. transitions responsible for emission1. transitions responsible for emission2. nature of transition determines bandwidth2. nature of transition determines bandwidth3. resonance cavity characteristics3. resonance cavity characteristics

Doppler bandwidth:Doppler bandwidth:

= [5.545 kT/Mc= [5.545 kT/Mc22]]½½ where M is the mass of the atom/moleculewhere M is the mass of the atom/molecule

www.wikipedia.org

Limiting Emitted Limiting Emitted s with a Fabry-Perot Etalons with a Fabry-Perot Etalon

Insert a pair of reflective surfaces that form a resonant cavityInsert a pair of reflective surfaces that form a resonant cavitytilted at an angle to the axis of the laser medium.tilted at an angle to the axis of the laser medium.

www.wikipedia.org

TransmittedTransmitted depends on: depends on:1.1. the angle the light travels through the etalon (the angle the light travels through the etalon ())2.2. the thickness of the etalon (l)the thickness of the etalon (l)3.3. the refractive index of the material between the 2 surfaces (n)the refractive index of the material between the 2 surfaces (n)

Emission ModeEmission Mode

Lasers can emit light in Lasers can emit light in continuous wave (cw)continuous wave (cw) mode or they can mode or they canproduce produce pulsespulses..

Heisenberg’s Uncertainty Principle places the limitations:Heisenberg’s Uncertainty Principle places the limitations:

Bandwidth (Hz) = 0.441/Pulse Length (s)Bandwidth (Hz) = 0.441/Pulse Length (s)

EEt t ≥≥ ħħ/2/2Consequences:Consequences:Long pulse – narrow bandwidthLong pulse – narrow bandwidthShort pulse – broad bandwidthShort pulse – broad bandwidth

Long pulse – high resolutionLong pulse – high resolutionShort pulse – low resolutionShort pulse – low resolution


Calculate the minimum pulse length for a laser with a 1-nmCalculate the minimum pulse length for a laser with a 1-nmemission bandwidth at a center wavelength of 500 nm.emission bandwidth at a center wavelength of 500 nm.


Calculate the best spectral resolution (in cmCalculate the best spectral resolution (in cm-1-1) that can be) that can beachieved with a pulse length of 368 fsec.achieved with a pulse length of 368 fsec.

Recall: ħ = 1.055 x 10Recall: ħ = 1.055 x 10-34-34 Js Js

Pulsed Laser Power ConsiderationsPulsed Laser Power Considerations

Consider a Gaussian beam profile:Consider a Gaussian beam profile:

Pea

k P

ower

FWHM

RiseTime

FallTime

Pow

er

Time

If power was constant: E = PtIf power was constant: E = PtIn this case, E = In this case, E = ∫P(t)dt∫P(t)dt

Average Power = Average Power = ΣΣE/t or Peak Power x Duty CycleE/t or Peak Power x Duty CycleDuty cycle = Pulse Length x Repetition RateDuty cycle = Pulse Length x Repetition Rate

Output PowerOutput Power

Output power will depend on:Output power will depend on:1.1. variations in power level with timevariations in power level with time2.2. efficiency of converting excitation energy into laser energyefficiency of converting excitation energy into laser energy3.3. excitation methodexcitation method4.4. laser sizelaser size

What is wall-plug efficiency?What is wall-plug efficiency?A practical measurement of how much energy put into theA practical measurement of how much energy put into thelaser system (from the wall plug) comes out in the laser beam.laser system (from the wall plug) comes out in the laser beam.

Active Mediumpowersupply

Accessible WavelengthsAccessible Wavelengths

Lasers have also been prepared for the Lasers have also been prepared for the vacuum UV (VUV, 100-200 nm) and vacuum UV (VUV, 100-200 nm) and XUV (eXtreme UltraViolet; also called XUV (eXtreme UltraViolet; also called the ultrasoft X-ray region; <100 nm).the ultrasoft X-ray region; <100 nm).

The shortest wavelength laser produced The shortest wavelength laser produced so far emits at 3.5 nm. Projects to so far emits at 3.5 nm. Projects to extend this range to 0.1 nm by 2011 are extend this range to 0.1 nm by 2011 are in progress.in progress.

Why x-ray lasers are so difficult to build:Why x-ray lasers are so difficult to build:AAjiji/B/Bijij = 8 = 8 h h 33 / c / c33

Intensity of stimulated emission (B) is Intensity of stimulated emission (B) is proportional to intensity of spontaneous proportional to intensity of spontaneous emission (A).emission (A).

Tallents, G.J. Tallents, G.J. J. Phys. DJ. Phys. D 20032003, , 3636, R259., R259.Dattoli, G.; Renieri, A. Dattoli, G.; Renieri, A. Nucl. Inst. Meth. Phys. Nucl. Inst. Meth. Phys. Res. A Res. A 20032003, , 507507, 464., 464.

www.mellesgriot.comwww.mellesgriot.com

Overall Ingle and Crouch, Spectrochemical Analysis.

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