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

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

Three - Level SystemThree - Level System

No saturationNo saturation

Not very efficientNot very efficient

Better for pulsed mode operationBetter for pulsed mode operation

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

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

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

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

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

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

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

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:

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

bnn thij

2

)/1ln()( 21

bnn thij

2

)/1ln()( 21

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

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

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

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

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

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:

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