eugene hecht, optics, addison-wesley, reading, ma, 1998. light amplification in resonance cavity...

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.

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

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

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

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)

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

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.

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

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

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

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

Controlling Laser Pulse CharacteristicsControlling Laser Pulse Characteristics

There are 3 primary methods to control laser pulse time:There are 3 primary methods to control laser pulse time:

Q Switched Lasers – cavity mirrors are temporarily unavailableQ Switched Lasers – cavity mirrors are temporarily unavailableso the laser medium stores energy rather than releasing it. so the laser medium stores energy rather than releasing it. When the mirror is made available, a high energy pulse isWhen the mirror is made available, a high energy pulse isreleased. released.

Cavity dumped lasers – an extra cavity mirror momentarilyCavity dumped lasers – an extra cavity mirror momentarilydiverts photons from a fully reflective cavity after photon energydiverts photons from a fully reflective cavity after photon energyhas accumulated for awhilehas accumulated for awhile

Modelocked lasers – “lock” together multiple longitudinal modesModelocked lasers – “lock” together multiple longitudinal modesso that a laser simultaneously oscillates on all of them to emit so that a laser simultaneously oscillates on all of them to emit very short pulsesvery short pulses

Q-SwitchingQ-Switching

Build up population inversion by preventing lasing while pumping.Build up population inversion by preventing lasing while pumping.

SystemSystem is momentarily realigned to allow lasing.is momentarily realigned to allow lasing.

Results in short (~10-200 nsec), high-intensity (up to MW) pulse.Results in short (~10-200 nsec), high-intensity (up to MW) pulse.

Only possible if the laser can store energy in the excited state Only possible if the laser can store energy in the excited state longer than the Q-switched pulse.longer than the Q-switched pulse.

Demtröder, W. Demtröder, W. Laser Spectroscopy, Laser Spectroscopy, Springer, Berlin: 1996.Springer, Berlin: 1996.

switch )1(

2L Length Pulse

c

n)1(

2L Length Pulse

c

n

Cavity DumpingCavity Dumping

Laser cavity has to “fully” reflective mirrors.Laser cavity has to “fully” reflective mirrors.

A steady power grows inside the cavity during normal operation.A steady power grows inside the cavity during normal operation.

Momentarily, a third mirror enters the light path and directs the Momentarily, a third mirror enters the light path and directs the beam out of the cavity.beam out of the cavity.

All energy is dumped in one pulse lasting as long as it takes the All energy is dumped in one pulse lasting as long as it takes the light to make a round trip in the laser cavity.light to make a round trip in the laser cavity.

Demtröder, W. Demtröder, W. Laser Spectroscopy, Laser Spectroscopy, Springer, Berlin: 1996.Springer, Berlin: 1996.

c

n2L Length Pulse c

n2L Length Pulse

Mode - LockingMode - Locking

Edward Piepmeier, Edward Piepmeier, Analytical Applications of LasersAnalytical Applications of Lasers, , John Wiley & Sons, New York, 1986.John Wiley & Sons, New York, 1986.

Method for producing very short pulse widths (~10Method for producing very short pulse widths (~10-12-12 s). s).

Synchronize longitudinal modes.Synchronize longitudinal modes.

44.0 Duration Pulse Minimum

44.0 Duration Pulse Minimum

Are you getting the concept?Are you getting the concept?A laser has a bandwidth of 4.4 GHz (4.4 x 10A laser has a bandwidth of 4.4 GHz (4.4 x 1099 Hz). What is the Hz). What is theshortest modelocked pulse it can generate, according to theshortest modelocked pulse it can generate, according to thetransform limit? transform limit?

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

Characteristics of a Few Commercial LasersCharacteristics of a Few Commercial Lasers

Data from www.mellesgriot.comData from www.mellesgriot.com

Typical Characteristics

HeNe Ion (Ar, Kr, mixed gas)

He-Cd Diode Diode-pumped solid state

P/mW 0.1–40 4–400 2–130 1-40 5–5000

Efficiency good poor good excellent very good

Battery operation yes no no yes yes

Current supply (for typical P)

na 20 A @ 115 Vac

na 60–100 mA @4–6Vdc

2 A @ 5 Vdc

Noise <0.05% to <3%

na <2% na <2% (peak to peak)

Weight / kg na 11.4 7.7–10.9 na na

Beam diver-gence / mrad

0.7–2.4 1.0–2.0 0.5–2.9 <1.5x0.5 <1.25

Warm-up time <15 min <15 min <15 min to <30 min

<5 min <15 min

Price 0.5–4 k$ 6–11 k$ 8–25 k$ 0.8–4 k$ 4–33 k$