Lecture 6 Proper,es of laser beams - KTHmiya/files/laser/FRL-6.pdfLecture 6 Proper,es of laser...
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Lecture 6 Proper,es of laser beams * Min Yan Op,cs and Photonics, KTH 12/04/16 1 * Some figures and texts belong to: O. Svelto, Principles of Lasers, 5th Ed., Springer.
Transcript of Lecture 6 Proper,es of laser beams - KTHmiya/files/laser/FRL-6.pdfLecture 6 Proper,es of laser...
Lecture6Proper,esoflaserbeams*
MinYanOp,csandPhotonics,KTH
12/04/16 1*Somefiguresandtextsbelongto:O.Svelto,PrinciplesofLasers,5thEd.,Springer.
Reading
• PrinciplesofLasers(5thEd.):Chapter11.• Skip:11.3.4,11.7.• Squeeze:11.3.3,11.3.5,11.4.3.
• Web(withvideo)– MitsubishiCO2laser
http://www.mcmachinery.com/products-and-solutions/ex-plus-series/– Mitsubishifiberlaser
http://www.mcmachinery.com/products-and-solutions/nx-f-series/
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Laser
12/04/16
Mirror1 Gainmedium
Iin Iout
Pump
Mirror2
• Amplitude,frequency,andphasevaryw.r.t.,me.• Alwaysmorethanonefrequencyexist.
Contents
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Content Time
1. Monochromaticity 10’
2. Coherence - Spatial - Temporal
30’
3. Directionality 20’
4. Brightness 10’
5. Laser speckle 10’
Total: 80’
Contents
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Content Time
1. Monochromaticity 10’
2. Coherence - Spatial - Temporal
30’
3. Directionality 20’
4. Brightness 10’
5. Laser speckle 10’
Total: 80’
Monochromaticity
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Causesforfrequencyfluctua0on:- Amplitudefluctua,on(changeinpumporcavityloss,<1%)- Phasefluctua,on(zero-pointfluctua,onlimit+vibra,onandthermaleffects)
Ac0vestabiliza0on:10-50kHz→0.1Hz
Q-switchedormode-lockedlaser:ΔνLcanbe100MHzeven50THz
NarrowΔνL(10-100kHz):metrology,coherentapplica,onsBroadΔνL(1MHz):othercommonapplica,ons(e.g.DWDM)
Puremonochroma,clightjustdoesnotexist.
DWDM:channelspacing50GHz(0.4nm)
Contents
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Content Time
1. Monochromaticity 10’
2. Coherence - Spatial - Temporal
30’
3. Directionality 20’
4. Brightness 10’
5. Laser speckle 10’
Total: 80’
Coherence
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z
xy
Spa0alcoherence:wavesattwolateralpoints(alongx/ydirec,on)Temporalcoherence:wavesattwo,meinstances(sameposi,on)
Order,harmony,consistency
Quan,fica,on
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The1st-ordercorrela,onfunc,on:
t
xy
t1 t2
Forsta,onarybeam
Complexdegreeoftemporalcoherenceγ(1)(r1,r1,τ):
Degreeoftemporalcoherence:|γ(1)|
r=r1
γ(1)(r1,r1,τ)
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Proper0es:1. γ(1)=1forτ=02. γ(1)(r1,r1,-τ)=γ(1)*(r1,r1,τ)3. |γ(1)(r1,r1,τ)|≤1
Twoextremi0es:• Perfecttemporalcoherence:|γ(1)|=1forτ ≥0• Zerotemporalcoherence:|γ(1)|=0foranyτ>0
Generalcase:
• Coherence,meτco• CoherencelengthLc=cτco
γ(1)(r1,r2,0)
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Complexdegreeofspa,alcoherence
Againtwoextremi,esexist,andingeneral:|γ(1)(r1,r2,0)|≤1for|r1-r2|>0
• Coherencearea
Complexdegreeofcoherence:[Temporal+spa,al]
Measurem’t:Spa,alcoherence
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Method:Young’sinterferometer
Lightbeam PL1
L1
FringevisibilityatP:
Itcanbeshownthat where
IfL1=L2
Measurem’t:Temporalcoherence
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Method:Michelsoninterferometer
where
Hence
Vp
Lc
10.5
Moreremarksoncoherence
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• Temporalcoherenceandmonochroma,city
• Single-modelaser:spa,allycoherent,τcolimitedbyΔυL
• Thermallight:τco<1ps,spa,alcorrela,on↑asdistance↑
Example:IfΔυL=20kHz,τco=?Lc=?
• Single-transverse-mul0-longitudinal-modelaser:• Spa,allycoherent,τcolimitedbyΔυ0• (ifmode-locked:spa,allycoherent,τcolimitedbyΔυL)
• Mul0-transverse-mul0-longitudinalmodelaser:• par,alspa,alcoherence,τcolimitedbyΔυ0
Coherencelength:single-pinholetest
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Lightbeam
Pinholediameter:600μm
Laserpointer Supercon,nuumsource
CoherencelengthofSun
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PhotocourtesyofGunnarBjörk
PhototakenwithaThorlabs50μm-diameterpinholemountedabout50mmfromtheCMOS-detectorofaSonyα300digitalcameramountedonatripod.Exposure,me¼satISO200.
Contents
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Content Time
1. Monochromaticity 10’
2. Coherence - Spatial - Temporal
30’
3. Directionality 20’
4. Brightness 10’
5. Laser speckle 10’
Total: 80’
Direc,onality(divergence)
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Measurementmethods:• Measurespotsizeataverylargedistance:θd=W/z
• Measurebeamspotatalens’focus:
∝spa,alcoherence
θd
θd=r/f
r
f
Perfectspa,alcoherence
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Laser
• Hard-edgeplane-wavebeam
Perfectspa,alcoherence
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Laser
f
• Hard-edgeplane-wavebeam
Perfectspa,alcoherence
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Airybeam:
Atlensfocus• Hard-edgeplane-wavebeam
• Gaussianbeam
with
50%ofhard-edgecase
D:aperture(lens)diameter
Diffrac,onlimitedbeam:
Par,alspa,alcoherence
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Un-correlatedsmallbeams:θd=βλ/d
Correlatedsmallbeams:θd=βλ/D
θd=βλ/Dc
Ac:coherencearea
Generalcase:
M2factor
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Eliminatesambiguityofbeam-diameterdefini,on
Simplifieddefini0on:QualityofageneralbeamcomparedtoaGaussianbeam
M2≥1,being1forTEM00Gaussianmode.
Amul0modelaserbeampropaga,ngalongzaxis,itsbeamwaist(acrossx)
As
Hence
Contents
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Content Time
1. Monochromaticity 10’
2. Coherence - Spatial - Temporal
30’
3. Directionality 20’
4. Brightness 10’
5. Laser speckle 10’
Total: 80’
Brightness
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• Brightness(powerperunitareapersolidangle)≠Irradiance(powerperunitarea)• Propor,onaltothemaxpeakintensityachievablebyfocusingabeam
• Cause:Coherence→direc,onality→brightness
P:powerA:areaΩ:Solidangle
Example:o Arlaser(TEM00,1W,λ=514nm):B=4P/λ2=1.6×109W/cm2⋅sro Lamp(10Woutput,examinedatλ=546nm):B=95W/cm2⋅sr
• Use:Materialprocessing
Contents
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Content Time
1. Monochromaticity 10’
2. Coherence - Spatial - Temporal
30’
3. Directionality 20’
4. Brightness 10’
5. Laser speckle 10’
Total: 80’
Laserspeckles
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Cause:highdegreeoflaserlightcoherence
Calcula,onandimpact
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dg=2λL/D
• Grainsizedg
• Impact:Limitstheimageresolu,onofanobjectilluminatedwithlaser(specklenoiseratherthandiffrac,onlimit)
dg=2λL’/D’
Scawerersizeds
if
D<<L
• Use:Sensors(stress,vibra,ons)
Contents
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Content Time
1. Monochromaticity 10’
2. Coherence - Spatial - Temporal
30’
3. Directionality 20’
4. Brightness 10’
5. Laser speckle 10’
Total: 80’
Onemoreslide
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10W→10-18W
• Laserv.s.Thermallight
