Combining laser light with synchrotron radiation

Part 2http://www.joachimschulz.de/laser/

Literature

Orazio Svelto, “Principles of Lasers”, Plenum Press, New York (1989)

Wolfgang Demtröder, “Laser spectroscopy”, Springer, Berlin (2005)

Max Born and Emil Wolf, “Principles of optics”, Cambridge University Press (1999)

Laser PrincipleLight Amplification byStimulated Emission of Radiation

Stimulated emission amplifies theexisting light wave

often within an optical resonator

active medium excited by:

flash lamp

discharge

laser

Rate Equation

∣2 〉

∣1〉

d dt

=

Absorption stim. Emission

dN 1dt

=

spont.Emiss.dN 2

dt= P

pump Relaxation

−h

-N2 A21

+N2 A21

+N1 B12 ρ

-N1 B12 ρ

-N1 B12 ρ

-N2 B21 ρ

+N2 B21 ρ

+N2 B21 ρ

-N2R2

-N1R1

Rate Equations

dN 2dt

=P−N 2 A−N 2−N 1B−N 2 R2

dN 1dt

=N 2 AN 2−N 1B −N 1R1

d dt

=N 2−N 1B−h

Lasing occurs only if N2>N1: Inversion

Two level system

dN 2dt

=−N 2 A−N 2−N 1B

N 2N 1

=BAB

No inversion!No lasing!

Three level system

Fast transition

1

2

3

dNdt

=W pN t−N −2BN−N tN A

Nt=N2+N1 N=N2-N1

Four level system

Fast transition

1

2

3

dNdt

=W pN t−N −BN−NA

Fast transition0

N1=0

Laser System at MAX II - I411

MAX II time structure

100 Mhz repetition rate: 10ns distance

Laser System at MAX II - I411

desired properties:

chosen system:

Titanium dotted Saphire: 770-1000nm

laser dyes: 550- nm

wide tuning range

for absorption spectroscopy

for reaching different targets

continuous wave

no timing necessary

very high resolution

Titanium:Sapphire laser

Sapphire Al2O3 dotted with Ti ionsA vibronic solid state laser

Fast transition

1

2

3

Fast transition

Liquid Dye Laser

O

N

N

O

O

Rhodamine

Liquid Dye Laser

Rhodamine 6G

absorps 532 nm

fluorescence555-585 nm

Crystal pumped with 10 W VerdiFolded ring resonator

Gross wavelength selection withbirefringent filter

Optical diode chooses light direction

Ti:Sa Ring Resonator

Single mode selection by a setof Fabry-Perot-etalons

Scans and stabilization withBrewster plate and piezo-mirror.

Verdi

Nd:YVO 4Neodymium Vanadate

Fundamental wavelength: 1064 nm

Intra cavity frequency doubling: 532 nm (2.33 eV)

Up to 10 W output power

Neodynium dotted solid state lasers

Three 4f electrons

4I9/2

4I7/2

4F3/2

4F5/2 and others

1064nm Doubled to 532nm

Laser System at MAX II - I411

1 mW alignment laser

Alignment Procedures

Four degrees of freedom specifying alaser beam:

1 mW alignment laser

Position on the last mirror

Direction to the target

Spot size

Adjusting the Beam Diameter

Kepler telescope

Galileo telescope

With pinhole: spacial filter

Placing Windowswith Low Losses

vertical linear polarization

all objects in Brewster Angle

90°

i

Brewster Angle

No reflection for light polarized inplane of incidence.

no longitudinal light waves

Brewster Angle

For laser optics:

no reflection losses for the parallel polarization

used in polarization crystals

For classical optics:easy way to produce polarized light

defines the polarization of the laser mode

No reflection for light polarized inplane of incidence.

tan i=n1815 by David Brewster:

For Glass ~56°

90°

i

Birefringence

n2different indexes of refraction

n1

n1=1.55for Quartz n2=1.54

retards one polarization with respect to the other

/2 -retarding plateflips linear polarization around

the principal axis/4 -retarding plate

produces circularly polarized light

n1=1.49for Calcite n2=1.66

Maxwell's equations

∇×E=− B t

∇× H=J D t

∇⋅D= ∇⋅B=0

D=0 EP B=0 H M

Gauß' Law

Faraday's law Ampère's Law

No magnetic monopoles

Polarization of the medium

D=0 EP

P=0 E

D=01 E= E

No birefringence:

More general case: χ is a tensor

Pi= ∑j=1,2 ,3

0ijE j

Frequency doubling

D=0 EP

P=0 Ee 202E2

More general case

Er , t =12 [

E r ,eitc.c. ]

PNL2 r , t =1

2 [P2 r ,2e2i tc.c. ]

Pi2= ∑

j ,k=1,2 ,30d i , j ,k

2 E jEk