3 BO LASERPropertiesAndSystems - umm.uni-heidelberg.de · 11/13/2018 1 3. LASER Properties and...

11/13/2018

1

3. LASER Properties and

Systems Simon Hubertus, M.Sc.

Computer Assisted Clinical Medicine

Medical Faculty Mannheim

Heidelberg University

Theodor-Kutzer-Ufer 1-3

D-68167 Mannheim, Germany

[email protected]

www.ma.uni-heidelberg.de/inst/cbtm/ckm

Biomedical Optics – „LASER Properties and Systems“

Simon HubertusI Slide 2/61 I 11/13/2018

Outline: Biomedical Optics

1. Lecture – Basic Optics

2. Lecture – LASER Physics

3. Lecture – LASER Properties and Systems

• Wave Equation

• Beam Properties

• LASER Systems

• Gas LASER

• Solid-State LASER

• Tunable LASER

4. Lecture – Tissue Interactions I

5. Lecture – Tissue Interactions II

6. Lecture – Biomedical Applications

Wednesday, 19.12.2018, 1-3pm

House 22, Level 2, Lecture Hall 10



Wave Equation



Wave Equation

),( 1

),( 2

2

2

2 trEtc

trEvrvr

¶¶

=Ñ

2

2

2

2

2

22

zyx

¶¶

+¶¶

+¶¶

=Ñ

…with Laplacian

Maxwell's Equations

t

BE

¶¶

-=´Ñ

vv

t

DJH f ¶

¶+=´Ñ

vvv

D rÑ × =DÑ × =D 0BÑ × = 0BB ( ) ( ) ( )EEE ÑÑ-ÑÑ=´Ñ´Ñ

Vector Identity ...and

wave equation in vacuum:

wave equation in dielectric:

? ),( ),( 2

22

2 trEtc

ntrE

vrvr

¶¶

÷ø

öçè

æ=Ñ

tiertrE ×-×= we )(),(vvr

monochromatic solution

rkiervvr ×=

0 )( ee t )( ×-= we iet

space dependence

time dependence

c2 = 1/(ε0μ 0)



Monochromatic Fields

rkiervvv ×=

0 )( ee

Plane Wave

rkier

Ar

vvv ×= )(e

Spherical Wave



Paraxial Wave Equation

),( 1

),( 22

2 trEtc

trEvrvr

¶¶

=Ñ

wave equation in vacuum

0)(

2)( 2 =¶

¶+Ñ

z

rikrT

vv e

e22 yx

¶¶

+¶¶

=Ñ2

T

transverse Laplacian

Amplitude

Paraxial approximation: ! " 1#### $ ####% &' = ( &' )*+,

- &'. / = %0&'230/2

45% &' = 675% &'

Helmholtz equation

% &. 8 = ( & )*+, with & = 95 : ;5

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% &. 8 = ( & )*+,

Gaussian Beams

“beam – like” wave propagation in z-direction:

Gaussian beam intensity profile

( )222

2

2

02

)(~)()( zw

r

ezw

wrrI

-

×=rr

e

Ansatz:

0)(

2)( 2 =¶

¶+Ñ

z

rikrT

vv e

e

% &. 8 = %<><>082

exp6&5

>0825exp ? 78 : 7

&5

@A0826 B082

%<:! amplitude at z = 0!

><: beam waist

>082: beam width

R: radius of curvature

of wavefront

B: Gouy phase



Beam Properties



Beam Waist

Intensity Profile

( )222 )(2

2

2

0 )(

~),,( zw

yx

ezw

wzyxI

+-

×

Gaussian Beam

w(z): beam width/spot size

w0: beam waist (i.e. w(z) at z=0)

z

2

0

2

0 1z

zw)z(w +=

beam width varies with

propagation distance:



Beam Waist – Rayleigh Range

lp202

002

wkwz ==

The Rayleigh range is a measure of the length of waist region



Radius of Curvature

for z >> z0 : z)z(R »z

zz)z(R

2

0+=



Divergence Angle

pl

q00

0

wz

w

z

)z(w=»»

for w(z) << z :

analogy

àopening angle θ proportional to λ divided by “beam waist“!

à opening angle θ proportional to λ divided by “gap size“!

Interference Patern

Transverse Mode

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Resonator Modes: Definition

longitudinal modes

Resonator Mode:

interference of waves propagating

from left to right between the

mirrors

L

transverse modes



Resonator Modes: Definition

L = n·λ/2 f = n·c/(2L)

longitudinal modes

Resonator Modes:

interference of

right-going and left-going

beam between the mirrors

L

L



Transverse Mode Patterns

cylindrical LASER geometry

C = @DE

FE with spot size w of the mode GHI: associated Laguerre polynomial of

order p and index l

L

transverse radial mode orders

φ ρ

# nodes along ρ and φ

paraxial wave equation

à Combination of a Gaussian beam profile with a Laguerre polynomial!



Transverse Mode Patterns

à Combination of a Gaussian

beam profile with a Hermite

polynomial!

rectangular LASER geometry

# nodes along x and y

transverse Cartesian

mode orders

x

y

paraxial wave equation



Gaussian Beam: Thin Lens

fw

w ×»pl

0

0 'new beam waist: with

w(z) = ?

1 JK 1

1 K6LM

1 =1 6 N

MJ

6LM

1=

O PQ R

d

2w0’ 2w0

z1 z2

f

fd »



Example: HeNe LASER

spot size at the waist: w0 = 1 mm

LASER wave length: l = 632.8 nm w0’ » 202 nm

pl

0

0 'w

fw =w0’ w0

focus : f = 1 mm

Gaussian beams significantly focused!

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Tabelle14.1, S. 490

(paraxial electric field)

Gaussian Beams: Summary



LASER Systems



Natural Abundance of LASER/MASER

Cosmic LASERs:

• source of intense, coherent light fields

• ‘hot-star’: radiation spectrum from IR to UV (black-body)

• abundance of hydrogen atoms

• UV light leads to sustained inversion in H2 molecules

• IR light leads to stimulated emission in the microwave range (MASER)

MWC349 discovered in 1988

l = 169 µm



LASER Types

source: P.W. Milonni, J.H. Elberly. Lasers. Wiley 1988

• gas LASER (HeNe, CO2, excimer, N2)

• solid-state LASER: ruby, Nd:YAG (neodymium-doped yttrium-

aluminium-garnet)

• LASER diode

• dye LASER (dye: coloured substance in aqueous solution)



Gas LASER



Properties of Gas LASER

• active medium: substances in gaseous phase at room temperature

noble gases, e.g. argon, krypton

• good beam quality

• high frequency stability

• low energy consumption

• high output power in continuous wave operation

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HeNe-LASER: Setup

• capillary tube: S T 1 mm

• tube length: l T 1 m

• UV~16 @ kV

• He-discharge: several mA

• power: KWX 6 XK mW

• mixing ratio: He/Ne=10/1

• He pressure: p = 1K mbar

https://commons.wikimedia.org/wiki/File:Hene-1.png#/media/File:Hene-1.png



HeNe-LASER: Amplifier

He:

Pumping

Ne:

LASER Transition

• red line: 632.8 nm line $ used as length

standard

• interfereometric and reading devices,

holography

https://commons.wikimedia.org/wiki/File:Hen

e-2.png#/media/File:Hene-2.png

no photonic

transition!



Ar-Ion-LASER: Setup

• tube with argon plasma,

i.e. ionised gas

• gas pressure: Y = KWK1 6 KW1 mbar

• tube length: l = KWX 6 1WX m

• Ar+ ions diffuse to cathode:

extra gas reservoir

• high plasma temperature:

erosion of walls

copper or BeO elements for

fast heat conduction

magnetic field to focus

plasma on axis



Ar-Ion-LASER: Amplifier

• highest output power in optical range

• LASER lines: blue, green, yellow-green

• optical transitions up to UV (Z~1KK#nm)

• applications in entertainment, holography,

medicine

• pumping LASER for other tunable LASER,

e.g. dye and titan-sapphire LASER

excitation of Ar+ states by step-wise e--impact



Metal-Vapour-LASER

Example: copper-vapour amplifier • excitation by discharge (e--impact)

• 3-level system

• pumping: 1 $ @

• laser transition: @ $ [\ and @ $ []

• important LASER lines: yellow, green

D high operation temperature (1XKK#^)

C high power (~100 W)

C quasi CW: pulsed (10 kHz, 10 ns)

C Large excitation probability; strong

coupling of dipole-allowed transitions

2

3a

1

3b



Kinetic Energy Levels

molecules: additional kinetic energy level

!

!

!

!

!

!

_-`ab c _-dfg c _-hihj

• complex spectrum of transition frequencies $

LASER lines

• rotational and vibrational before electronic

excitation

• microwave range: MASER

rotational vibrational

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CO2-LASER: Setup

• infrared LASER: Z = kWm#nm

and 1KWo#nm

(kinetic energy level transition)

• high power output:

• Y = qK kW

• -rsith~1KK kJ

• high efficiency ~ 20%

• low production costs

industrial material

processing https://de.wikipedia.org/wiki/Datei:Co2_laser_funktionsprinzip.svg



CO2-LASER: Amplifier

• discharge excitation of metastable N2

• energy transfer to CO2 molecules

• 3-level system

• pumping: 1 $ @

• LASER transition: @ $ [

• deexcitation: [ $ 1

(collision processes, vibrational

relaxation)

• CO2 gas heating

add He to increase thermal

conductivity (cooling) vibrational energy states: v1, v2, v3 à vibrational quantum

numbers

2

3

1

symmetric

stretching

bending anti-symmetric

stretching



Eximer-LASER

• eximer = ‘excited dimer‘

diatomic molecules that

exist only in an excited state

• lifetime u 10 ns $ pulsed LASER

• ground state: dissociation into two unbound atoms

dissociation time u one vibrational period (10-13 s)

inversion: no lower level population



Excimer-LASER: Amplifier

• noble gas: Ar, Kr, Xe

e.g. ArF*, KrF*, XeF*, XeCl*

• excitation: electric discharge

• wavelength

• KrF: Z = @mq nm

• ArF: Z = 1k[ nm

• F2: Z = 1Xv nm



Excimer-LASER

Applications

• medicine: cutting with minimal heating of surrounding tissue

• lithography

LASIK surgery

(Laser-assisted in-situ

Keratomileusis)

IBM logo on human hair



Gas LASER: Overview

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LASER Applications

excimer LASER:

~ 50 mW

solid-state LASER:

~ 500 kW

CO2 LASER:

250 W

LASIK surgery

(Laser-assisted in-situ

Keratomileusis)



Solid-State LASER



Properties of Solid-State LASER

• amplifier media: rare earth metals (lanthanides + yttrium + scandium)

• yttrium: higher abundance than chemically similar lanthanides

• non-tunable



Properties of Solid-State LASER: Crystals

• host lattice:

• doped with optically active ions

• ion concentrations of a few %

• impurity ion density w particle density in

gas LASER

higher gain density

• inhomogeneous temperature pattern

• ‘thermal lensing‘: refraction index

depends on temperature

• Active research: LASER crystals with

..reduced thermal lensing

..higher gain densities

..more LASER frequencies



Properties of Solid-State LASER

• compact design and robust construction

• low production costs; economical

• efficient excitation by diode LASER

• power conversion: electrical $ light

• efficiency: ~ 20%

• applications:

• pump LASER for excitation of tunable LASER

• material processing demanding high intensity LASER

• todays ‘workhorses‘

• Maiman's chromium-doped ruby LASER (Cr: Al2O3) in 1960



Properties of Solid-State LASER: Dopants

• rare earth ions: triply ionised with e-

configuration 4fi (1 T i T 14)

• optical properties of host crystal determined

by 4f electrons

• broadening of electronic states due to

weak phonon coupling

• wealth of spectrum due to high electron

number

rare earth ion electron configuration: 4fn energy levels of rare earth ions

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Nd:YAG-LASER: Amplifier

• neodymium-doped yttrium-aluminium-

garnet (Nd:Y3Al5O12)

• 4-level system

• Nd pumping with diode LASER: 1 $ @

• fast phonon relaxation: @ $ [

radiation-free electron-phonon

interaction

• LASER transition: [ $ m

• fast phonon relaxation: m $ 1

2 3

1

4

2S+1LJ



noble gas Xe

Neodymium

mirror mirror

drive

current

Classically pumped with Xe-lamp

pump lamp and LASER bar located at the two foci

of an elliptical resonator

until the late 1980s:

• high-pressure noble gas

lamps, e.g. Xe

• significant heat production

Nd:YAG-LASER: Configurations

End-pumped LASER

Nd LASER longitudinally pumped with a diode

LASER

today:

• high-power LASER diodes

• higher efficiency



Er:YAG-LASER: Amplifier

• erbium-doped yttrium-aluminium-garnet

(Er:Y3Al5O12)

• 3-level system

• Er pumping with diode LASER: 1 $ @

• LASER transition: @ $ [

medical applications, eye-safe operation

wavelength

• LASER transition: [ $ 1

infrared

2

3

1 2S+1LJ



Erbium-Doped Fiber Amplifier (EDFA)

Er-doped optical fibers

• D. Payne, E. Desurvire 1989

• amplification at Z = 1WXX#nm

• breakthrough for long distance

data transmission



Frequency-Doubled Nd-LASER

• has replaced expensive Ar-LASER

• pump energy applied through fiber

bundles (high power)

• LBO crystal

• lithium triborate (LiB3O5)

• non-linear $ frequency doubling

• wavelength: Z = 1Komy@ nm = X[@ nm

(visible light)

non-linear crystal properties

• quantum mechanics: high-intensity light causes frequency doubling in a crystal; ‘two

photons are absorbed, only one is emitted‘

• electrodynamics: light forces atomic dipoles to oscillate at the same and higher

frequencies



LASER Diodes

• most common type of LASER

..fiber optic communications

..barcode reader

..LASER pointer

..CD/DVD

..LASER printing

..LASER scanning

• pumping: electrical

• active medium: p-n junction

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LASER Diodes: p-n Junction

• semiconductor

• small energy gap between valence and

conduction band

• non-conducting at low temperature

• strongly conducting with increasing

temperature (threshold)

• e.g. silicon (Si), germanium (Ge)

• doping: impurities with different number of

valence electrons

• n-type: higher number of valence

electrons (donator)

• p-type: lower number of valence

electrons (acceptor)

• p-n junction: combination of p- and n-doped

semiconductors

conduction band

valence band

_-

donator energy level

n-doped

acceptor energy level

p-doped



LASER Diodes: p-n Junction

diffusion driven charges

anode cathode conducting direction

IDC

conducting direction



LASER Diodes

• electric current forces recombination of electrons and holes

• annihilation leads to photon emission $ light emitting diode (LED)

• high current and optical resonator $ LASER

Cathode Anode IDC

Mirror 100%

Mirror 90%

Photon Photon + Phonon



Tunable LASER



Tunable LASER: Materials

• transition metal ions in host crystal

• colour centres (crystal defects absorbing light)

• dyes: organic molecules with a C double bond (C=C)



Tunable LASER: Materials

dyes

transition metal ions à wide frequency range

optical range

transition metal ions

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Transition-Metal-Ion-LASER

electron configuration: 3dn

à strong coupling of the ions to the

lattice b/c the 3d-electrons form the

outermost shell



Vibronic-LASER

• tunable over large range

• different positions of ground and

excited state in thermal equilibrium

• large separation of absorption and

emission frequency

• 4-level system

• pumping: 1 $ @

• v-v relaxation: @ $ [

• LASER transition: [ $ m

• v-v relaxation (1KzL5): m $ 1

Spectra of Ti-Sapphire Crystal spontaneous

emmison of

photons after

excitation of

atoms

Vibronic States of Solid-State Ions

2

3

1

4

thermal distribution in

the configuration

coordinate Q



Colour Centres

• no impurities but rather vacant

lattice sites (holes)

• vacancy: effective charge relative

to crystal

• binding of e- and holes

• electronic states $ LASER

• wavelength: near-infrared

(Z = 1 6 [#nm)

• costly

• operation temperature 77K (liquid nitrogen)



Dye-LASER

..LASER using an organic dye, e.g. dissolved in alcohol, as medium

Dyes: organic molecules with

C=C double bond

gold standard of tunable LASERs: 550 – 630 nm

Singlet state Triplet state

band structure:

rotation-vibration fine structure of dye

broadened to continuous bands because of

interaction with the solvent (similar to

vibronic ions)



Repetition

• light intensity inside resonator

• Maxwell‘s equation à paraxial wave

equation

• solution: Gaussian beam intensity

profile

• opening angle θ=λ/w0/π

• reduction of spot size with thin

lens

• resonator modes

• longitudinal: L=λ/2*n

• transverse: solution of paraxial wave

equation with boundary conditions

• cylindrical symmetry: Laguerre

polynomials

• rectangular symmetry: Hermite

polynomials

( )222 )(2

2

2

0 )(

~),,( zw

yx

ezw

wzyxI

+-

× fw

w ×=pl

0

0 '



Repetition

Gas LASER:

Solid State LASER:

• rare earth ion amplifier: host crystal doped with ions

• ion concentration few %

• broadened electronic states due to weak coupling of electronic to lattice

• Neodymium LASER & Erbium LASER pumped with LASER Diodes

• Erbium Doped Fiber Amplifier à long distance signaling

LASER Diodes – most common type of LASER

• pn-junctions operated with direct current in conduction direction

Tunable LASER

fixed

frequency

11/13/2018

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Next Lecture

4. Tissue Interactions I

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