Laser - matter interactionsBoris Lukiyanchuk

Singapore, 15 October 2018

Lecture 1.

Laser matter interactions

Compton effect Feynman Diagramm

About 29 000 000 Results

LASER MATTER INTERACTIONS

The purpose of these six lectures is to give brief introduction into the very broad field of laserinteraction with matter where one can find contributions of many Nobel Prize winners.Traditionally there are distinguished courses on resonant and nonresonant processes which aretypically discussed in a semester`s University courses. For example, the book of D. Bauerle“Laser Processing and Chemistry” devoted to material processing with lasers (basicallynonresonant processes) consists of about 850 pages and 32 Chapters devoted to different aspectsof these interactions. The classical courses on nonlinear optics see e.g. Guang S He and Song HLiu “Physics of Nonlinear Optics” or Robert W. Boyd “Nonlinear optics” contain a fewhundreds of pages and dozens of Chapters. The same refers to the books on Laserthermochemistry, see e.g. N.V.Karlov et al “Laser Thermochemistry. Fundamentals andApplications”, Cambridge International Science Publishing, 2000 - 380 pp. In contrast to thesedetailed and systematic courses the given course presents just a few selected typical problemssolving in different fields of “Laser matter interactions”. However, it demonstrates the specific ofdifferent fields and their instrumentalism and can be consider as a first step for more detailexamination of corresponding topics.

LASER MATTER INTERACTIONS

Planck Einstein Bohr Compton Raman Heisenberg Schrödinger Dirac Rabi Pauli

Basov Prokhorov Townes Feynman Schwinger Tomonaga Kastler Gabor Bloembergen Schawlow

Ramsey Chu Cohen-Tannoudji Phillips Cornell Wieman Ketterle Glauber Hall

HänschKao Haroche Wineland Akasaki Amano

Nakamura Weiss Thorne

Barish Ashkin Mourou Strickland

42

About 109 results (0.48 seconds)

The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-

scale physics experiment and observatory to detect cosmic gravitational waves and to develop

gravitational-wave observations as an astronomical tool. Two large observatories were built in

the United States with the aim of detecting gravitational waves by laser interferometry. These

can detect a change in the 4 km mirror spacing of less than a ten-thousandth the charge

diameter of a proton, equivalent to measuring the distance from Earth to Proxima

Centauri (4.0208x1013km) with an accuracy smaller than the width of a human hair.

James Clerk Maxwell become the first Cavendish Professor of Physics in 1871.

In the III century. BC. Alexandrian scientist Eratosthenes for the first time determined thedimensions of the globe, proceeding from the deviations of the sun from the zenith in thecity of Siena (present Aswan), and in Alexandria. Eratosthenes correctly concluded thatAlexandria is about a fifth of the Earth's circumference from Siena. To know thecircumference of the Earth, it remained to measure the distance from Alexandria to Siena.This distance was determined by the number of days that camel caravans spent on thetransition between cities.

ℓ = vt

School ruler

Laser meter

I`ll ask experimentalists to enhance accuracy of their measurements by the order of magnitudes per year.

Laser - matter interactions

Nonresonant processes Resonant processes

Physical Processes

Chemical Processes

Vapor PlasmaProcesses

Plasmonics Photonics

NonlinearOptics

Resonant Chemistry

Lecture 1.

Nonresonant Physical Processes

ABSORPTION of LASER RADIATION

Maxwell`s equations

EE

Hctc

rot

4 0Ediv

tcrot

HE 0Hdiv

The properties of concrete environment are included into these equations as three factors:

permeability , permittivity and electrical conductivity . With the exception of a

magnetic field from the Maxwell equations, we obtain the wave equation

tctc

EEE

22

2

2

4

)](exp[),( tit rkErE 0

One can search the solution of this equation in the form

2/14

i

ckFor the wave vector we obtain In vacuum

inin

2/14~Complex refractive index:

2/12/1

22

22

n

2/12/1

22

22

Values of n and kappa are:

20 ck

zktznkieetz

00),(

0EE

Light propagation

20 ck

Laser intensity I cE 2 8/ )/2exp( czThus, variation of the intensity is given by

c/2 zI /ln= 4Absorption coefficient

Light reflection

tznkix eEE

~0

2At z > 0 (within the media)

At z < 0 (in vacuum) we have superposition of incident and reflected light

tzkitzkix eEeEE

0

10

0

At z = 0 continuity of Ex yields 210 EEE

Continuity of Hytc

rot

HE

z

E

k

iH x

y

0210

~EnEE

n

n

E

Er ~1

~1

0

1

Amplitude reflection coefficient

22

2222

)1(

)1(~1

~1

n

n

n

nrREnergy reflection coefficient

Augustin-Jean

Fresnel

1788-1827

Light reflectivity, absorptivity and transmittivity 1 TAR For half space T = 0

221

41

n

nRAAbsorptivity

Averaged energy density [J/cm3] in dielectric media is given by

Thus, averaged energy density in vacuum is constant

Time averaged Poynting vector

Intensity at normal incidence is given by Sz component of the Poynting vector:

Incident intensity in vacuum Absorbed intensity in medium

Distribution of intensity inside the medium

Bouguer's law. (Or Beer's law, Bouguer–Lambert law; sometimes

called Lambert's law of absorption.) Attenuation of a beam of light by an optically homogeneous (transparent) medium.

E4

E3E

2

E1

1

2

3

E0

h

0

z

Pierre Bouguer

1698-1758

(experiment 1729)

Johann Heinrich Lambert

1728-1777 (theory 1760)

August Beer

1825-1863

law N, 1852

Mandelstam’s paradox2

rR 2

dT

-4 -2 0 2 4 60.0

0.5

1.0

1.5

2.0

-2 -1 0 1 2 30.0

0.5

1.0

1.5

2.0

E2 / E

0

2

z / h

h = / 4 n

(a)

E2 / E

0

2

z / h

h = / 2 n

(b)

5.1~ nSolid lines

Dashed lines 1.05.1~ in

-4 -2 0 2 4 60.0

0.5

1.0

0.0 0.5 1.00.7

0.8

0.9

-2 -1 0 1 2 30.0

0.5

1.0

0.0 0.5 1.00.6

0.8

1.0

0.0 0.5 1.0

0.4

0.6

0.8

1.0

0.0 0.5 1.0

0.2

0.4

0.6

0.8

1.0

I/I 0

z/h

(a)

h = / 4n

2

I/I 0

z/h

1

I/I 0

z/h

(b)

h = / 2n

2

I/I 0

z/h

1

2

1

I/I 0

z/h

(c)

h = 5 / 2 n h = 9 / 2 n

(d)

2

I/I 0

z/h

1

Curves 1 – exact

Curves 2 - Bouguer

hzsnikeEE

~0

43

E4

E3E

2

E1

1

2

3

E0

h

0

z

Film on the substrate

23122

232

12

0

1

rre

rer

E

Er

i

i

s

s

nn

nnr ~~

~~

23

23122

2

0

2~1

2

rre

e

nE

Ei

i

23122

23

0

3~1

2

rre

r

nE

Ei

23122

0

4~~~1

~4

rre

e

nnn

n

E

Ei

i

s

See also Landau, Lifshits Electrodynamics of continuous media, Problem 4 for § 86.

0 20 40 60 80 1000.0

0.5

1.0

0 1 2 3 4 50.0

0.2

0.4

A

bsorp

tivity

h, m

Cu + Cu2O

= 10.6 m

A

h, m

6.10 m

027.026.2~ in Сu2O

1.528.12~ is

n Сu

snn Film with can diminish total reflection

0 50 100 150

0

1

2

3

4

Reflectivity, R

%

h, nm

1

2

3

524 nm 52.1sn

4.1n (1) 233.152.1 n (2) 1.1n (3)

23122

232

12

0

1

rre

rer

E

Er

i

i

Antireflective coating

124

n

h 12 ie 2312 rr

snn

smnnn

If instead of vacuum we have some media with mn

Antireflective coating with

Bunkin F. V., Kirichenko N. A., Konov V. I., Luk'yanchuk B. S.

Interference effects in laser heating of metals in an oxidizing medium.

Quantum Elektronics, vol. 7, Issue 7, pp. 1548-1556 (1980)

23122

232

12

0

1

rre

rer

E

Er

i

i

Multilayer structures

L. P. Shi, T. C. Chong "Nano Phase Change for Data Storage Application",

Journal of Nanoscience and Nanotechnology, Vol. 7, pp. 1–29, (2007).

Recording layer GeSbTe

MLrr 23

For example, for two layers on the substrate 1h 1

~n( ) and 2h ( )2~n

MLi

MLi

rre

rerr

1212

1212

342322

3422

23

rre

rerr

i

i

ML

1101

~ hnk

2202~ hnk

1

112 ~1

~1

n

nr

21

2123 ~~

~~

nn

nnr

s

s

nn

nnr ~~

~~

2

234

0 5 10 15 20 250.0

0.5

1.0

Absorp

tivity

h (Cu2O), m

Cu/Cu2O/CuO

= 1.06 m

h1/h

2 = 0.2

06.1 m

005.05.1~1

in (СuO)

035.06.2~2

in (Сu2O)

1.736.0~ is

n (Cu).

Arzuov M. I., Barchukov A. I., Bunkin F. V., Kirichenko N. A., Konov V.I.,

Luk'yanchuk B. S. Influence of interference effects in oxide films on the kinetics of

laser heating of metals. Quantum Elektronics, vol. 6, Issue. 3, pp. 466-472 (1979)

Reflectivity of the system from two materials with a refractive index of 1.3 and 1.5 for radiation with a wavelength of nm. The thicknesses of each of the layers are, respectively, and

. The figures show the reflective capacity of two (a), four (b) and six layers (c).

266 1h

2h

0

h2

22 11

Vacuum

1 2

....h

1

z

The limiting case of an infinite periodic layered system of layers of matter withdifferent refractive indices (superlattice). Consider, for example, the situationwhen such a sandwich is made up of materials 1 and 2.

1

101 ~1

~1

n

nr

21

2112 ~~

~~

nn

nnr

1221 rr

1

11 ~1

~1

n

nr

1

11

1

1~

r

rn

12

122 ~~

~~

nn

nnr

MLi

MLi

rre

rerr

0112

1201

1

21222

222

12

rre

rerr

i

i

ML

1r

21

2

221

1

121 sincos~

1~cossin~1~

nn

nnie

i

,52cos2cos32cos2cos2

12121

212

ie ,2sin2sin~

~

~

~2sinsin~

~

~

~2 21

1

2

2

12

21

2

21

22

22

21

n

n

n

n

n

n

n

n

.sinsinsincos1

cossin1

21

2

1

1

221

2

221

1

1

21

n

n

n

n

nni

nni

ei

0 50 100 1500.0

0.5

1.0

R

h2, nm

n1 = 1.3

n2 = 1.5

h1 = 50 nm

= 266 nm

Reflectivity of superlattice versus thickness of the second layer.Reflectivity tends to unity in some range of thickness.

A photonic crystal is a periodic optical nanostructure that affects

the motion of photons in much the same way that ionic lattices

affect electrons in solids. Photonic crystals occur in nature in the

form of structural coloration and animal reflectors, and, in

different forms, promise to be useful in a range of applications. In

1887 the English physicist Lord Rayleigh experimented with

periodic multi-layer dielectric stacks, showing they had a

photonic band-gap in one dimension. Research interest grew with

work in 1987 by Eli Yablonovitch and Sajeev John on periodic

optical structures with more than one dimension—now called

photonic crystals.

Photonic crystals can be fabricated for one, two, or three dimensions. Two-dimensional photonic-crystal

fibers are used in nonlinear devices and to guide exotic wavelengths. Three-dimensional crystals may one day

be used in optical computers. Three-dimensional photonic crystals could lead to more efficient photovoltaic

cells as a source of power for electronics, thus cutting down the need for an electrical input for power.

Photonic crystal

Floquet–Bloch theorem൯𝐸(𝑧 + 2𝑑) = 𝑒𝑖𝑘2𝑑𝐸(𝑧

0x

2

k2

k1

1

Media

1 M

edia

2

E

k

z

x

1

(a)

0

(b)

H

2

k2

z

k1

1

1

k

Media

1 M

edia

2

ТМ – wave, p-polarization ТE – wave, s-polarization

zzkyykxxkii ee

kr

i

iz

iy

ix kkkk 2

0

222

20

ck

sinsinsin2011010

kkk

1Reflection law Snell's law

2

1

sin

sin

,cos10 kkz

,cos101 kkz

,sincos 212020

2 kkkz

Incident wave

Reflected wave

Transmitted wave

21212

21212

0

1

sincos

sincos

H

Hrp

2121

2121

0

1

sincos

sincos

E

Ers

0 45 900.0

0.5

1.0

0 45 900.0

0.5

1.0

Rs,

Rp

, grad

(a)

1 = 1

2 = 1.5

2

B =

56.3

o

p

s

s p

r = 41.8

o

B =

33.7

o

1 = 1.5

2

2 = 1

(b)

Rs,

Rp

, grad

1212sin nnr

Brewster angle 1212 nntg B

Total internal reflection

Sir David Brewster

1781-1868

There is a layer of matter on the surfacewhich is optically different from thesubstrate substance. The thickness of thislayer is h. The incidence of radiation isinclined.

ppi

pip

prre

rer

H

Hr

23122

232

12

0

1

21212

21212

12

sincos

sincos

pr

2123

2132

2123

2132

23

sinsin

sinsin

pr

Frustrated Total Internal Reflection

ssi

sis

srre

rer

E

Er

23122

232

12

0

1

2121

2121

12

sincos

sincos

sr

213

212

213

212

23

sinsin

sinsin

pr

4.1:1:5.1:: 321 nnn

The ratio of the components of the Poynting vector in

the medium 3 to the component of the Poynting vector

in the incident wave in the medium 1 (a). A contour

graph of the same function (b). The geometry of the

radiation drop is shown in Figure, the case of s-

polarization is considered.

321 nnn 23 nn TIR FTIR

0 2 4 6 8 100.0

0.5

1.0

Sz/S

0

k0 h

n = 1.2

n = 1.5

n = 2

= 70o

FTIR between materials

with refractive indices n1

= n3 = n separated by a

vacuum. The angle of

incidence 70 degrees

exceeds the angle of total

internal reflection.

Heat equation

cvr¶T

¶t=Ñ k ÑT( )+Q

Heat diffusivity [cm2/s]

Q =a 1-R( ) I t( )e-az

T t = 0( ) =T¥ -k

¶T

¶zz=0

= 0

T z = 0( ) =T¥

+a

crI t - t

1( )0

t

ò ea2Dt

1 erfc a2Dt1dt

1

D =k

cr

Schrödinger equation

erf x( ) =2

pe-t2 dt

0

x

ò

erfc x( ) =1- erf x( ) =2

pe-t2 dt

x

¥

ò

Error function

Complimentary Error function

Energy balance

mc T -T¥( ) = SF Temperature rise depends on fluence

Which pulse shape with the same fluence yields the highest surface temperature?

Optimal laser heating

Ramanujan1887-1920

Kantorovich1912-1986

Pontryagin

1908-1988

Laser cleaning

1. Light focusing and near-field enhancement 2. Temperature under the particle

3. Thermal expansion and dynamics of the particle motion in adsorption potential

ProblemsProblem 1. If the degree of monochromatic of the incident light is low, then the interferenceeffects caused by reflection from two faces of the plate does not occur, and addition ofintensities of light play the dominant role. Find the coefficient of plate transmission undersuch approximation.

I0 R

(1)

A(1)

T(1)

A(2)

A(3)

R(2)

T(2)

0

h

z

R

1-R

A(4)

1i

iR

1i

iTT

22

22

1

1

n

nRSolution. heRA 11

heRT 21 1

heRRA 22 1

h

hhhh

eR

eReRReRReRT

22

25243222

1

1...111

h

h

eR

eRR

22

2

1

211

0 500 1000 15000.0

0.5

1.0

1

2

Tra

nsm

ittivity,

T

h, nm

= 530 nm

n = 1.5

= 0.1

Problem 2. Find a maximum absorptivity of the thin film h<<1 with a high complex dielectricpermeability , .

nn

nr ~

21~1

~112

2

122

122

0

1 1

re

re

E

Er

i

i

Solution.

ih

hr

~

~

inn ~~ 1,1 n

ih

ihnd

~

~2

14

22222

22222

2

hn

hn

hn

rR

14

144

22222

22222

2

hn

hn

hhn

dT

TRA 1 Finding of maximum A yields h << h0 22

nh

1

For Cu and CO2 laser =10.6 m the optical constants are n= 12.8 and = 52.1. This yields h 1.17 nm approximately three atomic layers.

0 10 20 30 40 500.0

0.1

0.2

0.3

Absort

ptivity, A

h, nm

1

2

Cu

= 10.6 m

n = 12.8

= 52.1

Problem 3. Find an approximation for the absorptivity of weakly absorbing << n , and thin h << 1 dielectric film on the surfaces of high reflecting metal substrate A0 << 1. The film thickness h can be comparable with the radiation wavelength .

Solution. For a metal substrate with A0 << 1 and 1sn 1s

14

122

2130

ss

s

n

nrA

ss inr 2113

22

2

121

2

1

1

n

i

n

nr

With << 1 For h << 1 hii ehe 12

n4where . However h is not a small value.

2sin111

sin21

222

02

2

hhnhnnn

hhAnrhA

1hFor one can find

2

222

022

2

2

0 1414

11

hnAh

n

nAhA

2sin1

sin21

222

02

2

hnn

hhAnrhA

0 2 4 6 8 10 120.0

0.5

1.0

4

3

3

2

A

h, m

1

Cu + Cu2O

= 10.6 m

Problem 4. Optical discs (CD, DVD, Blue Ray) using the variation of the reflectivity of the thinmetal film between layers of transparent dielectric . Find the film thicknesswhich produces the highest contrast for the change of reflectivity. In optical recordingGeSbTe films the crystalline state approximately twice higher than in the amorphous state,e.g. for = 650 nm the crystalline material has n = 3.9 and = 3.6 while the amorphousmaterial has n = 3.9 and = 2.1 . Refractive index for dielectric is . Consider astrong absorption coefficient .

0,~ sss nn

Solution. where . After some algebra one can find

5.1sn

12 hez

23122

232

12

0

1

rre

rer

E

Er

i

i

nn

nnrr

s

s~

~

2312

23210

2

02

2cos2sin2

2cos21

zbhbhbzb

zhzarR

nnk 42 0 where and coefficients

2222220 4 ss nnnna 222

0 snnb 2221 4 ss nnnb

2222222 22 ssss nnnnnnb 222

3 snnb

1zFor

2cos22sin8

1 22222

222

2

hnnnnnhnn

nn

enRR sss

s

hs

m

22

22

s

sm

nn

nnRwhere

2222

2

02

2

ss

ss

nnnn

nnnnnhktg

The equation for the optimal thickness with highest reflectivity is

This yields h = 37.5 nm for crystalline and h = 38.4 forAmorphous film.

This yields h = 37.5 nm for crystalline and h = 38.4 nm for amorphous film. Solid line – exact solution, dashed line is approximation.

In reality for optical recording the opticalcontrast is important, i.e. the difference inreflectivity for different states. Typical contrastis about 15% and CST thickness h is about 80nm.

Problem 5. Find formulas for absorptivity versus incidence angle for good metal.

Solution. where and . After some algebra one can find 2 in 1n 1

1cos

1cos

pr

21 pp rA

221cos

cos4

n

nAp

Maximal absorptivity at whereB 2122cos

nB

nnnAp 12

2

max At IR range where n % 83122max pA

22cos

cos4

n

nAsFor s-polarization

one can see monotonous dependence

Literature

1. Landau, L. D., Bell, J. S., Kearsley, M. J., Pitaevskii, L. P., Lifshitz, E. M., Sykes, J. B., Electrodynamics of continuous media (Vol. 8). Elsevier, 2013.

2. Born, M. and Wolf, E., Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Elsevier, 2013

3. Mandelstam, L.I., 1971. Lectures on optics, relativity theory and quantum mechanics. Nauka Eds., Moscow, 1972. 440 pp.

4. Stratton, J.A., Electromagnetic theory. John Wiley & Sons, 2007.

5. Karlov, N.V., Kirichenko, N.A. and Luk'yanchuk, B.S., Laser thermochemistry. Cambridge International Science Pub., 2000.

6. Landau, L. D. & Lifshitz E. M., The Classical Theory of FieldsButterworts–Heinemann, London, 1973

7. I. L. Hooper, T. W. Preist, J. R. Sambles, Making Tunel Barriers (Including Metals) Transparent, Phys. Rev. Lett. 97, 053902 (2006)

Home work

1. Reproduce solutions of the Problems 1 – 5

2. Suggest a new problem and its solution