www.helsinki.fi/yliopisto

Lecture #5

Recap of the first 4 lectures

Dr. Ari Salmi

29.3.2018 1

• ”Sound that has a wavelength or is confined in

nanometer scale structures”

• What does this mean in practice?

• Sound and heat approach each other

• What is heat?

29.3.2018 2

What is nanoacoustics?

https://www.youtube.com/watch?v=Xscn-QSmFo4

Cremons et al., Nature Comm. 2016

• Maldovan, Nature (2013)

29.3.2018 3

What is nanoacoustics?

• Phonons and photons closely resemble each other

29.3.2018 4

Phonons and photons

Phonon Photon

Quantized normal modes of

vibrations in a medium (’particles of

sound’)

Quantized normal modes of

electromagnetic waves (’particles

of light’)

E = hv/λ E = hc/λ

p = h/λ p = h/λ

Wavelength (’size’) = 10-10 m and up Wavelength of visible light = 10-7 m

• The previous dispersion relation is for acoustic

phonons

• The name comes from the fact that they converge to

acoustic waves at large wavelengths

• ”Classical acoustic waves”

29.3.2018 5

Acoustic phonons

• This has two solutions

29.3.2018 6

Phonons

k

Optical

Acoustical

• The upper branch (higher frequencies) = optical

phonons

• Name comes from the fact that they can be excited

with infrared radiation

29.3.2018 7

Optical phonons

http://www.chembio.uoguelph.ca/educmat/chm729/phonons/opt1.gif

• So, heat is phonons

• What is sound then?

• Coherent vs. incoherent phonons

29.3.2018 8

What is heat?

http://www.ceres.dti.ne.jp/~hideo-t/profile.html

• In this course, we deal with coherent (acoustic)

phonons (CAPs)

• CAPs exibit classical wavemotion like behavior

• Longitudinal and transverse phonons

• Also surface waves!

29.3.2018 9

Coherent phonons =

nanoacoustics

• What happens when a laser pulse hits matter?

• Electron heating via inverse Brehmsstrahlung (~ 1 fs)

• Heat transfer to the lattice (~1 ps)

• Three important time scales

• Duration of the laser pulse tL

• Electron cooling time tE

• Lattice heating time tI

29.3.2018 10

Light to sound

When the excitation pulse length

goes down (to femtoseconds!)...

• The excited frequencies go up!

• Up to the point when the absorption is faster than diffusion

• Several generation mechanisms

• Deformation potential (DP)

• Thermoelasticity (TE)

• Inverse piezoelectric process (PE)

• Electrostriction (ES)

• The pulse length matters less, material properties and other

beam characteristics more

Light reflectivity vs strain

• If there is a localized area of strain in the material

• localized change in the permittivity

Pump-probe

• Combining all we have learned so far, one can generate an

experimental scheme for generating and detecting CAPs

Pump-probe

• How does one measure this in practice?

Pump-probe

• Combining all we have learned so far, one can generate an

experimental scheme for generating and detecting CAPs

• Beam shape

• Beam ’color’ = wavelength

• Energy (+ energy density)

• Pulse length

29.3.2018 16

Four parameters of laser

ultrasonics

Et

E

• Changes the shape of the ’transducer’

• Circle

• Point

• Line (reduces the situation to a 2D-problem)

• Circular line

• Alters the energy density (= E/A)

29.3.2018 17

Beam shape

• Alters the heated volume and amount of absorbed

energy

• Also affects laser safety!

• Higher absorption coefficients mean smaller

’transducer volumes’

• Double tap:

• First pulse changes material

• Second pulse excites ultrasound

29.3.2018 18

Beam color = wavelength

• Affects the regime (thermoelastic/ablation)

• As high energy as possible without surface damage

• Ablation threshold depends on power density

‒ For metals, approx. 1-10 MW/cm2 for infrared laser at room

temperature

29.3.2018 19

Energy(density)

Thermoelastic

Ablation

Scruby & Drain 1990

• Affects two things

• Generation mechanism (P = E/t)

‒ Leitz et al., 2011: nanosecond pulses differ from pico- and

femtosecond pulses in ablation

• Frequency content

29.3.2018 20

Pulse length

• Spectrum as a function of pulse duration

• Levels off at some point, why?

Pulse length

• Amplitude of the acoustic echo as a function of pulse

duration

• Levels off at a certain point, why?

Pulse length

What does this look like in

practice?

• Different color pump and probe

Blue probe, NIR adjustable pump

Blue pump, NIR adjustable probe

What does this look like in

practice?

• Absorption has an effect on the pulse shape

• Change of absorbance Length of oscillations

1.

2.

3.

4.

5.

6.

7.

What does this look like in

practice?

• Large absorbance = large ”bandwidth” = short Brillouin

oscillations

• How to generate shear CAPs?

• Counterquestion – why cannot we with ”normal” laser

ultrasonic means?

• Rossignol et al., PRL 2005

• Spot size dependence

29.3.2018 26

Exciting shear CAPs

• In isotropic crystals, either

• Small spot size

• Shear generation by mode conversion in reflections

from surface

‒ Only works up to a few GHz

• Break axial symmetry of the elastic tensor

29.3.2018 27

Exciting shear CAPs by

TE/DP/PE

• This means that the polarization is scattered from p

to s (or the other way around)

29.3.2018 28

Detecting shear CAPs

• Debye frequency ωD

• Maximum frequency of phonons in a certain lattice

‒ 2 times the interatomic distance

29.3.2018 29

Limit frequencies of phonons

• ’Frenkel line’

• Bolmatov et al., Sci. Rep. 2015

• Above Frenkel line – rigid, solid-like

• Below Frenkel line – soft, gas-like

29.3.2018 30

Fluids

• Frenkel frequency ωF

• Minimum frequency of shear phonons in a liquid

‒ Only for liquids/solids above the Frenkel line

• Inversely dependent on the liquid relaxation time

29.3.2018 31

Limit frequencies of phonons

• Average interatomic distance different in different

phases

• For solids (metals) ~ 2.5 Å

• For liquids (water) ~ 4 Å

• For gases (air) ~ 60 nm

• What does this mean for the allowed frequencies?

29.3.2018 32

Coherent phononics in fluids

http://www.middleschoolchemistry.com/img/content/multimedia/chapter_2/lesson_5/states_of_matter_big.jpg

• Erohkin, J. Russ. Las. Res. 4, 2002

29.3.2018 33

Attenuation of phonons in water

α = ~1000 dB/cm = 0.1 dB/µm @ 1 GHz

λ = 1.5 µm

α = ~10000 dB/cm = 1 dB/µm @ 10 GHz

λ = 150 nm

α = ~70000 dB/cm = 7 dB/µm @ 100 GHz

λ = 15 nm

α = ~1000000 dB/cm = 100 dB/µm @ 1 THz

λ = 1.5 nm

• Che et al., Ultrasonics 2015

• Coherent phononic acoustic microscope

29.3.2018 34

CAPs in water – practical

example

• Che et al., Ultrasonics 2015

• Coherent phononic acoustic microscope

29.3.2018 35

CAPs in water – practical

example

• ~540 nm lateral resolution

29.3.2018 36

CAPs in water – practical

example

• Elastic vs. Inelastic scattering

• Elastic – Energy of the incident photon is conserved

• Example: Rayleigh scattering (from particles smaller

than the wavelength)

Scattering

Xkcd.com

http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/imgatm/raymie.gif

• Inelastic scattering – Energy of the incident photon is

changed

• Raman scattering

• Photon inelastically scatters from the intramolecular

vibration

Scattering

• Brillouin scattering

• Photon scatters from a phonon (intermolecular

vibration)

Scattering

http://www.icmm.csic.es/brillouin/SBS-bulk.jpg

• Stokes and anti-Stokes events

• Stokes = photon loses energy and translates it to the

molecule (Raman) or phonon (Brillouin)

• Anti-Stokes = photon gains energy by absorbing a

phonon (Brillouin) / molecule vibrational energy

(Raman)

29.3.2018 40

Stokes and anti-Stokes events

• Electromagnetic wave

• Acoustic wave (phonon)

• The electromagnetic wave scatters into an angle

• Meng et al., Advances in optics and photonics

Brillouin scattering

• The frequency of the scattered light is increased or

decreased by the Brillouin shift (+ = Stokes, - = Anti-

Stokes)

• Depending on the attenuation, the Brillouin peaks

widen

(Spontaneous) Brillouin

scattering

• Thus, one can determine the entire complex

elasticity at hypersonic frequencies from the

frequency and peak width:

Brillouin scattering

Speziale et al., Rev. Min. & Geol., 2014

• This means that one can determine the mechanical

properties at a certain frequency of phonons by light

scattering

• Dependent on the color of the probing beam

Brillouin scattering

• Koski et al., Nature Materials 2013

• Measured the full mechanical properties of spider

silk

• Anisotropic material different orientation of

measurements required

• Reveals different acoustic modes

Spider silk

• Brillouin scattering is a ’static’ process

• Stimulated Brillouin scattering (SBS) uses beat

frequency of two laser beams to generate phonons

• This beat frequency has to match the desired mode

Brillouin frequency

SBS

• This can also be shown in the omega-k space more

intuitively

SBS

• Massively increased SNR compared to Brillouin

scattering

• Only 1 in 107 photons is passively Brillouin scattered

• E.g. Ballmann et al., Sci. Rep. 2015

Uses of SBS

• Cooling using SBS

• Bahl et al., Nature Physics 2012

• Custom made silica resonator with one acoustic and

two optical whispering gallery modes

Uses of SBS

• Based on two optical modes

• Their beat frequency pumps the whispering gallery

acoustic mode

• The system amplifies the anti-Stokes process

resonantly

Uses of SBS

• Selectively either pump the Stokes (heating) or anti-

Stokes (cooling) process and observe the Brillouin

scattering from the acoustic mode

Uses of SBS

• Selectively either pump the Stokes (heating) or anti-

Stokes (cooling) process and observe the Brillouin

scattering from the acoustic mode

Uses of SBS

• Cooled down to 19K

Uses of SBS

• Storing light

• Zhu et al., Science 2007

• Based on data storage by stimulated Brillouin

scattering (Stokes and anti-Stokes)

Uses of SBS

• Stored light for up to 12 ns

Uses of SBS