1 Acoustic ↔ Electromagnetic Conversion in THz Range Alex Maznev Nelson group meeting 04/01/2010.

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Acoustic ↔ Electromagnetic Conversion in THz Range

Alex Maznev

Nelson group meeting 04/01/2010

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Piezoelectric effect

• Pierre and Jacques Curie, 1880

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Piezoelectric transducer

Thin film resonator - up to 20 GHz

~V

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EM-acoustic conversion at the free surface

Microwave ultrasonics circa 1966, up to 114 GHz!

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Generation of THz coherent phonons by free-space THz radiation

• Grill and Weiss, 1975 : reported piezoelectric surface excitation of coherent acoustic phonons in quartz at 0.891 and 2.53 THz

• Results not reproduced in subsequent experiments by several groups

• Bron et al., 1983: surface roughness and subsurface damage prevent coherent phonon generation at THz frequencies

far-IR laser

quartz sample 10x10 mmT=4K

Superconductingbolometer

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Picosecond ultrasonics

• Metal films – thermal expansion – up to ~400 GHz.

• III-V superlattices – deformation potential, – piezogeneration via screening of the internal

field – up to 1.4 THz at room temperature

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Conversion of picosecond acoustic pulses into THz radiation

• M.R. Armstrong, E.J. Reed et al., 2009

laser

0.7 mJ, 1 mm diam1 kHz rep rate

800 nm pump/800 nm probe

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Current Status

• Physical principles well established back in 1960s.

• Now is the time to move into THz range– Advances in both THz and picosecond acoustic research – Good interfaces can now be made.

• Acoustics → EM: first experiment just reported.

• EM → Acoustics: not convincingly demonstrated yet. – Early paper not reproduced– Indirect evidence: resonant terahertz absorption by confined

acoustic phonons CdSe nanocrystals, T.M. Liu et al., APL, PRB 2008.

• EM → Acoustics → EM ?

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Why do it?

• Generation and detection with ultrahigh bandwidth – only limited by quality of a single surface/interface.

• Transverse waves can be generated/detected as easily as longitudinal.

• New physics: to be uncovered– How short is the front of a shock wave?– Hybridization and resonant THz – acoustic conversion in superlattices

• Applications: acoustic ↔ EM conversion in piezoelectrics at lower frequencies proved very useful (works in every watch and every cellphone).

• We’re doing both THz and picosecond acoustics. Crazy not to get involved!

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piezoelectric constants

ik ijkl kl lik l

i ik k ikl kl

C u e E

D E e u

Coupled fields in piezoelectrics

2 2

2i ik

k

u

t x

0, 0

1 1,

D B

B DE H

c t c t

Newton’s 2nd law

Maxwell’s equations

Constitutive relations:

stressdisplacement

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• Effect on EM velocities negligible:

Coupled fields in piezoelectrics

• 5 plane wave solutions: 3 slow (acoustic), 2 fast (EM). • Effect on acoustic velocities

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2/ ~

vc c K

c

Electomechanical coupling coefficient ~0.5 in LiNbO3, ~10-3 in GaAs

221

/ ~2

ev v K

C

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ik ijkl kl lik l

i ik k ikl kl

C u e E

D E e u

Qasistatic approximation for acoustic waves

2 2

2i ik

k

u

t x

0, 0D E

Constitutive relations:

piezoelectric constants

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Mode conversion in reflection/transmission

• 10 boundary conditions (6 mechanical + 4 electromagnetic) determine the amplitudes of 5 transmitted and 5 reflected waves

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Acoustic – EM mode conversion

acoustic

EM

acoustic

EM

‘Total internal reflection’ angle ~v/c~10-4

Typical picosecond acoustic case:/a~10 nm/100 m~10-4

Outgoing acoustic wavevector always almost normal to the boundary

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Mode conversion: perturbative approach

Acoustic → EM• Solve acoustic reflection/transmission problem using

quasistatic approximation• Input polarization generated by acoustic waves as a

source term in Maxwell’s equations

EM → acoustic• Solve reflection/transmission using Fresnel equations.• Input piezoelectric stress generated by EM fields as a

source term in the equations of elasticity.

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Mode conversion beyond perturbative approach: Brewster angles (100% transformation)?

Acoustic reflection

angle of incidence

acoustic-EMconversion

EMEM

acoustic

yx

Hexagonal crystal class 6

M. K Balakirev, I.A. Gilinsky, Waves in piezoelectric crystals. (Novosibirsk: Nauka, 1982).

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Example: z-cut LiNbO3 normal incidence

x

ze15=3.8 C/m2 connects Ex and shear stress σxz

incident acoustic/EM

reflected acoustic/EM

transmitted EM

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z-cut LiNbO3 : EM → shear acoustic

x

ze15=3.8 C/m2 connects Ex and shear stress σxz

incident EM

reflected acoustic

transmitted EM

σxz=2e15 Ex , uxz=2e15 Ex/C44

Conversion efficiency: 2 2

444 152

0 0 44

4 10ac xz

EM x

P vC u ev

P c E c C

For E=100 kV/cm: σxz=7.6x107

,Pa, uxz=1.3x10-3

K2=0.5

Stress and strain in the reflected shear wave:

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reflected EM

incident acoustic

z-cut LiNbO3 : shear acoustic → EM

x

ze15=3.8 C/m2 connects Ex and shear stress σxz

transmitted EM

Ex =, 2(v/c)e15 uxz/0

Conversion efficiency: 2 2

40 152

44 0 44

4 10xEM

ac xz

c E eP v

P vC u c C

For uxz~10-3 :Ex ~15 V/cm

K2=0.5

Field in the reflected EM wave:

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Estimates for the experiment by Armstrong et al.

laser

GaN: hexagonal 6mme33=2.5 C/m2 connects Ez with longitudinal strain uzz

dipole source

From: Reed and Armstrong, PRL 101, 014302 (2008)

Estimated field for 10-3 strain in Al (4 times smaller in GaN): E~6 V/cm (near-field)However:• Detection in the far-field (6 mm away)• Transmission through interfaces• External angle of 450 corresponds to ~130 internally,dipole radiation inefficient• Source near the metal surface!

Detection at 450

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EM-acoustic coupling in a superlattice

wavevector

frequ

ency

/d

EM

acoustic

EM

acousticsymmetric

acousticantisymmetric

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Resonant EM-acoustic transformation

Conversion Efficiency ~ MN

N periods

M periods

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Discussion

Experiment• Start with EM- acoustic or acoustic-EM?

– reproduce Armstrong & Reed’s experiment?• Materials

– LiNbO3 : high piezoelectric constants; can excite/detect THz right there?

– GaN and similar: good interfaces, superlattices should help increase the signal

– SRO/PZT ?

Theory• Basic theory capable of accurate calculations for realistic cases.• Theory for superlattices• Brewster angles?