1 Acoustic ↔ Electromagnetic Conversion in THz Range Alex Maznev Nelson group meeting 04/01/2010.
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Transcript of 1 Acoustic ↔ Electromagnetic Conversion in THz Range Alex Maznev Nelson group meeting 04/01/2010.
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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
13
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
23
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?