Acoustic ↔ Electromagnetic Conversion in THz Range

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

2. Piezoelectric effect • Pierre and Jacques Curie, 1880

3. Piezoelectric transducer ~V Thin film resonator - up to 20 GHz

4. EM-acoustic conversion at the free surface Microwave ultrasonics circa 1966, up to 114 GHz!

5. Generation of THz coherent phonons by free-space THz radiation far-IR laser Superconducting bolometer • 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 quartz sample 10x10 mm T=4K

6. 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

7. Conversion of picosecond acoustic pulses into THz radiation • M.R. Armstrong, E.J. Reed et al., 2009 laser 0.7 mJ, 1 mm diam 1 kHz rep rate 800 nm pump/ 800 nm probe

8. 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 ?

9. 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!

10. Coupled fields in piezoelectrics displacement stress Newton’s 2nd law Maxwell’s equations Constitutive relations: piezoelectric constants

11. Coupled fields in piezoelectrics • 5 plane wave solutions: 3 slow (acoustic), 2 fast (EM). • Effect on acoustic velocities Electomechanical coupling coefficient ~0.5 in LiNbO3, ~10-3 in GaAs • Effect on EM velocities negligible:

12. Qasistatic approximation for acoustic waves 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

14. Acoustic – EM mode conversion EM EM acoustic acoustic Outgoing acoustic wavevector always almost normal to the boundary ‘Total internal reflection’ angle ~v/c~10-4 Typical picosecond acoustic case: l/a~10 nm/100 mm~10-4

15. 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.

16. Mode conversion beyond perturbative approach: Brewster angles (100% transformation)? Acoustic reflection Hexagonal crystal class 6 y EM EM x acoustic-EM conversion acoustic angle of incidence M. K Balakirev, I.A. Gilinsky, Waves in piezoelectric crystals. (Novosibirsk: Nauka, 1982).

17. Example: z-cut LiNbO3 normal incidence x e15=3.8 C/m2 connects Ex and shear stress σxz z transmitted EM incident acoustic/EM reflected acoustic/EM

18. z-cut LiNbO3 : EM → shear acoustic x e15=3.8 C/m2 connects Ex and shear stress σxz z transmitted EM incident EM reflected acoustic Stress and strain in the reflected shear wave: σxz=2e15 Ex , uxz=2e15 Ex/C44 Conversion efficiency: K2=0.5 For E=100 kV/cm: σxz=7.6x107,Pa,uxz=1.3x10-3

19. z-cut LiNbO3 : shear acoustic → EM x e15=3.8 C/m2 connects Ex and shear stress σxz z incident acoustic transmitted EM reflected EM Field in the reflected EM wave: Ex =, 2(v/c)e15 uxz/ee0 Conversion efficiency: K2=0.5 For uxz~10-3 : Ex ~15 V/cm

20. Estimates for the experiment by Armstrong et al. laser Detection at 450 dipole source GaN: hexagonal 6mm e33=2.5 C/m2 connects Ez with longitudinal strain uzz • 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! From: Reed and Armstrong, PRL 101, 014302 (2008)

21. EM-acoustic coupling in a superlattice EM EM acoustic antisymmetric acoustic symmetric frequency acoustic p/d wavevector

22. Resonant EM-acoustic transformation N periods M periods Conversion Efficiency ~ MN

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?