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

2. 2 Piezoelectric effect Pierre and Jacques Curie, 1880

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

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

5. 5 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 mm T=4K Superconducting bolometer

6. 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. 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. 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. 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. 10 piezoelectric constants Coupled fields in piezoelectrics Newton’s 2 nd law Maxwell’s equations Constitutive relations: stress displacement

11. 11 Effect on EM velocities negligible: 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

12. 12 Qasistatic approximation for acoustic waves Constitutive relations: piezoelectric constants

13. 13 Mode conversion in reflection/transmission 10 boundary conditions (6 mechanical + 4 electromagnetic) determine the amplitudes of 5 transmitted and 5 reflected waves

14. 14 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

15. 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. 16 Mode conversion beyond perturbative approach: Brewster angles (100% transformation)? Acoustic reflection angle of incidence acoustic-EM conversion EM acoustic y x Hexagonal crystal class 6 M. K Balakirev, I.A. Gilinsky, Waves in piezoelectric crystals. (Novosibirsk: Nauka, 1982).

17. 17 Example: z-cut LiNbO 3 normal incidence x z e 15 =3.8 C/m 2 connects E x and shear stress σ xz incident acoustic/EM reflected acoustic/EM transmitted EM

18. 18 z-cut LiNbO 3 : EM → shear acoustic x z e 15 =3.8 C/m 2 connects E x and shear stress σ xz incident EM reflected acoustic transmitted EM σ xz =2e 15 E x, u xz =2e 15 E x /C 44 Conversion efficiency: For E=100 kV/cm: σ xz =7.6x10 7, Pa, u xz =1.3x10 -3 K 2 =0.5 Stress and strain in the reflected shear wave:

19. 19 reflected EM incident acoustic z-cut LiNbO 3 : shear acoustic → EM x z e 15 =3.8 C/m 2 connects E x and shear stress σ xz transmitted EM E x =, 2(v/c)e 15 u xz /  0 Conversion efficiency: For u xz ~10 -3 : E x ~15 V/cm K 2 =0.5 Field in the reflected EM wave:

20. 20 Estimates for the experiment by Armstrong et al. laser GaN: hexagonal 6mm e 33 =2.5 C/m 2 connects E z with longitudinal strain u zz 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 45 0 corresponds to ~13 0 internally, dipole radiation inefficient Source near the metal surface! Detection at 45 0

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

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

23. 23 Discussion Experiment Start with EM- acoustic or acoustic-EM? –reproduce Armstrong & Reed’s experiment? Materials –LiNbO 3 : 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?