1. Phonon focusing patterns in cubic crystals Litian Wang Østfold University College Fall 2007

2. Waves in condensed matters Crystalline Solids: –Logitudinal waves –Transverse waves (SH,SV)

3. Waves in condensed matters Crystalline Solids: –Logitudinal waves –Transverse waves (SH,SV)

4. Anisotropy –Logitudinal waves (L) –Transverse waves (FT) – Slow transverse waves –Transverse waves (ST) – Fast transverse waves

7. Phonon focusing ? ?

8. The problem a)Given elastic constants, can we determine the dimension of the patterns analytically? b)Given a focusing pattern, can we determine the elastic constants? ? ?

9. Phonon focusing patterns in cubic crystals Theoretical analysis Numerical demonstration

10. Conclusion

11. Conclusions a)Given elastic constants, can we determine the dimension of the patterns analytically? Yes, with analytical result a)Given a focusing pattern, can we determine the elastic constants? Yes, with analytical accuracy. 2 x 26.44 o 2 x 19.64 o