Second harmonic generation of shear waves in crystals

Area of Science:

• Solid-state physics
• Nonlinear acoustics
• Materials science

Background:

• Nonlinear wave propagation is crucial for understanding material properties.
• Second harmonic generation (SHG) is a key phenomenon in nonlinear acoustics.
• Previous studies focused on longitudinal waves, leaving shear wave behavior less explored.

Purpose of the Study:

• To investigate the nonlinear self-interaction of shear waves in electro-elastic crystals.
• To analyze the distinct characteristics of shear wave second harmonic generation (SHG) compared to longitudinal waves.
• To establish SHG of shear waves as a method for determining third-order elastic constants.

Main Methods:

• Theoretical analysis using a rotationally invariant state function.
• Calculations for cubic, hexagonal, and trigonal crystal symmetries.
• Consideration of electromechanical coupling nonlinearity for specific crystal symmetries (6 mm and 3 m).

Main Results:

• Shear wave SHG is restricted to specific propagation directions.
• Geometrical nonlinearity from finite strain does not contribute to shear wave SHG.
• The nonlinear parameter for shear waves is anisotropic and crystal-symmetry dependent, unlike longitudinal waves.
• Electromechanical coupling nonlinearity was considered for 6 mm and 3 m crystals.

Conclusions:

• Nonlinear self-interaction of shear waves exhibits unique behaviors distinct from longitudinal waves.
• SHG of shear waves offers a complementary method to SHG of longitudinal waves for elastic constant determination.
• The study successfully applied the method to determine a third-order elastic constant (c444) in Z-cut lithium niobate (LiNbO3).