Surface Green's function of a piezoelectric half-space.

Area of Science:

• Solid State Physics
• Acoustics
• Materials Science

Background:

• Piezoelectric materials are crucial for wave propagation applications.
• Accurate computation of Green's functions is essential for modeling wave phenomena.
• Existing methods for Green's function computation in piezoelectric media have limitations.

Purpose of the Study:

• To develop a method for computing the two-dimensional harmonic spatial-domain Green's function for a piezoelectric half-space.
• To analyze the contributions of surface acoustic waves to the Green's function.
• To provide a computational framework applicable to materials like lithium niobate.

Main Methods:

• Starting with the spectral domain Green's function, singular contributions were isolated.
• Surface acoustic wave (pole) contributions were analyzed and related to Hankel functions.
• Asymptotic behaviors at infinity and the origin were explicitly addressed.
• The nonsingular part was computed numerically using fast Fourier transforms and quadrature.

Main Results:

• An anisotropic generalization of the Hankel function H0(2) was derived for surface acoustic wave contributions.
• The spatial Green's function was accurately computed, considering both singular and nonsingular parts.
• The method was successfully illustrated for a Y-cut lithium niobate substrate.

Conclusions:

• The developed method provides an accurate computation of the Green's function for piezoelectric half-spaces.
• The findings contribute to a deeper understanding of wave propagation in anisotropic piezoelectric materials.
• This work offers a valuable tool for the design and analysis of piezoelectric devices.