Nonlinear Photoelasticity to Explicate Acoustic Phonon Phase under Anharmonic and Extrinsic Decay

By measuring the continuously varying phase of optically detected acoustic (AC) wavepackets in degenerate pump-probe schemes as functions of compositional strain profiles and time, the previously concealed nonlinear interrelation between the refractive index changes and phonon-induced strain was found. The compositional strain of AC wavepackets was manipulated representatively in nanoscale InGaN-based piezoelectric diodes by combining a vertical electrical field and spatially selective excitations. The corresponding mathematical formulations of differential reflectivity were extended to incorporate both the conventionally used linear photoelastic (PE) regime where the amplitude of dynamic Fabry-Perot interference matches with the Fourier component at the same Brillouin frequency and the nonlinear PE regime where the whole Fourier components of AC spectrum should be additionally involved. From the time-dependent phase analysis, the abrupt phase shift at the point of AC surface reflection and gradual phase changes during phonon propagation in defect-abundant electron reservoir are both explicated in terms of the frequency-dependent AC decay only measurable in nonlinear PE regime which is further distinguished from velocity modulation due to phonon-electron interaction seen in both regimes.