Multi-slicing matrix method for calculating s-polarization reflectance modulation induced by picosecond acoustic pulses for stratified media

Abstract

Ultra short pulse lasers with sub-picosecond pulse duration can generate ultrasonic acoustic pulses with wavelengths in the sub-micrometer range. The reflectance modulation induced by the acoustic pulses can be detected by a probe laser. Once a method of calculating the acoustic pulse propagation and the reflectance modulation is established, it will be possible to extract information about the internal structures of a medium from measurements of the time-sequential reflectance modulation by fitting the calculations to experimental results. Thus, a multi-slicing matrix method of calculating the reflectance modulation with an arbitrary incident angle of the probe laser for s-polarization is proposed here. The method based on the Abeles transfer matrix method applicable to stratified media is mathematically validated and is shown to reproduce the analytical formula derived using the Born approximation. The method only uses matrix multiplications, which makes the calculation algorithm simple and is easy to code with matrix manipulation software. The thickness of a stratified layer of an amorphous carbon stacked on a substrate of silicon is demonstrated to be measured with the method.