1：Experimental Design and Method Selection:

The study involves the theoretical calculation of the photoacoustic effect for a single chromophore absorbing two laser beams modulated at two different frequencies and corresponding experiments with carbon particles of different sizes.

2：Sample Selection and Data Sources:

Carbon powders dispersed in agarose gel were used as samples to avoid precipitation of particulates during measurements.

3：List of Experimental Equipment and Materials:

Two laser beams (532 nm and 488 nm), acousto-optic modulator, electro-optic modulator, function generators, photoacoustic cell made from a cylindrical PZT cylinder, high input impedance preamplifier, lock-in amplifier, rf mixer, and low pass filter.

4：Experimental Procedures and Operational Workflow:

The two laser beams were amplitude modulated, combined to be colinear, and directed into the photoacoustic cell. The modulation frequencies were changed simultaneously to measure the photoacoustic amplitude as a function of frequency.

5：Data Analysis Methods:

The photoacoustic signal was analyzed using a lock-in amplifier set at a time constant of 300 ms and a slope of 12 dB/octave.