1：Experimental Design and Method Selection:

The study involved the preparation of three different kinds of nanoparticles (bare Au and Ag NPs, Au@Ag and Ag@Au core/shell NPs, and the mixture of Au and Ag NPs) in dye medium as a gain of the random laser. Samples were prepared by Laser Ablation in Liquid (LAL) method using the first harmonic of Q-switched Nd:YAG laser.

2：Sample Selection and Data Sources:

The samples were prepared at fixed energy and variable repetition rate and at fixed repetition rate of 10 Hz and variable energy from 9 mJ to 50 mJ.

3：List of Experimental Equipment and Materials:

The experimental setup included a Q-switched Nd:YAG laser, deionized water, Au and Ag metal targets, RhB and Rh6G dyes dissolved in methanol, and an ultrasonic bath.

4：Experimental Procedures and Operational Workflow:

The reflected light was focused on a rotated Au and Ag metal target in deionized water. For preparing bimetallic Au@Ag and Ag@Au core-shell NPs, a sequential two-step ablation method was used. Fabricated samples were stirred at room temperature in an ultrasonic bath for about 20 min, and mixed with different concentrations of Rh6G and RhB dye.

5：Data Analysis Methods:

The field emission scanning electron microscope (FE-SEM) was used to determine the size and shape of the produced NPs. UV–VIS absorption spectra of the samples were recorded to obtain the SPR response. The lasing was collected by an Avantes spectrometer.