Phase synchronization in a two-mode solid state laser: Periodic modulations with the second relaxation oscillation frequency of the laser output

•We study the intrinsic phase synchronization in a periodically pump-modulated two-mode solid state laser.•The empirical mode decomposition method is utilized to define the intrinsic phase synchronization.•The degree of phase synchronization is quantified by a proposed synchronization coefficient.

Phase synchronization (PS) in a periodically pump-modulated two-mode solid state laser is investigated. Although PS in the laser system has been demonstrated in response to a periodic modulation with the main relaxation oscillation (RO) frequency of the free-running laser, little is known about the case of modulation with minor RO frequencies. In this Letter, the empirical mode decomposition (EMD) method is utilized to decompose the laser time series into a set of orthogonal modes and to examine the intrinsic PS near the frequency of the second RO. The degree of PS is quantified by means of a histogram of phase differences and the analysis of Shannon entropy.