The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

Point-driven modern Chladni figures subject to the symmetry breaking are systematically unveiled by developing a theoretical model and making experimental confirmation in the orthotropic brass. The plates with square shape are employed in the exploration based on the property that the orientation-dependent elastic anisotropy can be controlled by cutting the sides with a rotation angle with respect to the characteristic axes of the brass. Experimental results reveal that the orientation symmetry breaking not only causes the redistribution of resonant frequencies but also induces more resonant modes. More intriguingly, the driving position in some of new resonant modes can turn into the nodal point, whereas this position is always the anti-node in the isotropic case. The theoretical model is analytically developed by including a dimensionless parameter to consider the orientation symmetry-breaking effect in a generalized way. It is numerically verified that all experimental resonant frequencies and Chladni patterns can be well reconstructed with the developed model. The good agreement between theoretical calculations and experimental observations confirms the feasibility of using the developed model to analyze the modern Chladni experiment with orientation symmetry breaking. The developed model is believed to offer a powerful tool to build important database of plate resonant modes for the applications of controlling collective motions of micro objects.

We quantitatively investigate the influence of high-order transverse modes on the self-mode locking (SML) in an optically pumped semiconductor laser (OPSL) with a nearly hemispherical cavity. A physical aperture is inserted into the cavity to manipulate the excitation of high-order transverse modes. Experimental measurements reveal that the laser is operated in a well-behaved SML state with the existence of the TEM(0,0) mode and the first high-order transverse mode. While more high-order transverse modes are excited, it is found that the pulse train is modulated by more beating frequencies of transverse modes. The temporal behavior becomes the random dynamics when too many high-order transverse modes are excited. We observe that the temporal trace exhibits an intermittent mode-locked state in the absence of high-order transverse modes.

Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz equation, whereas resonant modes should be solved from the inhomogeneous Helmholtz equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

We experimentally explore the polarization characteristics of broad-area square-shaped vertical-cavity surface emitting lasers with the cryogenic cooling to achieve a wide range of frequency detuning. At room temperature the lasing modes are subject to thermal effects and exhibit the phenomenon of polarization switching. For operating temperatures below 260 K, the transverse modes are confirmed to be mainly controlled by the lateral oxide boundary and usually do not display polarization switching. Near the maximum frequency detuning, the lasing modes are well localized on the ray trajectories and display a remarkable frequencylocking phenomenon from single-frequency to multi-frequency operation for the injected current changing from near to far above lasing threshold.