Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards

Structured transverse modes governed by maximum entropy principle

Based on the birefringent effect of the gain medium, a diode-pumped Nd-doped vanadate laser with nearly hemispherical cavity is exploited to emulate the quantum Green functions of two-dimensional commensurate harmonic oscillators. By matching the theoretical calculations to the far-field patterns of lasing modes, the resonant transverse frequencies can be accurately determined up to extremely high orders. The Shannon entropy is further employed to calculate the spatial entanglement of the quantum Green function as a function the transverse frequency. From the resonant transverse frequencies, all lasing modes are confirmed to be in excellent agreement with the maximum entropy states. This discovery implies that the formation of lasing modes is relevant to the coupling interaction between the pump source and the laser cavity.

High-power structured laser modes: manifestation of quantum Green's function

The distributions of resonant frequencies in an astigmatic cavity are theoretically confirmed to be analogously equivalent to the quantum energy structures of two-dimensional commensurate harmonic oscillators. In the first part [Opt. Lett.45, 4096 (2020)OPLEDP0146-959210.1364/OL.399251] of this two-part series study, the lasing modes were verified to reveal a variety of vortex array structures. Here, in the second part of this two-part series study, the lasing modes are confirmed to agree very well with the quantum Green's functions that correspond to a bundle of Lissajous figures in the high-order regime.