Exploring the formation of thermally detuned transverse patterns in a broad-area square VCSEL

The formation of thermally detuned transverse patterns of a broad-area square-aperture vertical-cavity surface-emitting laser (VCSEL) via cryogenic cooling is explored. It is found that the transverse wave vector gradually rotates from the horizontal or vertical direction to the diagonal direction of the square boundary as the transverse mode order increases. A model based on the quantum billiards with a finite potential well is developed to emulate the transition behavior of lasing modes. Combining the effective modal gain analysis with the response wave function of driven finite potential billiards, all experimental lasing patterns under different operation temperatures are well reconstructed.