TY - JOUR

T1 - Transverse oscillation in laser cavities

AU - Tsaur, Gin Yih

AU - Wang, Jyhpyng

PY - 2006

Y1 - 2006

N2 - Recent experiments on lasers with large Fresnel numbers have demonstrated a close correspondence between the transverse degrees of freedom (transverse modes) and the two-dimensional harmonic oscillator. Mode patterns that correspond to classical trajectories have been observed. These experiments suggest that such systems may serve as convenient platforms for studying quantum-classical correspondence. But why the paraxial wave equation for the laser leads to two-dimensional harmonic oscillation for the transverse degrees of freedom is yet to be clarified. We use two methods to show that such a correspondence is not a mathematical coincidence: the focusing mirror that stabilizes the laser gives rise to the transverse oscillation, and the reduced equation that governs the transverse degrees of freedom is the Schrödinger equation for the harmonic oscillator. For the fundamental Gaussian mode, the theory remains valid in the weakly nonlinear limit.

AB - Recent experiments on lasers with large Fresnel numbers have demonstrated a close correspondence between the transverse degrees of freedom (transverse modes) and the two-dimensional harmonic oscillator. Mode patterns that correspond to classical trajectories have been observed. These experiments suggest that such systems may serve as convenient platforms for studying quantum-classical correspondence. But why the paraxial wave equation for the laser leads to two-dimensional harmonic oscillation for the transverse degrees of freedom is yet to be clarified. We use two methods to show that such a correspondence is not a mathematical coincidence: the focusing mirror that stabilizes the laser gives rise to the transverse oscillation, and the reduced equation that governs the transverse degrees of freedom is the Schrödinger equation for the harmonic oscillator. For the fundamental Gaussian mode, the theory remains valid in the weakly nonlinear limit.

UR - http://www.scopus.com/inward/record.url?scp=33644692629&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.73.033804

DO - 10.1103/PhysRevA.73.033804

M3 - 期刊論文

AN - SCOPUS:33644692629

VL - 73

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 033804

ER -