We study the problem of paraxial propagation in two grade-index media by using invariant techniques that allow a continuous solution of the problem. By using the well-known fact that this problem is analogous to the time-dependent harmonic oscillator in quantum mechanics, known methods there may be imported producing on the one hand a solution to the propagation problem and on the other hand a realization of a quantum-mechanical invariant.
© 2009 Optical Society of America
Original Manuscript: December 19, 2008
Manuscript Accepted: March 17, 2009
Published: April 30, 2009
H. Moya-Cessa, M. Fernández Guasti, V. M. Arrizon, and S. Chávez-Cerda, "Optical realization of quantum-mechanical invariants," Opt. Lett. 34, 1459-1461 (2009)