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Moya-Cessa, H. M., Hojman, S. A., Asenjo, F. A., & Soto-Eguibar, F. (2022). Bohm approach to the Gouy phase shift. Optik, 252, 168468.
Abstract: By adapting the Madelung-Bohm formalism to paraxial wave propagation we show, by using Ermakov-Lewis techniques, that the Gouy phase is related to the form of the phase chosen in order to produce a Gaussian function as a propagated field. For this, we introduce a quantum mechanical invariant, that it is explicitly time dependent. We finally show that the effective Bohm index of refraction generates a GRIN medium that produces the focusing needed for the Gouy phase.