Bohm approach to the Gouy phase shift

Héctor M. Moya-Cessa, Sergio A. Hojman, Felipe A. Asenjo, Francisco Soto-Eguibar

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number168468
StatePublished - Feb 2022
Externally publishedYes


  • Bohm potential
  • Gouy phase
  • Lewis–Ermakov invariant


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