Equivalence between focussed paraxial beams and the quantum harmonic oscillator

Details Equivalence between focussed paraxial beams and the quantum harmonic oscillator Equivalence between focussed paraxial beams and the quantum harmonic oscillator

2003-12-18

arxiv.org/abs/physics/0312116v2

Am. J. Phys. 73, 625 (2005)

Physics

Optics

5 pages revtex, 11 figures

Scientific paper

10.1119/1.1900099

The paraxial approximation to the scalar Helmholtz equation is shown to be equivalent to the Schr\"odinger equation for a quantum harmonic oscillator. This equivalence maps the Gouy-phase of classical wave optics onto the time coordinate of the quantum harmonic oscillator and also helps us understand the qualitative behavior of the field and intensity distributions of focused optical beams in terms of the amplitude and probability distributions of quantum harmonic oscillators and vice versa.

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