# What is an intuitive explanation of Gouy phase?

In laser resonators, higher order modes (i.e. TEM01, etc) accumulate phase faster than the fundamental TEM00 mode. This extra phase is called Gouy phase. What is an intuitive explanation of this effect?

Gouy predicted and then experimentally verified the existence of this effect long before the existence of lasers. How did he do it, and what motivated him to think about it?

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A naive explanation says that a beam after its focal point is inverted, not only in the sense of its spatial distribution but also in the sense of the direction of the electrical field vector (minus sign = adding $\pi$ to the phase). It's perfectly compatible with the fact why even beam profiles change the phase by $\pi$ and odd do not.