# How is it that having a laser cavity geometry with one flat mirror and one curved mirror produces a more divergent beam?

I recently asked this question about the non-axial photons of a laser cavity. While doing further research on the subject, I read that exploiting the paraxial photons by having one mirror of the laser cavity be flat and the other be curved enhances stimulated emission. An example of this seems to be the "hemispherical" cavity geometry in the figure in user A. P. answer:

However, it is also said that this produces a (more) divergent beam.

How is it that such cavity geometries produce a more divergent beam, compared to if we had just two flat mirrors? For instance, if the flat mirror in the image above is less than 100% reflective, and so is the mirror from which the beam escapes the cavity, should it not actually be focused at a smaller point (that is, result in a less divergent beam), rather than a larger point (that is, result in a more divergent beam)? Or is it because, beyond some point, the two rays in the image above "cross over" (I think this is point is called the focal point?), and so the beam actually begins to diverge beyond this point?

Two flat regular mirrors do not form a cavity. Diffraction will always cause enough light to escape to make the setup useless.

In order for two flat mirrors to form a cavity they must be of infinite size so that light cannot escape. And the light in the cavity must be a plane wave (zero divergence).

Aha. You have one or two misunderstandings. Note that the orange lines are not straight. They are curved near the flat mirror. So what does that mean? What do the orange mirrors represent? The orange lines are perpendicular to the phase front. At the flat mirror the phase front is planar, and the orange lines are perpendicular to the plane of the mirror. If that mirror were partially silvered, the light that gets through would diverge in exactly the same way that it converges inside the cavity.

The field distribution in the cavity is not so simple. It is what's called a Gaussian beam. The profile of a Gaussian beam is displayed in this S.E. post. To make a cavity with a plane mirror the mirror must live where the phase front is planar, the narrow part of the beam, which is called the waist.

For a cavity to be made of two plane mirrors, the phase fronts must be planar everywhere, that is the wave must be a plane wave. A plane wave has zero divergence. It also has infinite cross-section, so the mirrors must be infinite.

Note that a Gaussian beam also has infinite cross-section. However, the field intensity drops off quickly away from the center so that very little light appears at the edge of the mirror. Very little is not zero, so there is always some loss from the cavity.

• Thanks for the answer. But does this answer my question of how such cavity geometries produce a more divergent beam? Mar 29, 2021 at 11:08
• Look at your diagram. The the orange lines diverge. Imagine the same diagram for plane mirrors. The equivalent lines in that case would be parallel. Mar 29, 2021 at 11:10
• But they only diverge out of the cavity if the curved mirror is the non-100%-reflective one, right? See the bottom of my post. Mar 29, 2021 at 11:11
• I've amended my answer to address this. Mar 29, 2021 at 11:27
• Ahh, the lines looked straight to me, but now that I look closer I can see how they might be subtly curved. Indeed, this concept of the "Gaussian beam" might be why I was confused. So what you're saying is that, if the beam emerged from the flat mirror, then it would look like / emerge as the right side of the Gaussian beam in this physics.stackexchange.com/q/189160/141502 question? Mar 29, 2021 at 11:47