# What happens to the non-axial photons of a laser cavity?

When a laser cavity is pumped, the axial photons are reflected back and forth by the cavity mirrors and so contribute to stimulated emission, but the non-axial photons do not have this opportunity. What happens to these non-axial photons? Furthermore, do these non-axial photons pose a safety risk (for instance, one can naively imagine less-powerful laser beams shooting through the sides of a laser)?

• Are you familiar with the cavity stability diagram? Mar 13, 2021 at 10:34
• @A.P. I am not. Mar 13, 2021 at 10:35
• I'm pretty sure you mean non-axial de-excitation photons, not non-axial pump photons, right?
– uhoh
Mar 14, 2021 at 9:45

In short: The part of the light with small enough deviation from the optical axis is kept in the resonator, the rest leaks out, but is stopped by the housing of the laser.

### Which light is kept?

Imagine a ray being tilted with respect to the optical axis.

Because the mirrors in a laser cavity are slightly concave the ray gets deflected more towards the middle of the cavity again and therefore doesn't walk off, as it would be the case with two planar mirrors. In the particular example I've chosen, the mirrors form a confocal cavity, i.e. the radii of curvature of the mirrors $$R_1$$, $$R_2$$ are equal to the cavity length $$L$$. Here, one can geometrically show that said ray will travel in a $$8$$-shaped loop and be identical to itself after 4 reflections:

This holds for any tilt angle as long as the ray still hits the mirror. So there is a whole class of rays which map onto itself after 4 reflections, not just the axial ray. Similarly, you can imagine what happens to a ray being shifted from the optical axis. Analogously, it will also travel in a $$8$$-shaped loop, irrespective of its exact displacement. For a mathematical proof using the ray tranfer matrix method see for example Kogelnik & Li, Appl. Opt. 5 (1966).

You can also model the situation with waves. Here, the mode formed in the cavity is given by the criterion that the wavefronts of the beam must match the mirror shape, so that the beam is mapped onto itself after a full round trip.

Of course the confocal cavity is just one possible geometry out of many. Which cavities are stable is summarized in the cavity stability diagram. It describes which cavity shapes allow mapping a ray/beam onto itself in terms of geometric parameters $$g_1 = 1 - \frac{L}{R_1}$$ and $$g_2 = 1 - \frac{L}{R_2}$$.

### And the light which deviates too much from the optical axis?

Regarding the safety issues, you are right, there is also light which is not kept in the resonator, as shown in the image below. This is why lasers are typically enclosed during normal operation. For alignment one uses low power to minimize the risks.
• Nice images, and for the first time since studying photonics 10 years ago, I suddenly understand how mode-locking works Mar 13, 2021 at 18:39
• So, "What happens to the non-axial photons of a laser cavity?"
– uhoh
Mar 14, 2021 at 10:16
• @A.P. ya exactly, there is a lot of good information here, but in SE it's always good to also point to the part that specifically answers the question if there is a one-liner asking of it, and in this case there is.
– uhoh
Mar 14, 2021 at 10:40
• @uhoh You're right, thanks for the advice. I've added a summary and headings to improve the readability. Mar 14, 2021 at 11:02
• IIRC the 8 W pump beam at ~532 nm is coaxial with the ultrafast pulses at 790 nm - so most of the green light is scatter in the gain media. Mar 14, 2021 at 14:31

Some hit the side wall of the cavity and are absorbed. Some hit the side wall of the cavity and go through. Most lasers are in an enclosure, and the light is absorbed in the walls of the enclosure. You might be able to find a helium neon laser without an enclosure. The cavity will be glowing red light a neon sign. That light is a combination of the glow discharge present in the cavity and photons that have been amplified by laser action. This is called amplified spontaneous emission or ASE. And some light is almost axial such that it misses the mirror but still gets out of the cavity. This is also ASE.

For the most part the intensity of the non-laser emission is not a health issue, but I wouldn't bet on it in all circumstances. I'd be more concerned about UV emission from the glow discharge in the case of gas lasers.

@garyp's answer is excellent and this supplements it.

Answers to What is the angular distribution of stimulated emission radiation? Is it zero at 90 degrees? explain that stimulated emission photons are emitted in the same direction as the photons that stimulate the emission.

A short, tl;dr-like answer to your question is roughly: "There aren't that many (non-axial photons), but the ones that do occur go everywhere."

There is spontaneous emission; the metastable excited state can be pumped because it is long lived, but it must couple at least weakly to a photon otherwise lasing wouldn't be possible. The states can also couple to other de-excitation channels, both radiative and non-radiative; in optical crystals that lase there are phonons, defects and impurities, in liquids and solid lasing materials there are collisions, and all of these can also trigger both radiative and non-radiative de-excitation, potentially at around the wavelength of interest or others as well.

So the excited state will have a natural half-life, and as soon as it is populated there will be a slow, exponential decay in this population, and some of that will be spontaneous emission.

### What happens to the non-axial photons of a laser cavity?

The bright red glow in the glass tube containing a HeNe laser cavity tube shown below is the photons you are asking about, and the answer is that they shoot off and then get absorbed in something. But it's usually but not always a small fraction of the total amount of light produced and

For some laser types where the gain region is not long and thin like a gas laser tube but instead is closer in cross-section to length, there can be strong amplified spontaneous emission or ASE; a photon in a random direction stimulates a second excitation to emit another one in the same direct. Since the spontaneous photons are isotropic, these will be too.

Source

### Do these non-axial photons pose a safety risk?

For ordinary visible light lasers, spontaneous emission light is emitted pretty much isotropically so by the time it reaches you it's not concentrated like the primary laser beam would be.

What's a lot more dangerous is accidental reflections of the laser beam itself. It can be off of any smooth surface, it doesn't have to be a perfect mirror to get a high brightness reflected beam into your eye.

Safety requires that you use safety goggles of the correct wavelength for your laser. Particularly dangerous are invisible laser wavelengths in the infrared and ultraviolet that you can never see without special equipment. But even visible laser beams can accidentally reach your eyes. So wear the correct goggles at all times.

• Oh, I see what you mean. Ok, that makes sense. I thought it was referring to the previous part of your statement. Mar 14, 2021 at 15:15
• @ThePointer feel free to edit it further; it's late here and I'm signing off for the night. Thanks!
– uhoh
Mar 14, 2021 at 15:16