Self focusing is an effect where light passing through a medium seems to focus to a point for no apparent reason. The truth is the material the wave is travelling through has a refractive index that changes based on external electric fields which the light itself is. This means that as the beam progresses the refractive index changes and curves the edges towards the centre. This can only happen when the power of the beam exceeds a certain threshold for the medium to cause the change in refractive index and quite often the medium is made up of multiple layers.
Over the past fifty years the problem of pollution and more specifically fly tipping has become a serious problem. Maybe down here but also in space. It is estimated that there are over twenty two thousand pieces of space wreckage up there. With no bacteria to break them down we have to hope these pieces eventually fall and are incinerated on attraction but this takes a long time. Using a ground based laser to clear this debris is a suggested solution. The problem being that a laser of such power exceeds the self focusing threshold of the atmosphere by many multiples. This is actually a negative as any laser sent up, intended to hit like a shell, would instead strike like a needle in its new focused state.
In order to sort this out the beam will have to be defocused first so the atmosphere refocuses it to the required intensity. To this end a study has been published describing the mathematics the precise mathematics behind such an idea and it seems to be plausible. Using what’s known as a Thin Window model (imagining the atmosphere to be much thinner and ignoring the more diffuse parts) results have been generated that seem to match experimental evidence. With problems such as space pollution growing all the time it is reassuring to know that there is always someone thinking up a solution somewhere in the world.