Soliton (optics)

In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and linear effects in the medium. There are two main kinds of solitons:

In order to understand how a spatial soliton can exist, we have to make some considerations about a simple convex lens. As shown in the picture on the right, an optical field approaches the lens and then it is focused. The effect of the lens is to introduce a non-uniform phase change that causes focusing. This phase change is a function of the space and can be represented with ${\displaystyle \varphi (x)}$, whose shape is approximately represented in the picture.

The phase change can be expressed as the product of the phase constant and the width of the path the field has covered. We can write it as:

where ${\displaystyle L(x)}$ is the width of the lens, changing in each point with a shape that is the same of ${\displaystyle \varphi (x)}$ because ${\displaystyle k_{0}}$ and n are constants. In other words, in order to get a focusing effect we just have to introduce a phase change of such a shape, but we are not obliged to change the width. If we leave the width L fixed in each point, but we change the value of the refractive index ${\displaystyle n(x)}$ we will get exactly the same effect, but with a completely different approach.

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