Hi Sakshi,

**Sakshi wrote:**
I was expecting both LP modes and LG modes to have circular geometries and similar profiles.

That is where your problem is. You forgot that modes can be degenerate.

In a nutshell, if a mode is not degenerate, it sure will share the same symmetry as the system. But when you have a group of degenerate modes, the group should share the symmetry but not the modes individually. In the case of a multimode fiber, you could easily check that if you rotate by any arbitrary angle the modes in a given subspace (i.e. corresponding to the same propagation constant), they are still a basis of your subspace. However, each LP mode associated with a degenerate propagation constant is not circularly symmetric.

For instance, the two LP11 modes oriented horizontally and vertically are orthogonal modes with the same propagation constant. The same profiles oriented at + and -45 degrees are too.

If you play with the phase, you can find linear combinations of degenerate modes that look totally different from the ones you started with.

In the case of graded index fiber, it is interesting to notice that the size of the groups of degenerate modes increases when the propagation constant decreases. So that you can find more combination of modes.

I am not familiar with the LG modes for MMF, but it seems that they are a mode basis for graded index fiber but not for step index fibers.

To check if both representations are similar, simply project each LG modes on all the LP modes. If everything is right, for each LG mode, the only non-zero values should correspond to LP modes with the same propagation constant. This would show that the two representations are good.

Best,

Sebastien