# Optical waveguide modes

1. Jan 20, 2014

### nordmoon

Hi,

I am looking into some simulations of rib waveguide structures using Finite Element Method. I particularly solving modes for a 2D cross section of the optical waveguide, looking at TE and TM modes.

My questions is about modes called "degenerate" and "hybrid" modes. I haven't found any information what is a "degenerate" or "hybrid" modes are. Any one knows about this?

Can two modes interact/interfere with each other if the effective refractive indices of the mode are the same for different orders of the mode of TE and TM?

2. Jan 20, 2014

### Cthugha

Degenerate modes are different modes that have the same energy. Consider for example a rectangular waveguide or cavity. Here, the modes are usually labeled in terms of the k-vector components: $k_x=\frac{m_x \pi}{a}, k_y=\frac{m_y \pi}{a}$, where a is the side wall length and the m are integer numbers. It is easy to show that (mx,my) and (my,mx) modes are degenerate.

Hybrid modes are one of the four typical kinds of mode you encounter in a waveguide. Contrary to free space, you can have electric or magnetic field components in the direction of propagation of the mode. If you have no electric field in that direction, you have a TE mode. If you have no magnetic field in that direction, you have a TM mode. If you have neither, you have a TEM mode. If you have both an electric and a magnetic field component in the direction of propagation, you have a hybrid mode.

3. Jan 24, 2014

### Claude Bile

Modes nominally do not interact, since they are orthogonal; however in practice, perturbations in the waveguide shape means that different modes can weakly couple to one another.

Claude.