In single mode optical fibers, it is the fundamental mode.  There are some folks working on multiplexing different information on the different modes and so they use several of the lowest order modes.  In cylindrical metal waveguides, the TE01 is used because it is polarized tangential to the interfaces for lower loss.  The TE01 is something like the 5th order mode.

This old reference is quite descriptive of what is going on. Perhaps You can find some stuff pertinent to Your problems: http://www.dtic.mil/dtic/tr/fulltext/u2/674600.pdf

This type of wave guide is usually most useful for mm waves and up. Also the possibility for directly feeding dielectric antenna structures and such from the wave guide is interesting. Combinations with quasi optical lens and reflector wave guides can give good results in radar, radio astronomy and other low noise receiver front ends.  

Hello,

In my knowledge...

A dielectric waveguide employs a solid dielectric rod rather than a hollow pipe. An optical fibre is a dielectric guide designed to work at optical frequencies. Transmission lines such as microstrip, coplanar waveguide, stripline or coaxial cable may also be considered to be waveguides.

Dielectric rod and slab waveguides are used to conduct radio waves, mostly at millimeter wave frequencies and above.

The mode with the lowest cutoff frequency is termed the dominant mode of the guide. It is usual to choose the size of the guide such that only this one mode can exist in the frequency band of operation. In rectangular and circular (hollow pipe) waveguides, the dominant modes are designated the TE1,0 mode and TE1,1 modes respectively.

Regards

agreed with Respected Raymond.

There is classical books, e.g., one attached