What are EH and HE modes in corrugated horn?

I am designing a corrugated horn antenna. I read many papers.
I don't konw what is EH and HE mode in corrugate horn.
Who can tell me in detail?
Who can tell me how to get a book :
Microwave Horns and feeds. A.D.Olver etc. 1994

Thank you

EH and HE mode is the designation for wave types propagating in waveguide.

The simplest mode is TEM isn't able to propagate in waveguide.
TE or H mode and TM or E mode are the simplest wave, which can
propagate in normal hollow waveguide.
H modes have only H (magnetic field) component in propagation
direction for example H11. E modes have only E (electric field).

EH and HE modes are hybrid modes, having E and H in propagation direction.
These modes emerge due to discontinuities in waveguides, for example
through corrugationg.
Please refer to Balanis.

regards

Thank you

When we chang the number of slot in corrugate waveguid ,for example 1 or 2 slots, EH or HE could be obtain ?

Better than "Microwave Horns and feeds. A.D.Olver etc. 1994" is the "Corrugted horns for microwave antennas" - P.J.B. Clarricoats and A.D. Olver - Peter Peregrinus ltd - ISBN 0 86341 003 0

Also on IEEE website look for Articles by James, G.L. between years 1970 and 1990.

Just to add to mudrik's answer, EH Hybrid modes are looked for because, inside circular waveguide and circular horn, E field lines are very parallel each one to the other one. This help to reduce X-pol and rise the system illumination efficiency.