  An electron beam entering an accelerating cavity excites a wakefield. This
wakefield can be decomposed into a series of multi-poles or modes. The dominant
component of the transverse wakefield is dipole. This report summarizes the
higher order mode (HOM) signals of the third harmonic cavities of FLASH
measured at various stages: transmission measurements in the single cavity test
stand at Fermilab, at CMTB (Cryo-Module Test Bench) and at FLASH, and
beam-excited measurements at FLASH. Modes in the first two dipole bands and the
fifth dipole band have been identified using a global Lorentzian fit technique.
The beam-pipe modes at approximately 4 GHz and some modes in the fifth dipole
band have been observed as localized modes, while the first two dipole bands,
containing some strong coupling cavity modes, propagate. This report also
presents the dependence of the localized dipole modes on the transverse beam
position. Linear dependence for various modes has been observed. This makes
them suitable for beam position diagnostics. These modes, together with some
propagating, strong coupling modes, have been considered in the design of a
dedicated electronics for beam diagnostics with HOMs for the third harmonic
cavities.
