Note: In an optical fiber, a radiation mode is one having fields that are transversely oscillatory everywhere external to the waveguide, and which exists even at the limit of zero wavelength. Specifically, a radiation mode is one for which where β is the imaginary part (phase term) of the axial propagation constant, integer l is the azimuthal index of the mode, n (a ) is the refractive index, where a is the core radius, and k is the free-space wave number, k = 2π/λ, where λ is the wavelength. Radiation modes correspond to refracted rays in the terminology of geometric optics. Synonym unbound mode.
Source: from Federal Standard 1037C and from MIL-STD-188