Transverse Coupling in Fiber Optics Part II: Coupling to Mode Sinks

An expression for the coupling between lossy single-mode open waveguides was derived in Part I. 1 We now investigate the coupling of a waveguide with finite cross section with a waveguide with infinite cross section (called a substrate), the latter supporting radiation modes. Radiation losses are suffered whenever the propagation constant h of the guided mode is smaller than the highest propagation constant h, of the radiation modes carried by the substrate. Radiation then takes place at the Cerenkov angle 6 = cos - 1 (h/h,). By properly choosing the dimensions and permittivities of the waveguide and those of the 675 substrate, it is possible to reduce the number of modes that can propagate without attenuation (in the absence of dissipation and scattering losses). This arrangement is of great practical importance because optical fibers are usually highly overmoded to facilitate fabrication and splicing. 2 (For a coherent source, it is important to reduce the number of modes because different modes usually have different group velocities. If a short optical pulse is sent through the fiber, mode conversion takes place because of the imperfections of the fiber; this causes the pulse to spread in time.) The mode selection mechanism just described is also of practical importance in the microwave range for oversized waveguides such as oversized microstrips on dielectric substrates and oversized dielectric strips.* Multimoding in traveling wave tubes can also be avoided with the help of mode sinks.