Analysis of symmetrical waveguide junctions

Previous theory of consequences of sy mmetry in waveguide junctions has made limi ted use of mat hemat ical t ool s a vailable in t he t heory of group representa tions and has been limi ted t o t he considerat ion of nondi ssipat ive junction s. In t his paper group-t heoretical technique is u t ilized more full y (in mu ch t he same way as in t he analysis of t he ,vibrat ion of symmetrical molecules) in t he formula tion of an improved and general techl1lque for t he ana lysis of symmetrical waveguide junctions subject merely t o t he requirement of linearity. A waveg uide junction, for t he purpose of t his pa per, is a linear electromagnetic syste m possessing ideal waveguide leads, and is considered t o be subject to excitation solely through t he effects of nonattenuated modes in t he waveguide leads. Under t he condi tions of the problem, an arbi t ra ry elect ri c (or magnetic) . fi eld in a waveg uide junction is expressible linearly in terms of a fini te number of linearly Indepcndent electn c (or magnetic) baSIS fi e lds. F rom a ny given ordered pair of e lectric (or magnetic) basis fi e ld s one can in principle calculate a com plex llumber-an element of t he admittance (o r impeda nce) matr.ix characteri zing t he junction (relative to t he choice of basis fields) . The geometri c co ncep t of rotation and refl ection of fi elds (and stru ctures) is d isc ussed in te rms of a rotationreflection operato r, a nd the sy mmetry of a junction is characterized by a g roup of r?tation-refl ect ion operat io ns un de r whi ch the stru cture is invaria nt. A general procedure is given for the constru ctIOn o f a b aSIS in whi ch t he basis fi elds t ransform accordin g to irredu cible representations of t he symmet ry group involved. Such basis fi elds a re said to be of par ticula r symmetry species and from t he special propert ies of s lI ch fi eld s foll ow th e physical res ults , of whi ch p.crl.laps t he most conspi cuous is t he va nishing of t he matri x element between t wo fi eld s of distin ct sy mmetry species.