A new property of the complex Kummer function and its application to waveguide propagation

Abstract

It is proved numerically that if k /spl rarr/ -/spl infin/, the products |k|/spl zeta//sub k,n//sup (c)/ and |a|/spl zeta//sub k,n//sup (c)/, where /spl zeta//sub k,n//sup (c)/ is the nth positive purely imaginary zero of the complex Kummer confluent hypergeometric function /spl Phi/(a, c; x) in x(n = 1, 2, 3, ...), with a = c/2-jk (complex, with k real), c = 2Re(a) (restricted positive integer) and x = jz (positive, purely imaginary, with z real and positive), tend to the finite positive real number L(c, n), though the zeros themselves in this case become infinitesimal. Applying this fact to the investigation of the azimuthally magnetized circular ferrite waveguide for normal TE/sub 01/ mode, an envelope curve is found at which the phase characteristics for negative magnetization terminate, and the condition for phaser operation of the structure is obtained. It shows that the latter exhibits phase shifting properties only in a bounded frequency band whose limits depend on its material and geometry parameters and the number L(c, n).