A Note Concerning Optical-Waveguide Modulation Transfer Functions

A Note Concerning Optical-Waveguide Modulation Transfer Functions By. I. W. SANDBERG (Manuscript received March 9, 1978) A necessary and sufficient condition is given for the modulationtransfer-function of certain multimode optical fiber guides to be zero free in the closed right-half of the complex plane, and to be structurally stable with respect to that property. The condition is of interest, for example, in connection with the possibility of determining the phase of a modulation-transfer-function from its amplitude. I. INTRODUCTION AND PRELIMINARIES Reference 1 considers the range of validity of a Hilbert-transform approach in which the measured magnitude of the modulation-transfer-function of an optical fiber guide is used to compute the guide's impulse response.* It is argued there that a key "minimum-phase assumption" can fail to be satisfied in important cases, and a few closely related experimental and analytical results are presented. T h e purpose of this note is to report on a result along the same lines as a proposition given in Ref. 1 to the effect that, for a fiber guide that can propagate a finite number of discrete modes without mode mixing, the modulation-transfer-function (more precisely, the Laplace transform version of the modulation-transfer-function) is zero-free in the closed right half of the complex plane, and that property is structurally stable in a certain sense, if and only if a certain condition is met. T h e theorem described in Section II is concerned with a more realistic and far more interesting case in which mode mixing is not ruled out.