Stopband and transmission zero widening via nonuniformities in linear distributed systems

The behavior of transmission zeros and stopbands of uniform distributed linear systems is studied when nonuniformities are introduced. It is shown that transmission zeros expand into stopbands (or bandgaps) and existing stopbands are widened. The introduced nonuniformities could be intrinsic in the design of the system itself as in specially designed photonic crystals and in functionally graded materials, or extrinsic via an environmental factor, such as temperature or stress. This work presents a unified analysis based on the general properties of a linear distributed system that explains the observed appearance of stopbands and widening of existing ones in various fields, and identifies the conditions under which they occur.