Frequency dependence of Fresnel zone plates focus

Abstract

Fresnel zone plates (FZPs) focus waves through constructive interference of diffracted fields. They are used in multiple fields, such as optics, microwave propagation or acoustics, where refractive focusing by conventional lenses is difficult to achieve. FZPs are designed to work and focus at a design frequency. At this frequency, the behavior of the FZP is optimum and focusing at a certain focal length is achieved. In most medical applications using lenses, it is critical to have a fine and dynamic control on the lens focal length. In this work, the variation of the FZP focus parameters when working at operating frequencies different from the design frequency is analyzed, and a focal length control mechanism is proposed. It is shown that the FZP focal length shifts linearly with the operating frequency, becoming a dynamic control parameter that can be useful in many different applications. However, other focusing parameters, such as focal depth and distortion, are also affected by the operating frequency. These parameters establish a limit on the frequency span in which the operating frequency can be shifted, and therefore they restrict the range of focal lengths available with a single FZP.