Eigenchannel analysis of super-resolution far-field sensing with a randomly scattering analyzer

Abstract

A method of analysis for a randomly scattering analyzer offering far-subwavelength spatial resolution with coherent light is presented, and the attributes are supported by numerical simulations. Without constraints, far-field detection generally results in a spatial resolution of about one wavelength, mathematically explained through the loss of the evanescent field information in a plane-wave expansion. Enhanced spatial resolution is shown to be possible because of relative motion with a structured field and the resulting information available. It is shown that detected information through a scattering analyzer results in enhanced spatial sensitivity with motion of an object in a structured field, and that this is accompanied by changes in the relative distribution of significant eigenvalues of the transmission matrix modeling the analyzer. Thus, the character of the random analyzer is shown to influence the far-field spatial resolution. A random analyzer, in principle, allows subwavelength sensitivity whose resolution is limited only by measurement accuracy and precision, when fields are scattered from a moving object or when some other relative change causes a modified field. Consequently, use of a random analyzer offers substantial impact in a variety of applications.