Circular Bessel field statistics and the pursuit of far-subwavelength resolution

Yulu Chen, Purdue University

Abstract

The statistical description of wave propagation in random media is important for many applications. While polarized light in systems with weakly interacting scatterers and sufficient overall scatter has zero-mean circular Gaussian statistics, the underlying assumptions break down in the Anderson localization and weakly scattering regimes. Although probability density functions for wave intensity and amplitude exist beyond Gaussian statistics, suitable statistical descriptions for the field with strong and weak random scatter were unknown. The first analytical probability density function for the field that is effective in both the Anderson localization regime and the weakly scattering regime is derived by modeling the field as a random phasor sum with a random number of contributing terms. This provides a framework for modeling wave propagation in random media, facilitating random media characterization, imaging in and through scatter, and for random laser design. The resolution of far-field imaging systems is diffraction limited. Super resolution techniques that break the diffraction limit are important in the physical, chemical, and biological sciences, and in technology. An imaging method based on object motion with structured illumination and far-field measurement data that results in far-subwavelength image information is proposed. Simulations show that this approach, with generous detector noise, will lead to the ability to distinguish image features on the nanometer scale with visible light. Along different lines, a perfect negative refractive index can act as a superlens, but realistic materials render this approach ineffective. A method to tune the lens material properties is shown to provide enhanced resolution.

Degree

Ph.D.

Advisors

Webb, Purdue University.

Subject Area

Electrical engineering|Electromagnetics|Optics

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