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Here we report a method for visualization of volumetric structural information of live biological samples with no exogenous contrast agents. The process is made possible through a technique that involves generation, synthesis and analysis of three-dimensional (3D) Fourier components of light diffracted by the sample. This leads to the direct recovery of quantitative cellular morphology with no iterative procedures for reduced computational complexity. Combing with the fact that the technique is easily adaptive to any imaging platform and requires minimum sample preparation, our proposed method is particularly promising for observing fast, volumetric and dynamic events previously only accessible through staining methods., Comment: 20 pages, 10 figures

Light carrying orbital angular momentum (OAM) has been shown to be of use in a disparate range of fields ranging from astronomy to optical trapping, and as a promising new dimension for multiplexing signals in optical communications and data storage. A challenge to many of these applications is a reliable and dynamic method that sorts incident OAM states without altering them. Here we report a wavelength-independent technique capable of dynamically filtering individual OAM states based on the resonant transmission of a tunable optical cavity. The cavity length is piezo-controlled to facilitate dynamic reconfiguration, and the sorting process leaves both the transmitted and reflected signals in their original states for subsequent processing. As a result, we also show that a reconfigurable sorting network can be constructed by cascading such optical resonators to handle multiple OAM states simultaneously. This approach to sorting OAM states is amenable to integration into optical communication networks and has implications in quantum optics, astronomy, optical data storage and optical trapping.

The ability to tailor a coherent surface plasmon polariton (SPP) field is an important step towards a number of new opportunities for a broad range of nanophotonic applications such as sensing [1,2], nano-circuitry [3,4], optical data storage [5,6], super-resolution imaging [7,8], plasmonic tweezers [9,10] and in-plane communications [11]. Scanning a converging SPP spot or designing SPP profiles using an ensemble of spots have both been demonstrated previously [12-14]. SPPs, however, are normally excited by intense, coherent light sources-lasers. Hence, interference between adjacent spots is inevitable and will affect the overall SPP field distributions. Here we report a reconfigurable and wavelength-independent platform for generating a tailored 2D SPP field distribution by considering the coherent field as a whole rather than individual spots. The new perspective also enables us to reveal the inherent constraints implied in a 2D coherent field distribution. Our generic design methodology works not only for SPP waves but also for other two-dimensional wave systems like surface acoustic waves [15].

Metasurfaces are promising two-dimensional metamaterials that are engineered to provide unique properties or functionalities absent in naturally occurring homogeneous surfaces. Here, we report a type of metasurface for tailored reconstruction of surface plasmon waves from light. The design is generic in a way that one can selectively generate different surface plasmon waves through simple variation of the wavelength or the polarization state of incident light. The ultra-thin metasurface demonstrated in this paper provides a versatile interface between the conventional free-space optics and a two-dimensional platform such as surface plasmonics., Comment: 7 figures, supplementary information at the end of the document

Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogenous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.