Kehan Tian

Hyper-spectral imaging with volume holographic lenses

We present a hyper-spectral imaging system with volume holographic lenses. The Bragg selectivity of the volume holographic lenses enables the system to achieve high resolution in three spatial dimensions as well as the spectral dimension.

Cross talk in resonant holographic memories.

We analyze cross talk in resonant holographic memories and derive the conditions under which resonance improves storage quality. We also carry out the analysis for both plane-wave and apodized Gaussian reference beams.

Diffraction from deformed volume holograms: perturbation theory approach

We derive the response of a volume grating to arbitrary small deformations, using a perturbative approach. This result is of interest for two applications: (a) when a deformation is undesirable and one seeks to minimize the diffracted fields sensitivity to it and (b) when the deformation itself is the quantity of interest and the diffracted field is used as a probe into the deformed volume where the hologram was originally recorded. We show that our result is consistent with previous derivations motivated by the phenomenon of shrinkage in photopolymer holographic materials. We also present the analysis of the gratings response to deformation due to a point indenter and present experimental results consistent with theory.

Coherence patterns originating from incoherent volume sources.

We derive the complex degree of coherence that originates from generalized incoherent two- and three-dimensional sources. Further, we find the locus of maximum coherence and analyze the dependence of the decay of coherence on source thickness.

Three dimensional optics for three dimensional imaging: physics, fabrication, and computation

In three-dimensional (3D) optical elements, light interacts with the element throughout its entire volume (as opposed to a discrete set of surfaces, which is done in traditional optics.) This allows for more degrees of freedom in shaping the optical response, in particular creating shift-variant responses. We have used this property in a number of ways to acquire 3D object information from both reflective and fluorescent objects under a variety of illumination conditions, including laser-line-scan, rainbow and uniform white light. The key benefits of using 3D optics are summarized as excellent resolution over long working distances, reduced or completely eliminated scanning, and simultaneous spectral imaging. Our research addresses the physics of 3D optical elements, their fabrication, and computational methods for maximal information extraction. In this paper, we first overview the properties of 3D optical elements and then we describe a fabrication and assembly method. Our approach, termed Nanostructured Origami, is appropriate for manufacturing micro-scale optical components which also include sub-wavelength optical elements and non-optical components, e.g. energy storage.

Localized propagation modes guided by shear discontinuities in photonic crystals.

We propose and analyze shear discontinuities as a new type of defect in photonic crystals. This defect can support guided modes with minimum group velocity dispersion (GVD) and maximum bandwidth, provided that the shear shift equals half the lattice constant. A mode gap emerges when the shear shift is different than half the lattice constant. The shear shift can be used to tune the bandwidth, group velocity, and group velocity dispersion (GVD) of the guided mode. The necessary condition for the existence of guided modes along the shear plane is discussed.

Volume holographic imaging

We overview the properties of volume holographic imaging properties and design framework for depth-selective and hyperspectral imaging. The Bragg selectivity and degeneracy properties of volume holograms are used for optical slicing and space-selective dispersion.

3-D Optics for Ultra Thin Cameras

In 3D optics, the optical transfer function is determined by light interaction with an entire refractive-index-modulated volume. We discuss the physics of sub-wavelength, non-periodic 3D optical elements, and their applications to ultra-thin computational imagers.

Localized guided propagation modes in photonic crystals with shear discontinuities

Shear discontinuities in photonic crystals are a new type of defect which can support guided modes. We analyze the guided mode properties, including dispersion diagrams and group velocity dispersion, dependence of the confinement on the shear shift and shear position and the coupling between two shear discontinuity wave guides.

Localized Propagation Modes in Photonic Crystals Guided by Shear Discontinuities

We proposed shear discontinuities, new defect in photonic crystals, which can support guided modes. We analyzed their transmission efficiency, dependence on the shear shift and shear position, dispersion and the coupling between two shear discontinuities.