Three dimensional (3D) optical information processing

Abstract

Light exhibits dramatically different properties when it propagates in or interacts with 3D structured media. Comparing to 2D optical elements where the light interacts with a sequence of surfaces separated by free space, 3D optical elements provides more degrees of freedom to perform imaging and optical information processing functions. With sufficient dielectric contrast, a periodically structured medium may be capable of forbidding propagation of light in certain frequency range, called band gap; the medium is then called a photonic crystal. Various "defects", i.e. deviations from perfect periodicity, in photonic crystals are designed and widely used as waveguides and microcavities in integrated optical circuits without appreciable loss. However, many of the proposed waveguide structures suffer from large group velocity dispersion (GVD) and exhibit relatively small guiding bandwidth because of the distributed Bragg reflection (DBR) along the guiding direction. As optical communications and optical computing progress, more challenging demands have also been proposed, such as tunable guiding bandwidth, dramatically slowing down group velocity and active control of group velocity. We propose and analyze shear discontinuities as a new type of defect in photonic crystals.

(cont.) We demonstrate that this defect can support guided modes with very low GVD and maximum guiding 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, and the mode gap can be tuned by changing the amount of the shear shift. This property can be used to design photonic crystal waveguides with tunable guiding bandwidth and group velocity, and induce bound states. The necessary condition for the existence of guiding modes is discussed. By changing the shape of circular rods at the shear interface, we further optimize our sheared photonic crystals to achieve minimum GVD. Based on a coupled resonator optical waveguide (CROW) with a mechanically adjustable shear discontinuity, we also design a tunable slow light device to realize active control of the group velocity of light. Tuning ranges from arbitrarily small group velocity to approximately the value of group velocity in the bulk material with the same average refractive index. The properties of eigenstates of tunable CROWs: symmetry and field distribution, and the dependence of the group velocity on the shear shift are also investigated.

(cont.) Using the finite-difference time-domain (FDTD) simulation, we demonstrate the process of tuning group velocity of light in CROWs by only changing the shear shift. A weakly modulated 3D medium diffracts light in the Bragg regime (in contrast to Raman-Nath regime for 2D optical elements), called volume hologram. Because of Bragg selectivity, volume holograms have been widely used in data storage and 3D imaging. In data storage, the limited diffraction efficiency will affect the signal-noise-ratio (SNR), thus the memory capacity of volume holograms. Resonant holography can enhance the diffraction efficiency from a volume hologram by enclosing it in a Fabry-Perot cavity with the light multiple passes through the volume hologram. We analyze crosstalk in resonant holographic memories and derive the conditions where resonance improves storage quality. We also carry out the analysis for both plane wave and apodized Gaussian reference beams. By utilizing Hermite Gaussian references (higher order modes of Gaussian beams), a new holographic multiplexing method is proposed - mode multiplexing.

(cont.) We derive and analyze the diffraction pattern from mode multiplexing with Hermite Gaussian references, and predict its capability to eliminate the inter-page crosstalk due to the independence of Hermite Gaussian's orthogonality on the direction of signal beam as well as decrease intra-page crosstalk to lower level through apodization. When using volume holograms for imaging, the third dimension of volume holograms provided more degrees of freedom to shape the optical response corresponding to more demanding requirements than traditional optical systems. Based on Bragg diffraction, we propose a new technique - 3D measurement of deformation using volume holography. We derive the response of a volume grating to arbitrary deformations, using a perturbative approach. This result will be interesting for two applications: (a) when a deformation is undesirable and one seeks to minimize the diffracted field's 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.

(cont.) 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 grating's response to deformation due to a point indenter and present experimental results consistent with theory.