Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor

Chemical shift anisotropic mapping of a coherent optical absorber using magnetic field induced quantum beats

A new method for mapping the spatial structure of optical coherent materials which relies on imposing a set of linear orthogonal gradient magnetic fields for a controlled hyperfine splitting of energy levels to create characteristic quantum beats when illuminated with a laser pulse with sufficient bandwidth to excite these levels is proposed. In this approach, a spectroscopic fingerprint of the dopant sites due to concentration and field susceptibilities in the sample is achieved through a Fourier decomposition of the radiative relaxation decay in an approach analogous to nuclear magnetic resonance spectroscopy due to the imposition of a controlled spatial-spectral encoding scheme. A three pulse sequence necessary to interrogate a gradient resolved voxel is also discussed. This three pulse approach can be combined with the conventional confocal imaging technique to provide information about the underlying chemistry of dopant distribution along each imaging plane which is useful in guiding the design and manufacturing process of optical crystals. In combination with gradient induced quantum beats, the entire inhomogeneous bandwidth can be interrogated. The proposed approach would scan this entire bandwidth at much faster rate enabling characterization of a large number of crystals than is currently possible through mechanical scanning with a confocal microscopy based spectroscopic technique as well as providing functional dopant profiling which is not currently possible with conventional approaches.

Multidimensional spatial-spectral holographic interpretation of NMR photography

A spectral holographic interpretation arises naturally in nuclear magnetic resonance (NMR) photography from either the intrinsic chemical shift anisotropy of the spin system or the field inhomogeneity due to the applied spatial encoding gradients. We can thus think of NMR photography as arising from a "diffraction" off a spatial-spectral holographic grating. The spatial holographic component arises from a high dielectric constant (>50) of the NMR medium at high field strength (>4 T) when the excitation wavelength is commensurate with the size of the NMR sample; otherwise, it is a volume spectral holographic grating. In this paper, the NMR localized spectroscopy (imaging) equation is derived from the principles of spatial-spectral holography. Holographic properties of storage and programmable time delay and time reversal are shown to follow naturally from this viewpoint and are experimentally demonstrated in an inhomogeneously broadened NMR sample. These ideas are shown to be extendable to complex signal processing functions such as recognition, correlations, and triple products.

Holographic method of cohering fiber tapped delay lines

We propose, analyze, and demonstrate the use of a holographic method for cohering the output of a fiber tapped delay line (FTDL) that enables the use of fiber-remote optical modulators in coherent optical processing systems. We perform a theoretical examination of the phase-cohering process and show experimental results for a radio frequency (RF) spectrum analyzer that uses a lens to spatially Fourier transform the output of a holographically phase-cohered FTDL providing 50 MHz resolution and bandwidths approaching 3 GHz. Substantial improvements in bandwidth should be achievable with better fiber length-trimming accuracy and improvements in resolution can be obtained with longer fiber delay lines. We also analyze and demonstrate the use of a parallel holographic technique that compensates for polarization state scrambling induced by propagation through an array of single-mode fibers. Both the phase-cohering holography and the polarization fluctuation compensation can operate on hundreds of fibers in parallel, enabling both coherent optical signal processing with FTDLs and coherent fiber remoting of optically modulated RF signals from antenna arrays.