Through a holographic recording a property from the third dimension, the depth, is obtained in the form of a phase map of the incident light. One wavelength holography will have a unique phase for the depth range corresponding to the wavelength of the light and outside this range the real depth can not be resolved. By introducing more wavelengths to the measurement the unique phase combination of the waves will have a wider range and larger objects can be resolved. Up to six wavelengths can be simultaneous recorded by making them occupy different spatial frequencies. A set of spatial frequencies together describing a property of the wave is referred to as a lobe. For more than 6 wavelengths and a larger depth range produced by a more seldom repeated unique phase combination the individual waves will occupy the same frequencies, i.e. the lobes overlap. The separation of overlapping lobes is essential in order to make precise and time independent measurements of large and/or moving objects. To separate the lobes the complex fields, i.e. the phases together with the amplitudes, were simulated to propagate a distance and again recorded. The propagation leads to a phase shift of the spatial frequencies which reveals the complex fields in the case of two overlapping wavelengths. For three overlapping wavelengths the resolution, i.e spatial frequencies describing the object, has to be reduced in order to determine the individual complex fields. Since the propagation is a linear transformation for the frequencies that do not overlap, only the overlapping elements whose propagation is nonlinear produce new information. The new information gained is therefore independent of the number of wavelengths used which limits the exact determination of the fields to two wavelengths. Through the holographic recording another property of the complex field is obtained which is the superimposed individual intensities. This bounds the complex fields to certain values, i.e. restricts the possible amplitude of the waves. The recording in the two planes produces two intensity distributions which both must be satisfied by the complex fields. The optimization model for this was formulated and a simple optimization algorithm was implemented. Instead of an equality constraint of the intensities the inequality constraint was implemented, mainly due to that the optimization process was out of the scope of the thesis and the inequality constraint resulted in a simple implementation. The result pointed out important properties even though the optimization could not separate the fields satisfactorily for more than three wavelengths. The inequality constraint contains enough information to solve the case of three overlapping wavelengths.

<div>Increasing flexibility of light manipulation is vital for various domains including both biomedical and military applications, where a lack of photon control could become critical. The efforts conducted and projected within this proposal are focused on three major areas: semi-continuous planar thin film photomodification for infrared (IR) filtering, nanosphere core-shell structures for obscurance, and all-dielectric sub-wavelength focal lenses for advanced IR sensing.Through a collaborative effort with the Army Research Office, we advanced the tunability of planar plasmonic filters with cutoff wavelengths in the 10–16μm range with photomodification using a 10.6μm CO2laser. Surface-enhanced molecular absorption in concert with three-dimensional (3D) Au nano-structures with inherent broad absorption in the IR band was a novel approach utilized to create such planar filters.Expanding on these, efforts and the results of the 2-dimensional (2D) semicontinuous Au plasmonic planar filtering, we further advanced our research with 3D Au nano-coreshell structures to enable levitated long-wavelength pass filter obscurants. We exploited the radiative effects of Au nano-structures that mimic conventional apertures or antennas, though these structures are on the nanometer scale and demonstrated the filtering characteristics through flow cell.In parallel with our plasmonic filtering we designed, manufactured and tested low loss dielectric microlenses for IR radiation based on a dielectric metasurface layer by patterning a SI substrate and etching to sub-micron depths. For a proof-of-concept lens demonstration,we chose a fine patterned array of nano-pillars with variable diameters.Merging our plasmonic filtering and dielectric microlens efforts, we created a holographic lenslet by designing and simulating a low loss focusing metasurface lens with engineered nano-scaled features to converge off-axis IR radiation. An array of nano-pillars with varied diameter and fixed height and periodicity was chosen for ease of fabrication with single layer etching</div>