My research on the new concepts for spectrometer has been focused on the development of true multi-dimensional spectrometers, which use a multi-dimensional [two-dimensional (2D) or 3D] mapping of the spectral information into space. I showed that by combining a simple dispersive element (a volume hologram) formed in very inexpensive polymers with a basic Fabry-Perot interferometer, we can form a spectrometer with ultra-high resolution over a large spectral bandwidth, which surpasses all conventional spectrometers. I strongly believe that the extension of this mapping into three dimensions by using synthetic nanophotonic structures with engineered dispersion can further improve the performance and reduce the overall spectrometer size into the micron regime. The need for efficient modeling and simulation tools comes from the sophisticated nature of the new 3D nanophotonic structures, which makes their simple analysis using well-known simple formulas for the propagation of the electromagnetic fields in bulk materials impossible. In my Ph.D. research, I developed new approximate modeling tools for both the modeling of incoherent sources in nanophotonics, and for the propagation of such optical beams inside the 3D nanophotonic structures of interest with several orders of magnitude improvement in the simulation speed for practical size devices without sacrificing accuracy. To enable new dispersive properties using a single nanophotonic structure, I have focused in my Ph.D. research into polymer-based 3D photonic crystals, which can be engineered using their geometrical features to demonstrate unique dispersive properties in three dimensions that cannot be matched by any bulk material even with orders of magnitude larger sizes. I have demonstrated the possibilities of using a very compact structure for wavelength demultiplexing and also for spectroscopy without adding any other device.