We present the analysis and design of three-dimensional photonic crystal demultiplexers in which the simultaneous
existence of the superprism effect and the diffraction compensation results in a compact structure. First, we report on a
diffractive index model developed to facilitate the simulation of the beam propagation in three-dimensional photonic
crystals. Then, we use tetragonal woodpile photonic crystals to design a demultiplexer.
Compact and efficient spectrometers are of great interest for biological and environmental sensing. In this paper, we
describe a new class of spectrometers that work based on diffractive properties of spherical beam volume holograms
(SBVHs) and cylindrical beam volume holograms (CBVHs). The hologram in these spectrometers acts as a spectral
diversity filter (SDF) that maps different input wavelengths onto different locations in the output plane. The main
properties of these holographic SDFs and new techniques for removing the ambiguity between incident wavelength (or
the input channel) and incident angle (or the input spatial mode) are discussed. By using CBVHs, we show that the
spectral mapping of the input beam can be obtained in one direction and the beam can be independently modified in the
perpendicular direction. Using this unique property, we demonstrate a spectral wrapping technique to considerably
increase the operation spectral range of spectrometers, without sacrificing their resolution. Finally, it is also shown that
by combining CBVHs with a Fabry-Perot interferometer, a true two-dimensional spatial-spectral mapping can be
formed, and an ultra-high resolution of 0.2 nm with large spectral bandwidth is demonstrated for this tandem
We present an efficient model for the simulation of spatially incoherent sources based on Wiener chaos expansion (WCE) method with two orders of magnitude shorter simulation time over the brute-force model. In this model the stochastic wave propagation equation is reduced to a set of deterministic partial differential equations (PDEs) for the expansion coefficients. We further numerically solve these deterministic PDEs by finite difference time domain (FDTD) technique. While the WCE method is general, we apply it to the analysis of photonic crystal spectrometers for diffuse source spectroscopy.
In order to efficiently model and optimize photonic crystal structures under diffuse light we have to first develop a simulation tool to generate a spatially incoherent source. Here we present a new technique for modeling wide-band spatially incoherent source and implement this technique using finite difference time-domain (FDTD) method. We compare this new method with the conventional method of simulating an incoherent source. We show that this method reduces the computation time by more than one order of magnitude with less than 10% error.