Majid Badieirostami

Model for efficient simulation of spatially incoherent light using the Wiener chaos expansion method

We demonstrate a new and efficient technique for modeling and simulation of spatially incoherent sources using the Wiener chaos expansion method. By implementing this new model, we show that a practical-size photonic structure with a spatially incoherent input source can be analyzed more than 2 orders of magnitude faster compared with the conventional models without sacrificing the accuracy.

Accurate and efficient techniques for the analysis of reflection at the interfaces of three-dimensional photonic crystals

We present two efficient and accurate models for the analysis and optimization of reflection at the interface of three-dimensional (3D) photonic crystal structures. For the most general photonic crystal interfaces, we develop a rigorous technique based on mode matching at the interface. We also explain a more efficient (yet accurate) model based on effective impedance definition for the analysis of 3D photonic crystals (PC) structures that are highly desired for practical applications. The two techniques are used to model practical 3D PC structures, and the issue of reflection minimization at the interface of such structures is addressed.

Investigation of physical mechanisms in coupling photonic crystal waveguiding structures

We explain the fundamental physical mechanisms involved in coupling triangular lattice photonic crystal waveguides to conventional dielectric slab waveguides. We show that the two waveguides can be efficiently coupled outside the mode gap frequencies. We especially focus on the coupling of the two structures within the mode gap frequencies and show for the first time that the diffraction from the main photonic crystal structure plays an important role on the reflection of power back into the slab waveguide. The practical importance of this effect and possible strategies to modify it are also discussed.

Very-high-resolution tandem Fabry-Perot etalon cylindrical beam volume hologram spectrometer for diffuse source spectroscopy

We demonstrate a compact and slitless spectrometer with high resolution formed by cascading a Fabry-Perot etalon (FPE) and a cylindrical beam volume hologram (CBVH). The most significant advantage of this combined spectrometer is that we can independently encode spectral information of a diffuse beam in a 2D plane. Also, we show that in this slitless configuration we can simultaneously benefit from the advantages of both elements: the high resolution of the FPE and the large spectral range of the CBVH. Here, we report on the experimental demonstration of a spectrometer with better than 0.2 nm resolution.

Wiener Chaos Expansion and Simulation of Electromagnetic Wave Propagation Excited by a Spatially Incoherent Source

First, we propose a new stochastic model for a spatially incoherent source in optical phenomena. The model naturally incorporates the incoherent property into the electromagnetic wave equation through a random source term. Then we propose a new numerical method based on Wiener chaos expansion (WCE) and apply it to solve the resulting stochastic wave equation. The main advantage of the WCE method is that it separates random and deterministic effects and allows the random effects to be factored out of the primary partial differential equation (PDE) very effectively. Therefore, the stochastic PDE is reduced to a set of deterministic PDEs for the coefficients of the WCE method which can be solved by conventional numerical algorithms. We solve these secondary deterministic PDEs by a finite-difference time domain (FDTD) method and demonstrate that the numerical computations based on the WCE method are considerably more efficient than the brute-force simulations. Moreover, the WCE approach does not require gener...

Modeling the propagation of optical beams in three-dimensional photonic crystals

We show that the propagation effects of optical beams in three-dimensional photonic crystal structures can be modeled using a direction-dependent effective diffractive index model. The parameters of the model (i.e., the effective diffractive indices) can be calculated using the curvatures of the band structure of the photonic crystal at the operation point. After finding these indices, the wave propagation inside the photonic crystal can be analyzed using simple geometrical optics formulas. We show that the model has good accuracy for most practical applications of photonic crystals. As an example, the application of the model for diffraction compensation in a tetragonal woodpile photonic crystal is demonstrated.

Compact spectrometer based on focusing superprism effect in photonic crystals for integrated sensing applications

Compact spectrometers are one of important building blocks needed in implementing optical lab-on-a-chip sensing devices. Photonic crystal superprism demultiplexers due to their unique and strong dispersion properties are proper candidates for realizing such integrated spectrometers. We use a recently demonstrated device idea, i.e., focusing superprism photonic crystal demultiplexers, to implement an integrated compact spectrometer that can be used in sensing applications. In this device, a diffraction compensation scheme is used to cancel the broadening of the optical beam throughout the structure, which significantly improves the resolution of the device (compared to the conventional superprism demultiplexers). In addition, by designing the photonic crystal in negative refraction regime, stray and unwanted portions of the input signal are filtered out inside the structure and this improves the output signal-to-noise ratio. A least-square algorithm is used to extract the spectrum of the signal from measured output power at different channels.

Efficient modeling of photonic crystal structures under diffuse light illumination

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.

Three-dimensional photonic crystal demultiplexers

We present the analysis and design of three-dimensional (3D) photonic crystal (PC) demultiplexers in which the simultaneous existence of the superprism effect and the diffraction compensation results in a compact structure. We have used tetragonal woodpile PCs fabricated by 3D patterning of a polymer material through a direct laser writing technique for experimental demonstration of these devices.

Fast and efficient analysis and design of three-dimensional photonic crystal structures for functional dispersive devices

We show that the propagation of optical beams inside three-dimensional photonic crystals can be efficiently described by an approximate scalar diffraction model. The main advantage of this model is that it reduces the memory and computation time for direct simulations of three-dimensional photonic crystals by converting the problem into an equivalent problem for which simple geometrical optics can be applied. Then we use this model for efficient design of photonic crystal dispersive devices such as demultiplexers and microspectrometers. Finally, experimental verification of the results for the polymer woodpile structures will be given.