Osman S. Ahmed

Efficient Design Optimization of Ring Resonator-Based Optical Filters

We present a simple and fast technique for the design of ring resonator-based optical filters. The technique is based on tapering the ring scattering parameters to achieve the optimal filter response. A perturbation method is developed for the linearization of the resulting design problem. The design problem is then formulated as an optimization problem. The optimal filter design is achieved by solving a constrained linear least square problem. This optimization problem can be solved efficiently to get the global optimal design. Our technique has been verified using different proposed targeted filter responses.

Efficient Optimization Approach for Accurate Parameter Extraction With Terahertz Time-Domain Spectroscopy

We propose a novel optimization algorithm for the extraction of material complex refractive index in the terahertz (THz) frequency range. The algorithm is applied for materials with arbitrary frequency dependence. We utilize dispersive dielectric models for accurate parameter extraction of a sample of unknown thickness. This approach allows for simultaneously estimating the parameters and fitting them to one of the dispersive models of the materials in the THz frequency range. Our approach has been successfully illustrated through a number of examples with different dispersive models. The examples include the characterization of doped semiconductors used in surface plasmon plaritons in the THz regime. They also include characterizing carbon nanotubes.

Polarization-controlled excitation of multilevel plasmonic nano-circuits using single silicon nanowire

We propose a surface plasmon polarization-controlled beam splitter based on plasmonic slot waveguides (PSWs). It couples light of different polarizations from a silicon nanowire into multilevel plasmonic networks. Two orthogonal PSWs are utilized as the guiding waveguides for each polarization. The proposed structure overcomes inherent polarization limitation in plasmonic structures by providing multilevel optical signal processing. This ability of controlling polarization can be exploited to achieve 3-D multilevel plasmonic circuits and polarization controlled chip to chip channel. Our device is of a compact size and a wide band operation. The device utilizes both quasi-TE and quasi-TM polarizations to allow for increased optical processing capability. The crosstalk is minimal between the two polarizations propagating in two different levels. We achieve good transmission efficiency at a wavelength of 1.55 µm for different polarizations. We analyze and simulate the structure using the FDTD method. The proposed device can be utilized in integrated chips for optical signal processing and optical computations.

A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters

We present the first time-domain adjoint variable method (AVM) algorithm for materials with dispersive constitutive parameters. We develop our algorithm based on transmission-line modeling techniques for electromagnetic problems. The developed theory is based on utilizing the Z-domain representation of the dispersive materials, which can model arbitrary dispersive behavior. We develop a formulation similar to the original AVM theory for nondispersive materials. The theory has been successfully applied to problems with dispersive materials modeled by the Drude, Debye, and Lorentz models.

Modeling and design of nano-plasmonic structures using transmission line modeling.

For the first time, we demonstrate the application of the time domain transmission line method (TLM) to accurate modeling of surface plasmon polariton (SPP) structures. The constructed TLM node allows for modeling of dispersive materials through simple time-difference equations. Using such node, an ultra-wide band excitation can be applied to obtain the response over the band of interest. Bérengers perfectly matched layer (PML) boundary condition can readily be implemented using the same node. We illustrate our TLM approach through the modeling of different challenging structures including SPPs filters and focusing structures.

Wideband FDTD-Based Adjoint Sensitivity Analysis of Dispersive Electromagnetic Structures

We propose a wideband adjoint variable method for sensitivity analysis of dispersive structures utilizing finite difference time domain (FDTD). Using only one extra FDTD simulation, the sensitivities of the desired response are estimated over the frequency band of interest with respect to all the design parameters. The presented theory is based on direct discretization of Maxwells equations. We derive the equations of the adjoint system for problems with different types of dispersion profiles including the Lorentz, Drude, and Debye models. The validation of our approaches is done through comparison with the expensive finite-difference approach applied at the response level.

Realizing vertical light coupling and splitting in nano-plasmonic multilevel circuits

We present a novel technique for vertical coupling of light guided by nanoscale plasmonic slot waveguides (PSWs). A triangularly-shaped plasmonic slot waveguide rotator is exploited to attain such coupling with a good efficiency over a wide bandwidth. Using this approach, light propagating in a horizontal direction is efficiently coupled to propagate in the vertical direction and vice versa. We also propose a power divider configuration to evenly split a vertically coupled light wave to two horizontal channels. A detailed parametric study of the triangular rotator is demonstrated with multiple configurations analyzed. This structure is suitable for efficient coupling in multilevel nano circuit environment.

Towards 3D plasmonic circuits: controlled coupling to multilevel plasmonic circuits

We propose a surface plasmon multilevel coupler based on the orthogonal junction coupling technique between silicon nanowires and plasmonic slot waveguides (PSWs). It couples light of different polarizations from a silicon nanowire into multilevel plasmonic networks. Two orthogonal PSWs are employed to guide each polarization to its respective port. The proposed structure splits the polarizations and allows for simultaneous processing at different horizontal layers. Our device overcomes inherent polarization limitation in plasmonic structures by providing multilevel optical signal processing. This ability of controlling polarization can be exploited to achieve 3-D multilevel plasmonic circuits and polarization controlled chip to chip channel. Our device is of a compact size and a wideband operation. The device utilizes both quasi-TE and quasi-TM polarizations to allow for increased optical processing capability. The crosstalk is minimal between the two polarizations propagating in two different levels. We achieve -4.5 dB transmission efficiency at a wavelength of 1.55 μm for the different polarizations in the respective ports. A transmission efficiency of -21 dB is achieved in the subsidiary port. We analyze and simulate the structure using the FDTD method. The proposed device can be utilized in integrated chips for optical signal processing and optical computations.

Adjoint variable method for two-dimensional plasmonic structures

We present, for the first time, an adjoint variable method (AVM) for wideband sensitivity analysis of dispersive materials. The time domain transmission line modeling technique is exploited to calculate the response and its sensitivities with respect to all the designable parameters using at most one extra simulation. A z-domain representation of dispersive materials is utilized in the derivation of this technique. Our approach is illustrated through sensitivity analysis of a two-dimensional teeth-shaped plasmonic resonator. The AVM sensitivities are compared with the accurate and expensive finite difference approach and good agreement is achieved. This theory can be extended to other dispersive materials and dispersive metamaterials as well.

A Memory-Efficient Implementation of TLM-Based Adjoint Sensitivity Analysis

We present a memory efficient algorithm for the estimation of adjoint sensitivities with the 2D transmission line modeling (TLM) method. The algorithm is based on manipulating the local scattering matrices to reduce the required storage for the original structure simulation associated with lossy dielectric discontinuities. Only one value per cell is stored for two dimensional simulations. Moreover, the connection step for the scattered sensitivity storage is embedded during the adjoint simulation and the sensitivity estimates are calculated on the fly. The required memory storage for our implementation is only 10% of the original implementation of AVM sensitivity with TLM.