#### Title

Broadband electromagnetic analysis of dispersive, periodic structures for radiometer calibration

#### Date of Award

Spring 1-1-2012

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Electrical, Computer & Energy Engineering

#### First Advisor

Albin Gasiewski

#### Second Advisor

Dejan Filipovic

#### Third Advisor

Edward Kuester

#### Fourth Advisor

Bob McLeod

#### Fifth Advisor

David Walker

#### Abstract

This thesis primarily focusses on the full wave electromagnetic analysis of radiometer calibration targets using doubly dispersive 3D Finite Difference Time Domain (FDTD) formulation. The boundary conditions are set up to solve for doubly periodic structures. The thesis contains very detailed derivation and equations regarding this formulation. One of the novelty in this formulation is the handling of magnetically and electrically dispersive media (usually it is just the electrical dispersion which is incorporated). Using a custom developed code which can be run on a distributed computing system, the reflectivity spectrum of calibration targets of different geometries, coating thicknesses and aspect ratios are analyzed. The results are well validated using commercial simulation software and custom Geometric Optics (GO) code. The geometries analyzed include square pyramids, conical pyramids, truncated square pyramids and truncated conical pyramids with spherical top. The coating thicknesses used are 1 mm, 2 mm and 3 mm. The aspect ratios (ratio of base to height) used include 1 : 1, 1 : 2 and 1 : 4. The nominal target structure has 1 : 4 aspect ratio and 2 mm coating thickness. The material used for simulation is ECCOSORB MF112. The material properties of other materials such as MF110 and MF114 are listed. It should be remarked that measured material properties are available only in the frequency range [8, 26] GHz and a Debye series extrapolation was used for simulation at frequencies outside this range. Throughout this work 0.5′′ base was used. Some significant conclusions include the following: 1) 1:4 aspect ratio or better is required to achieve a -50 dB reflectivity or lower 2) Low frequency reflectivity is independent of the target geometry. 3) At high frequencies, the conical target results in better performance when compared to square pyramids (by about 10 dB). 4) The reflectivity spectrum exhibits a general trend of high reflectivity at low frequencies followed by decreasing reflectivity as frequency is increased. There is a reflectivity jump at frequencies where non-specular Floquet modes start propagating. This is followed by nearly sinusoidal oscillations at high frequencies. 5) Asymptotic techniques can be used at high frequencies instead of full wave analysis. The plane wave reflectivity estimated using full wave analysis is an approximate method to calculate brightness temperature as measured by antenna during radiometer calibration. It assumes two conditions: 1) The calibration targets have a uniform temperature profile. 2) Antenna is in the far field. These two conditions are never met in practice. In order to estimate the near field thermal emission, Fluctuation Dissipation Theorem (FDT) must be used. Dyadic Green Function (DGF) along with FDT can be used to calculate the thermal emission from simple geometries. Analytical formulations to this end is given in this thesis.

The rest of the thesis (∼ 50%) contains work related to numerical methods applied to radiative transfer and computational electromagnetics. In the first part, a novel method to calculate the absorption coefficient, scattering coefficient, backscattering coefficient and phase asymmetry parameter of a polydispersed distribution of liquid water and ice hydrometeors is presented. The conventional method of calculating these coefficients can be time consuming, because of the Mie series summation to calculate Mie coefficients and the numerical quadrature over a distribution of spheres to calculate the requried coefficients. By using spline interpolation on a precomputed look up table, the calculation procedure can be accelerated. The second part deals with time domain analysis of dispersive, periodic structures for oblique plane wave incidence. This is a difficult problem with only one work available in literature till now. The proposed method uses Laguerre Marching-In-On-Degree (MoD) where time dependant quantities are expressed as an expansion of Laguerre basis functions. Using several properties of Laguerre basis functions, the time dependant problem is converted to a time independent problem in Laguerre basis coefficients. This in turn is solved using the familiar finite difference format. The novel method was validated with analytical results for incident angles as large as 75^{o}.

#### Recommended Citation

Sandeep, Srikumar, "Broadband electromagnetic analysis of dispersive, periodic structures for radiometer calibration" (2012). *Electrical, Computer & Energy Engineering Graduate Theses & Dissertations*. 48.

http://scholar.colorado.edu/ecen_gradetds/48