Modal Analysis of Millimetre-wave and Terahertz Imaging Systems

This thesis presents the theory and applications of electromagnetic field calculation using orthogonal Gaussian beam modes within the context of far-infrared imaging systems. Laguerre and Hermite-Gaussian modes have been frequently reported in the analysis of paraxial millimetre-wave propagation in astronomical optical systems. Here the method of Gaussian beam mode analysis (GBMA) is extended to fields of optical research that have until recently been associated with wavelengths in the visible band. Using recently derived expressions for the non-paraxial diffraction of Hermite-Gaussian modes, the author demonstrates the modal calculation of far-field intensity distributions with less angular restriction on the accuracy of the method compared to the conventional paraxial description of orthogonal Gaussian modes. This method shows excellent agreement with predictions from more rigourous fullwave numerical methods such as the finite-difference time-domain algorithm, which is also described as a software tool in the modelling of horn and lens antennas. The properties of diffraction limited Bessel beams is described using the Laguerre-Gaussian expansion of conical lenses, and experimental measurements of a conical lens is presented to explore the validity of the use of these optical elements as horn coupled devices in millimetre wave imaging systems. A study of diffractive Fresnel lenses has been undertaken with a comparison of experimentally measured fields with those predicted by the modal techniques. The effects of such lenses on ultrashort paraxial pulses are also investigated using a novel numerical description of few-cycle fields as a superposition of pulsed Laguerre- Gaussian modes. The application of digital holography in the far-infra red band has the prospect of diffraction limited imaging systems without creating distortions and aberrations which is a common problem in conventional techniques using lenses and mirrors. The author presents results from a simple proof-of-concept system which exhibits the potential of this technique for application in, for example, mm-wave security imaging

Modal Analysis of Millimetre-wave and Terahertz Imaging Systems

This thesis presents the theory and applications of electromagnetic field calculation using orthogonal Gaussian beam modes within the context of far-infrared imaging systems. Laguerre and Hermite-Gaussian modes have been frequently reported in the analysis of paraxial millimetre-wave propagation in astronomical optical systems. Here the method of Gaussian beam mode analysis (GBMA) is extended to fields of optical research that have until recently been associated with wavelengths in the visible band. Using recently derived expressions for the non-paraxial diffraction of Hermite-Gaussian modes, the author demonstrates the modal calculation of far-field intensity distributions with less angular restriction on the accuracy of the method compared to the conventional paraxial description of orthogonal Gaussian modes. This method shows excellent agreement with predictions from more rigourous fullwave numerical methods such as the finite-difference time-domain algorithm, which is also described as a software tool in the modelling of horn and lens antennas. The properties of diffraction limited Bessel beams is described using the Laguerre-Gaussian expansion of conical lenses, and experimental measurements of a conical lens is presented to explore the validity of the use of these optical elements as horn coupled devices in millimetre wave imaging systems. A study of diffractive Fresnel lenses has been undertaken with a comparison of experimentally measured fields with those predicted by the modal techniques. The effects of such lenses on ultrashort paraxial pulses are also investigated using a novel numerical description of few-cycle fields as a superposition of pulsed Laguerre- Gaussian modes. The application of digital holography in the far-infra red band has the prospect of diffraction limited imaging systems without creating distortions and aberrations which is a common problem in conventional techniques using lenses and mirrors. The author presents results from a simple proof-of-concept system which exhibits the potential of this technique for application in, for example, mm-wave security imaging

Modeling and Simulation of Photonic Crystal Fibers and Distributed Feedback Photonic Crystal Fiber Lasers

A photonic crystal fiber (PCF) is comprised of a solid or air core surrounded by periodically arranged air holes running along the length of the fiber, which guides light in a fundamentally new way compared to conventional optical fibers, affecting almost all areas of optics and photonics. To analyze the dispersion and loss properties of PCFs, a two-dimensional (2D) finite-difference frequency-domain (FDFD) method combined with the technique of perfectly matched layer (PML) is developed. The propagation constant and loss can be obtained with accuracies in the orders of ∼10-6 and ∼10 -3, respectively. The Bragg fiber is a kind of PCF with alternate layers surrounding a solid or air core. To improve the performance of the above algorithm, a 1D FDFD method in the cylindrical coordinates is proposed to fully utilize the rotational symmetry property of the Bragg fiber. In addition to improving the accuracy, this method reduces the computation region from 2D to a straight line, significantly relieving the computation burden. A second method, called Galerkin method, is also developed under cylindrical coordinates. The mode fields are expanded using orthogonal Laguerre-Gauss functions; and the method is accurate and stable. However, it cannot do the loss analysis. For photonic-band-gap-guiding PCFs, the properties of the confined modes are closely related to the band structures of the cladding photonic crystals. Therefore, a third FDFD method using periodic boundaries is developed in a generalized coordinate system. Various lattice geometries are analyzed in the same manner, and the results are comparable to those obtained by the plane wave expansion method which is commonly used in the literature. Finally, a theoretical model for analyzing distributed feedback (DFB) PCF lasers has been presented. Two structures are investigated: PCFs with triangular lattice (TPCF) and PCFs made of capillary tube (CPCF). The modeling and simulation of erbium-doped and erbium/ytterbium (Er/Yb) co-doped DFB lasers are aimed at finding suitable PCF geometry to achieve low threshold and high output power. Various steps involved in this model are: (1) the properties of PCFs are analyzed by the FDFD method; (2) the Bragg grating is investigated by coupled mode theory; (3) the coupled wave equations are solved by transfer matrix method; and (4) Er atom is modeled as a three-level medium while energy transfer between Yb and Er atoms is considered for Er/Yb co-doped fiber. It is found that a CPCF laser with a smaller mode area is useful for lower-threshold applications and both of CPCF and TPCF lasers with larger mode areas are suitable for high-power operation

Loss and Dispersion Analysis of Microstructured Fibers by Finite-Difference Method

The dispersion and loss in microstructured fibers are studied using a full-vectorial compact-2D finite-difference method in frequency-domain. This method solves a standard eigen-value problem from the Maxwell’s equations directly and obtains complex propagation constants of the modes using anisotropic perfectly matched layers. A dielectric constant averaging technique using Ampere’s law across the curved media interface is presented. Both the real and the imaginary parts of the complex propagation constant can be obtained with a high accuracy and fast convergence. Material loss, dispersion and spurious modes are also discussed

Iterative nonlinear beam propagation method and its application in nonlinear devices

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 89-96).In this thesis, an iterative nonlinear beam propagation method is introduced and applied to optical devices. This method is based on Hamiltonian ray tracing and the Wigner distribution function. First, wave propagation simulation using Hamiltonian ray tracing is illustrated and verified with different examples. Based on this, the iterative method is presented for beam propagation in nonlinear media, which is validated with common Kerr effect phenomena such as self-focusing and spatial solitons. As the application to the analysis of nonlinear optical devices, this method is applied to nonlinear Lineburg lens. It is found that the nonlinear Liineburg lens is able to compensate the focal shift caused by the diffraction of Gaussian illumination. The iterative nonlinear beam propagation method is computationally efficient and provides much physical insights into the wave propagation. Since it is based on Hamiltonian ray tracing, a ray diagram can be easily obtained which contains the evolution of generalized radiances. Besides bulk nonlinear media, this method provides a systematic approach to beam propagation problem in complex media such as nonlinear photonic crystals and metamaterials. Also, it is applicable to both coherent and partially coherent illumination. Therefore, this method has potential applications in the design and analysis of nonlinear optical devices and systems.by Hanhong Gao.S.M

Broadband electromagnetic analysis of dispersive, periodic structures for radiometer calibration

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 75o

Numerical methods for computing Casimir interactions

We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria---choice of problem, basis, and solution technique---that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture Notes in Physics book on Casimir Physic

Review on Computational Electromagnetics

Computational electromagnetics (CEM) is applied to model the interaction of electromagnetic fields with the objects like antenna, waveguides, aircraft and their environment using Maxwell equations.  In this paper the strength and weakness of various computational electromagnetic techniques are discussed. Performance of various techniques in terms accuracy, memory and computational time for application specific tasks such as modeling RCS (Radar cross section), space applications, thin wires, antenna arrays are presented in this paper