Low observable technology is used in order to prevent detection, or to delay detection. Radar cross section is an important parameter in aircraft survivability since it measures how detectable an object is with radar. To find the radar cross section Maxwell's equations are solved numerically in the time-domain using a finite difference scheme. This numerical method called Finite Difference Time Domain is very suitable for structures including complex materials. However, this numerical method needs to be verified for large scale simulations, due to numerical dispersion errors. Therefore it is desirable to verify the accuracy of the numerical simulations. In this project, the analytical solution to the multiple scattering by two spheres is implemented using the T-matrix formulation. The analytical solution to the scattering problem is first validated with the analytical Mie-series solution then compared to the Finite Difference Time Domain implementation. The results imply that the difference between the numerical and analytical solution is larger for higher frequencies and larger computational volumes. / Smygteknik används för att förhindra detektering, eller för att fördröja detektion av ett flygplan. Radarmålarea är en viktig parameter för skyddsprestanda hos flygplan eftersom den mäter hur detekterbar ett föremål är med radar. För att hitta radarmålarean löses Maxwells ekvationer numeriskt i tidsdomänen med hjälp av ett finit differensschema. Den numeriska metoden som kallas Finita differensmetoden i tidsdomän, är mycket lämplig för strukturer med komplexa material. Den numeriska metoden behöver valideras för storskaliga simuleringar eftersom det förekommer felaktigheter på grund av den numeriska dispersionen. Därför är det önskvärt att kontrollera riktigheten av de numeriska simuleringarna. I detta projekt, är den analytiska lösningen till multipelspridning av två sfärer implementerad med hjälp av T-matrismetoden. Den analytiska lösningen på spridningsproblemet valideras först mot den analytiska Mie-serielösningen och sedan jämförs den med resultatet av simuleringarna med Finita differensmetoden i tidsdomän. Resultaten antyder att skillnaden mellan den numeriska och analytiska lösningen är större för högre frekvenser och större beräkningsvolymer.

In this work a Finite Difference Time Domain (FDTD) simulation is employed to explore local field enhancement, plasmonic coupling, and charge distribution patterns. This 3D simulation calculates the magnetic and electric field components in a large matrix of Yee cells using Maxwell’s equations. An absorbing boundary condition is included to eliminate reflection back into the simulation chamber, and a sample system of cells is checked for convergence. In the specific simulations considered here, a laser pulse of single wavelength is incident on a silicon substrate, travels through an embedded ZnO nanowire (NW) waveguide only (due to an Ag filter), then incites plasmonic coupling at the gap between an Au nanoparticle tip and an Au substrate, an Au nanoparticle (NP), or a trio of Au nanoparticles incident on an angled Si substrate. The angle between the axis of the NW and the normal of the substrate is varied from 0-60°. The NP perpendicular deflection with respect to the NW axis is also varied from -115 - 75 nm. The enhancement patterns reveal superior signal to noise ratio compared to Near Field Scanning Optical Microscopy (NSOM), three times smaller than the NP diameter 100 nm, as well as resolution and spot size of less than 50 nm. This method of Apertureless NSOM (ANSOM) using a NW waveguide grown on a transparent microcantilever therefore shows promise for imaging of single molecules incident on a substrate and NP-labeled cell membrane. / text

This thesis presents a very efficient hybrid method for analysis and design of optical and passive photonic devices. The main focus is on unbounded wave structures. This class of photonic systems are in general very large in terms of the wavelength of the driving optical sources. The size of the problem space makes the electromagnetic modelling of these structure a very challenging problem. Our approach and main contribution has been to combine or hybridize three methods that together can handle this class of photonic structures as a whole. <br /><br /> The basis of the hybrid method is a novel Gaussian Beam Tracing method GBT. Gaussian Beams (GB) are very suitable elementary functions for tracing and tracking purposes due to their finite extent and the fact that they are good approximations for actual laser beams. The GBT presented in this thesis is based on the principle of phase matching. This method can be used to model the reflection and refraction of Gaussian beams from general curved surfaces as long as the curvature of the surface is relatively small. It can also model wave propagation in free space. The developed GBT is extremely fast as it essentially uses simple algebraic equations to find the parameters of the reflected and refracted beams once the parameters of the incident beam is known. Therefore sections of the systems whose dimensions are large relative to the optical wavelength are simulated by the GBT method. <br /><br /> Fields entering a photonic system may not possess an exact Gaussian profile. For example if an aperture limits the input laser to the system, the field is no longer a GB. In these and other similar cases the field at some aperture plane needs to be expanded into a sum of GBs. Gabor expansion has been used for this purpose. This method allows any form of field distribution on a flat or curved surface to be expanded into a sum of GBs. The resultant GBs are then launched inside the system and tracked by GBT. Calculation of the coefficients of the Gabor series is very fast (1-2 minutes on a typical computer for most applications). <br /><br /> In some cases the dimensions or physical properties of structures do not allow the application of the GBT method. For example if the curvature of a surface is very large (or its radius of curvature is very small) or if the surface contains sharp edges or sub-wavelength dimensions GBT is no longer valid. In these cases we have utilized the Finite Difference Time Domain method (FDTD). FDTD is a rigorous and very accurate full wave electromagnetic solver. The time domain form of Maxwell's equations are discretized and solved. No matrix inversion is needed for this method. If the size of the structure that needs to be analyzed is large relative to the wavelength FDTD can become increasingly time consuming. Nevertheless once a structure is simulated using FDTD for a given input, the output is expanded using Gabor expansion and the resultant beams can then be efficiently propagated through any desired system using GBT. For example if a diffraction grating is illuminated by some source, once the reflection is found using FDTD, it can be propagated very efficiently through any kind of lens or prism (or other optical structures) using GBT. Therefore the overall computational efficiency of the hybrid method is very high compared to other methods.

"The time-of-arrival (ToA)-based localization technique performs superior in line-of-sight (LoS) conditions, and its accuracy degrades drastically in proximity of micro-metals and human body, when LoS conditions are not met. This calls for modeling and formulation of Direct Path (DP) to help with mitigation of ranging error. However, the current propagation tools and models are mainly designed for telecommunication applications via focus on delay spread of wireless channel profile, whereas ToA-based localization strive for modeling of DP component. This thesis provides a mitigation to the limitation of existing propagation tools and models to computationally capture the effects of micro-metals and human body on ToA-based indoor localization. Solutions for each computational technique are validated by empirical measurements using Ultra-Wide-Band (UWB) signals. Finite- Difference-Time-Domain (FDTD) numerical method is used to estimate the ranging errors, and a combination of Uniform-Theory-of-Diffraction (UTD) ray theory and geometrical ray optics properties are utilized to model the path-loss and the ToA of the DP obstructed by micro- metals. Analytical UTD ray theory and geometrical ray optics properties are exploited to model the path-loss and the ToA of the first path obstructed by the human body for the scattering scenarios. The proposed scattering solution expanded to analytically model the path-loss and ToA of the DP obstructed by human body in angular motion for the radiation scenarios."

This thesis presents a very efficient hybrid method for analysis and design of optical and passive photonic devices. The main focus is on unbounded wave structures. This class of photonic systems are in general very large in terms of the wavelength of the driving optical sources. The size of the problem space makes the electromagnetic modelling of these structure a very challenging problem. Our approach and main contribution has been to combine or hybridize three methods that together can handle this class of photonic structures as a whole. <br /><br /> The basis of the hybrid method is a novel Gaussian Beam Tracing method GBT. Gaussian Beams (GB) are very suitable elementary functions for tracing and tracking purposes due to their finite extent and the fact that they are good approximations for actual laser beams. The GBT presented in this thesis is based on the principle of phase matching. This method can be used to model the reflection and refraction of Gaussian beams from general curved surfaces as long as the curvature of the surface is relatively small. It can also model wave propagation in free space. The developed GBT is extremely fast as it essentially uses simple algebraic equations to find the parameters of the reflected and refracted beams once the parameters of the incident beam is known. Therefore sections of the systems whose dimensions are large relative to the optical wavelength are simulated by the GBT method. <br /><br /> Fields entering a photonic system may not possess an exact Gaussian profile. For example if an aperture limits the input laser to the system, the field is no longer a GB. In these and other similar cases the field at some aperture plane needs to be expanded into a sum of GBs. Gabor expansion has been used for this purpose. This method allows any form of field distribution on a flat or curved surface to be expanded into a sum of GBs. The resultant GBs are then launched inside the system and tracked by GBT. Calculation of the coefficients of the Gabor series is very fast (1-2 minutes on a typical computer for most applications). <br /><br /> In some cases the dimensions or physical properties of structures do not allow the application of the GBT method. For example if the curvature of a surface is very large (or its radius of curvature is very small) or if the surface contains sharp edges or sub-wavelength dimensions GBT is no longer valid. In these cases we have utilized the Finite Difference Time Domain method (FDTD). FDTD is a rigorous and very accurate full wave electromagnetic solver. The time domain form of Maxwell's equations are discretized and solved. No matrix inversion is needed for this method. If the size of the structure that needs to be analyzed is large relative to the wavelength FDTD can become increasingly time consuming. Nevertheless once a structure is simulated using FDTD for a given input, the output is expanded using Gabor expansion and the resultant beams can then be efficiently propagated through any desired system using GBT. For example if a diffraction grating is illuminated by some source, once the reflection is found using FDTD, it can be propagated very efficiently through any kind of lens or prism (or other optical structures) using GBT. Therefore the overall computational efficiency of the hybrid method is very high compared to other methods.

In this thesis, we used the E-Beam lithography to fabricate a device of coupled microdisk-ring laser on the sample which was grown by molecular beam epitaxy (MBE), and analyzed the coupled effect of the device. The active layer was composed of six compressively strained InGaAs quantum dots (QDs) that were designed to support gain at 1200nm. Under the active layer, we replaced sacrificial layer by distributed bragg reflector (DBR). The purpose of the DBR was used like a mirror to reflect the particular wavelength which located at DBR¡¦s stop band, so the energy would be confined in the active layer. The device was composed of a microdisk and a ring. The diameter of the microdisk was 3£gm, and the width of the ring is 250nm. The microdisk was placed in the ring, and the gap of both was 100nm. After design, we simulated whether the device could generate coupled modes by Finite-Difference Time-Domain (FDTD). In experiment, we used the E-Beam lithography to define negative pattern on the sample which is spread with the PMMA. We also used the thermal evaporation to evaporate the metal, and lift the metal to form our pattern. Finally, we used the dry etching to transform the pattern to the epitaxial layer, and then the device was completed. In measurement, we used the micro-PL to measure our device, and got a successful result. The result showed our device generated eight resonant modes. The measured result matched the simulation result. Through simulation, the device generated three coupled modes, 1173.8nm, 1206nm, and 1214nm. We expect that the device will be used to generate terahertz source in the future.

The single scattering properties of atmospheric particles are fundamental to radiative simulations and remote sensing applications. In this study, an efficient technique, namely, the pseudo-spectral time-domain (PSTD) method which was first developed to study acoustic wave propagation, is applied to the scattering of light by nonspherical particles with small and moderate size. Five different methods are used to discretize Maxwell’s equations in the time domain. The perfectly matched layer (PML) absorbing boundary condition is employed in the present simulation for eliminating spurious wave propagations caused by the spectral method. A 3-D PSTD code has been developed on the basis of the five aforementioned discretization methods. These methods provide essentially the same solutions in both absorptive and nonabsorptive cases. In this study, the applicability of the PSTD method is investigated in comparison with the Mie theory and the T-matrix method. The effects of size parameter and refractive index on simulation accuracy are discussed. It is shown that the PSTD method is quite accurate when it is applied to the scattering of light by spherical and nonspherical particles, if the spatial resolution is properly selected. Accurate solutions can also be obtained from the PSTD method for size parameter of 80 or refractive index of 2.0+j0. Six ice crystal habits are defined for the PSTD computational code. The PSTD results are compared with the results acquired from the finite difference time domain (FDTD) method at size parameter 20. The PSTD method is about 8-10 times more efficient than the conventional FDTD method with similar accuracy. In this study, the PSTD is also applied to the computation of the phase functions of ice crystals with a size parameter of 50. Furthermore, the PSTD, the FDTD, and T-matrix methods are applied to the study of the optical properties of horizontally oriented ice crystals. Three numerical schemes for averaging horizontal orientations are developed in this study. The feasibility of using equivalent circular cylinders as surrogates of hexagonal prisms is discussed. The horizontally oriented hexagonal plates and the equivalent circular cylinders have similar optical properties when the size parameter is in the region about from 10 to 40. Otherwise, the results of the two geometries are substantially different.

When the finite-difference time-domain (FDTD) method is applied to light scattering computations, the far fields can be obtained by either a volume integration method, or a surface integration method. In the first study, we investigate the errors associated with the two near-to-far field transform methods. For a scatterer with a small refractive index, the surface approach is more accurate than its volume counterpart for computing the phase functions and extinction efficiencies; however, the volume integral approach is more accurate for computing other scattering matrix elements. If a large refractive index is involved, the results computed from the volume integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation of a small refractive index. In my second study, a fourth order symplectic FDTD method is applied to the problem of light scattering by small particles. The total-field/ scattered-field (TF/SF) technique is generalized for providing the incident wave source conditions in the symplectic FDTD (SFDTD) scheme. Numerical examples demonstrate that the fourthorder symplectic FDTD scheme substantially improves the precision of the near field calculation. The major shortcoming of the fourth-order SFDTD scheme is that it requires more computer CPU time than the conventional second-order FDTD scheme if the same grid size is used. My third study is on multiple scattering theory. We develop a 3D Monte Carlo code for the solving vector radiative transfer equation, which is the equation governing the radiation field in a multiple scattering medium. The impulse-response relation for a plane-parallel scattering medium is studied using our 3D Monte Carlo code. For a collimated light beam source, the angular radiance distribution has a dark region as the detector moves away from the incident point. The dark region is gradually filled as multiple scattering increases. We have also studied the effects of the finite size of clouds. Extending the finite size of clouds to infinite layers leads to underestimating the reflected radiance in the multiple scattering region, especially for scattering angles around 90 degrees. The results have important applications in the field of remote sensing.

The Finite-Difference Time-Domain method ( FDTD ) is a numerical method introduced by K. S. Yee in 1966. However , it needs so much time to simulate circuits by applying the FDTD method and some extensional methods for simulating circuits are still incomplete . Therefore, the author combine the FDTD method with the data extrapolation method to improve the simulation effect. When applying the FDTD method to simulate circuits, it needs a large number of time steps; furthermore, if the structure we simulated is complicated, the simulation time will be so much longer that the efficiency of simulation will be bad as well. The author decrease the number of time steps of the FDTD method, and then extrapolate the time-domain data to reconstruct the complete frequency response, therefore, we can save the simulation time as well because the number of the time steps of the FDTD method decreased. Furthermore, in the thesis, we also introduce a new FDTD method combined with the S-parameter Matrix, called ¡§S-parameter Matrix method¡¨. People can simulate circuits without deriving the equivalent circuit by applying the S-parameter Matrix method. One only have to obtain the S-parameter Matrix by measurement, data sheet, calculation, etc, and then we translate it to time domain data by the IFT technique to apply the FDTD calculation , this way, we avoid the difficulty of deriving the equivalent circuit of general microwave circuits. However, the S-parameter data we can obtain are often limited in a finite bandwidth, we make it to be extrapolated to obtain the complete time-domain response, and this way, the S-parameter Matrix method can by apply to simulate circuits.

Many electromagnetic problems can be simulated by FDTD method. Mainly, we use orthogonal cartesian coordinate in normal situations when we deal with the electromagnetic problems. Because in most situations, the structures simulated are simply rectangular. But sometimes we may need to simulate the structures which are not rectangular like the sharps of arc and circle. For this kind of problems, the tranditional FDTD method no longer works, so the tranditional FDTD method must be modified to fit the simulation of irregular structures. Besides the FDTD method we mention above, we even combine it with non-uniform grid method in more applications. And the time to apply it is when the object simulated both has the rectangular and curved structures in the same time like the microstrip fed by the coaxial cable. The situations like that would be a good time to apply it.