In this thesis, we use E-Beam lithography to finish the process of DBR laser, 2D Photonic crystal, and Metallic nanoelectrodes. We use the new E-Beam system to define array patterns. By this test, we obtain the minimum linewidth of 50nm, and the maximum working range is 250£gm*250£gm. We fabricated the 2D photonic crystal microcavity and DBR laser on the InGaAs/InAlGaAs which was grown by molecular beam epitaxy (MBE) on InP substrate. For the DBR laser, the length of Multi-mode Interference (MMI) was 90£gm to satisfied the emission wavelength and optical modes. We apply a coupled DBR reflector on both sides of MMI. The mirror width was 361nm and the air gap was 388nm. For the 2D photonic crystal (2D PhC) microcavity, a triangular array of air columns was adopted. The lattice constant and air columns radius are 1137nm and 456nm, respectively. The TE-mode photonic band gap of this structure is corresponding to wavelength range in 1517.01 nm~1617.81 nm. We leave a single defect in the 2D PhC to form 2D PhC microcavity and the corresponding defect modes are 1546.32nm and 1547.74nm. The Micro-PL measurement shows that a defect mode at 1547nm (a/£f=0.74), a surface state at 1351nm (a/£f=0.85), and a standing wave at 1480nm (a/£f=0.78). The maximum Q value is about 400 for the defect mode.

Free vibration of beam with moderate thickness is analyzed in the present study. Plane strain finite element is employed, which is based on 2-D elasticity. The conventional displacement-type variational principle is combined with Reissner¡¦s principle and a mixed-type variational formulation is derived. With such formulation, stresses, as well as displacements, are the primacy variables and both boundary conditions can be imposed exactly and simultaneously. Beams with various aspect ratios and boundary conditions are analyzed. Vibration frequencies and modes are obtained and compared to those by Euler¡¦s beam theory, Timoshenko beam theory, higher-order theory and displacement-type plane strain finite element method to see the effects of 2-D elasticity beam analysis compared to traditional 1-D theories, and the satisfying of stress boundary conditions, in addition to the displacement ones.

In this thesis, we fabricated the 2D photonic crystal and modified 1D photonic crystal microcavity on the InGaAs/GaAs substrate by E-beam lithography. The wafer are grown by molecular beam epitaxy (MBE) on GaAs substrate. The active layer consists of six InGaAs quantum wells at 1050nm emission wavelength. For the 1D photonic crystal microcavity (DBR laser),we changed the cavity shape and length to match the mode of light in the cavity. It can increase the reflectivity of the laser. In our simulations, we scanned different cavity length and found the corresponding data. We designed two and three pairs of DBRs formed on the edge of laser cavity, respectively. The cavity length is 121µm and the mirror width is 230nm and the air gap is 263nm. For the 2D photonic crystal (2DPC) microcavity, a triangular array of air columns was adopted. The lattice constant and air columns radius are 742nm and 304nm, respectively. The TE modes photonic band gap of this structure are corresponding to wavelength range in 1026nm ~ 1089nm. We placed single defect in the 2DPCs to form 2DPC microcavities and the corresponding defect modes are 1051.58nm¡B1053.39nm and 1054.87nm. In addition, we reduced the air columns around the cavity and simulated the photonic bandgap and fabricated the devices by E-beam lithography and deep dry etching process.

In this thesis, the properties of the metamaterials are studied. We analyze and discuss the artificial structure called metamaterials. The the effects on the radiation pattern and antenna gain are discussed when the structure is placed above the antenna. First, the propagation of electromagnetic wave in metamaterials is discussed. The metamaterial composed of metal rod array and split-ring is introduced. Next, the effects on permittivity, permeability and refraction index are studied when the structure parameters are changing. Thirdly, according to the above-mentioned summary, we use the structures to achieve an antenna radome. The radome can reduce 3 dB beam-width by about 31.25 percent at 10.75 GHz. The maximum gain achieves 7.25 dBi. In the fourth part, we also discusse the method of reducing the frequency band where negative refraction index occurs. The metamaterial is used to be a radome at the lower frequency band. The maximum gain is about 7.87 dBi. The 3 dB beam-width reduces by about 37.25 percent by the radome structure. Fifthly, the methods of improving the bandwidth are discussed when the antenna radome over the antenna . The enhancement of the antenna performance can be applied to the point-to-point communication. It also can save the cost of the feed network and the numbers of array antenna.

In this thesis, we fabricated the 2D photonic crystal microcavity and laterally coupled distributed feedback laser on InGaAs/InAlGaAs wafers by E-beam lithography. We also fabricated the 2D photonic crystal microcavity on the InGaAs/GaAs substrate at 980nm emission wavelength. The wafer are grown by molecular beam epitaxy (MBE). For the laterally coupled distributed feedback laser (LC-DFB laser) , we changed the grating shape and length to form proper grating, and it will make constructive diffraction and coupling. We design the mirror width is 180.55nm and the air gap is 541.65nm. For the 2D photonic crystal (2DPC) microcavity, a triangular array of air columns was adopted. The lattice constant and air columns radius are 1139nm and 456nm, respectively. The TE modes photonic band gap of this structure are corresponding to wavelength range in 1522.72nm~1617.89nm. We placed single defect in the 2DPCs to form 2DPC microcavities and the corresponding defect modes are 1549.23nm and 1550.08nm. We have simulated the photonic bandgap and fabricated the devices by E-beam lithography and deep dry etching process. Also, we can use the same method to fabricate 980nm photonic crystal.

In the present study, the buckling behavior of beams is analyzed by a plane strain finite element. The displacement-type finite element formulation based on two-dimensional elasticity of a buckling beam leads to an eigenvalue problem and is transformed again into another type of eigenvalue problem to eliminate iterations and possible difficulty during iterations and to obtain the various critical loads simultaneously. Comparing with conventional beam theories, the present approach needs no approximations or assumptions except that the width-to thickness ratio should be large enough for the beam to be considered as a plane strain case. Theoretically the present method should be more accurate than conventional beam theories and attractive than iterative method if the same accuracy is obtained, due to the economy in computation of the present method. Buckling strength under different beam geometry, type of loading, and boundary condition by the present approach will be compared with those by iterative method and various beam theories to test its validation and accuracy.

This thesis deals with a systematic procedure for the derivation of exact expression for the frequency equation of composite beams undergoing forced vibration with damping. The governing differential equations of motion of the composite beam are derived analytically for bending and shear deformation. The basic equations of Timoshenko beam theory and assumption of maximum rate of dissipation are employed. The principle involved is that of vibration energy dissipation due to damping as a result of deformation of materials in sandwich beam. The boundary conditions for displacements and forces for the cantilever beam are imposed and the frequency equation is obtained. The expressions for the amplitude of displacements are also derived in explicit analytical form. Numerical results of the displacement amplitude in cantilever sandwich beam varying with damping coefficient are evaluated.

The application of focused ion beam (FIB) technology in microfabrication has become increasingly popular. Its use in microfabrication has advantages over contemporary photolithography or other micromachining technologies, such as the ability to process without masks and being accommodating for a variety of materials and geometries. With the surface modification of the LED/air interface, like microlens array, the light emitting at large angle can be extracted because the incident angle at the interface will be less than the critical angle without total internal reflection. A microlens feature has been fabricated on GaN LED top surface (p-GaN layer) and back side (sapphire substrate) by scanning a focused Ga ion beam. The lens shape can be modulated by using computer-controlled beam direct writing and dwell time during milling process. We have used this technique even to create a sophisticated lens surface of Fresnel microlens array which can't be created with the conventional etching methods. In addition, the resistivity of p-GaN layer is highly sensitive to the process-induced damages during surface texturing, it is difficult to apply dry etching to p-GaN layer. Our method of using gas-assisted focused ion beam etching (GAFIBE) can enhance the etching rate by the assistance of chemical reaction with minimized ion dose density to provide nearly damage-free etching by varying the beam current, pixel dwell time and refresh time. Our study emphasis on direct milling and maskless techniques which can distinguish the FIB technology from the contemporary photolithography process and provide a vital alternative to it.

In this study, a vector form intrinsic finite element (VFIFE) is derived and applied to study both the static and dynamic responses of deep short beams under dynamic loadings. It is already known that the application of classical beam theory known as Euler¡¦s beam theory to beams with large ratio of D/L (depth/span larger than 1/4), a short-deep beam, may not necessarily obtain satisfactory results for the stress analysis of the beam. One of the main presumptions from the classical Euler¡¦s beam theory is that the plane of the cross-section remains plane and normal to the neutral axis of the beam after deformation. This presumption is no more true when the beam subject to loadings is a short-deep beam because the bending stress is no longer a dominant stress while the other secondary effects may have more severe influences on the mechanical behavior of the beam. This study by utilizing the vector form intrinsic finite element method (VFIFE) to derive a new element for the Timoshenko beam provides an alternative method for the analysis of a short-deep beam, particularly, subject to dynamic loadings. By taking the advantage of the VFIFE that is a time-saving scheme for the dynamic analysis, the element of Timoshenko-beam is derived along with the dynamic solution procedure. The motions in transverse direction and the rotation at each node of the beam are calculated and presented into figures. The results from numerical analysis are also verified with theoretical solution (exact analytical solution) and further compared to the results obtained from traditional finite element method.

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