Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Developing Single-Laser Sources for Multimodal Coherent Anti-Stokes Raman Scattering Microscopy

Coherent anti-Stokes Raman scattering (CARS) microscopy has developed rapidly and is opening the door to new types of experiments. This work describes the development of new laser sources for CARS microscopy and their use for different applications. It is specifically focused on multimodal nonlinear optical microscopy—the simultaneous combination of different imaging techniques. This allows us to address a diverse range of applications, such as the study of biomaterials, fluid inclusions, atherosclerosis, hepatitis C infection in cells, and ice formation in cells. For these applications new laser sources are developed that allow for practical multimodal imaging. For example, it is shown that using a single Ti:sapphire oscillator with a photonic crystal fiber, it is possible to develop a versatile multimodal imaging system using optimally chirped laser pulses. This system can perform simultaneous two photon excited fluorescence, second harmonic generation, and CARS microscopy. The versatility of the system is further demonstrated by showing that it is possible to probe different Raman modes using CARS microscopy simply by changing a time delay between the excitation beams. Using optimally chirped pulses also enables further simplification of the laser system required by using a single fiber laser combined with nonlinear optical fibers to perform effective multimodal imaging. While these sources are useful for practical multimodal imaging, it is believed that for further improvements in CARS microscopy sensitivity, new excitation schemes are necessary. This has led to the design of a new, high power, extended cavity oscillator that should be capable of implementing new excitation schemes for CARS microscopy as well as other techniques. Our interest in multimodal imaging has led us to other areas of research as well. For example, a fiber-coupling scheme for signal collection in the forward direction is demonstrated that allows for fluorescence lifetime imaging without significant temporal distortion. Also highlighted is an imaging artifact that is unique to CARS microscopy that can alter image interpretation, especially when using multimodal imaging. By combining expertise in nonlinear optics, laser development, fiber optics, and microscopy, we have developed systems and techniques that will be of benefit for multimodal CARS microscopy.