Microstructure and photonic crystal fibers with periodic as well as random refractive-index distributions are investigated. Two cases corresponding to fibers with one-dimensional (1D) radial index distributions and two-dimensional (2D) transverse index distributions are considered. For 1D geometries with an arbitrary number of cladding layers, exact analytical solutions of guided modes are obtained using a matrix approach. In this part, for random index distributions, the average transmission properties are calculated and the influence of glass/air ratio on these properties is assessed. Important transmission properties of the fundamental mode, including normalized propagation constant, chromatic dispersion, field distributions, and effective area, are evaluated. For 2D geometries, the numerical techniques, FDTD (Finite-Difference Time-Domain) method and FDM (Finite Difference Method), are utilized. First, structures with periodic index distributions are examined. The investigation is then extended to microstructure optical fibers with random index distributions. Design of 2D microstructure fibers with random air-hole distributions is undertaken with the aim of achieving single-mode guiding property and small effective area. The former is a unique feature of the holey fiber with periodic air-hole arrangement and the latter is a suitable property for nonlinear fiber devices. Measurements of holey fibers with random air-hole distributions constitute an important experimental task of this research. Using a section of a holey fiber fabricated in the draw tower facility at Virginia Tech, measurements of transmission spectra and fiber attenuation are performed. Also, test results for far-field pattern measurements are presented. Another objective of this dissertation is to explore new applications for holey fibers with random or periodic hole distributions. In the course of measuring the holey fibers, it was noticed that robust temperature-insensitive pressure sensors can be made with these fibers. This offers an opportunity for new low-cost and reliable pressure fiber-optic sensors. Incorporating gratings into holey fibers in conjunction with the possibility of dynamic tuning offers desirable characteristics with potential applications in communications and sensing. Injecting gases or liquids in holey fibers with gratings changes their transmission characteristics. These changes may be exploited in designing tunable optical filters for communication applications or making gas/liquid sensor devices. / Ph. D.

We describe the theory and implementation of a multipole method for calculating the modes of microstructured optical fibers (MOFs). We develop tools for exploiting results obtained through the multipole method, including a discrete Bloch transform. Using the multipole method, we study in detail the physical nature of solid core MOF modes, and establish a distinction between localized defect modes and extended modes. Defect modes, including the fundamental mode, can undergo a localization transition we identify with the mode�s cutoff. We study numerically and theoretically the cutoff of the fundamental and the second mode extensively, and establish a cutoff diagram enabling us to predict with accuracy MOF properties, even for exotic MOF geometries. We study MOF dispersion and loss properties and develop unconventional MOF designs with low losses and ultra-flattened near-zero dispersion on a wide wavelength range. Using the cutoff-diagram we explain properties of these MOF designs.

We describe the theory and implementation of a multipole method for calculating the modes of microstructured optical fibers (MOFs). We develop tools for exploiting results obtained through the multipole method, including a discrete Bloch transform. Using the multipole method, we study in detail the physical nature of solid core MOF modes, and establish a distinction between localized defect modes and extended modes. Defect modes, including the fundamental mode, can undergo a localization transition we identify with the mode�s cutoff. We study numerically and theoretically the cutoff of the fundamental and the second mode extensively, and establish a cutoff diagram enabling us to predict with accuracy MOF properties, even for exotic MOF geometries. We study MOF dispersion and loss properties and develop unconventional MOF designs with low losses and ultra-flattened near-zero dispersion on a wide wavelength range. Using the cutoff-diagram we explain properties of these MOF designs.

Microstructured optical fibres (MOFs), also commonly called photonic crystal fibres or holey fibres, describe a type of optical fibre in which continuous channels of (typically) air run their entire length. These `holes' serve to both confine electromagnetic waves within the core of the fibre and to tailor its transmission properties. In order to understand and quantify both of these functions, a new computational algorithm was developed and implemented. It solves for the eigenvalues of Maxwell's wave equations in the two-dimensional waveguide cross-section, with radiating boundary conditions imposed outside the microstructure. This yields the leaky modes supported by the fibre. The boundary conditions are achieved exactly using a novel refinement scheme called the Adjustable Boundary Condition (ABC) method. Two implementations are programmed and their computational efficiencies are compared. Both use an azimuthal Fourier decomposition, but radially, a finite difference scheme is shown to be more efficient than a basis function expansion. The properties of the ABC method are then predicted theoretically using an original approach. It shows that the method is highly efficient, robust, automated and generally applicable to any implementation or to other radiating problems. A theoretical framework for the properties of modes in MOFs is also presented. It includes the use of the Bloch-Floquet theorem to provide a simpler and more efficient way to exploit microstructure symmetry. A new, but brief study of the modal birefringence properties in straight and spun fibres is also included. The theoretical and numerical tools are then applied to the study of polymer MOFs. Three types of fibres are numerically studied, fabricated and characterised. Each is of contemporary interest. Firstly, fabrication of the first MOFs with uniformly oriented elliptical holes is presented. A high degree of hole ellipticity is achieved using a simple technique relying on hole deformation during fibre draw. Both form and stress-optic birefringence are characterized over a broad scaled-wavelength range, which shows excellent agreement with numerical modelling. Secondly, an analysis of leaky modes in real air core MOFs, fabricated specifically for photonic band gap guidance, is then used to identify alternative guiding mechanisms. The supported leaky modes exhibit properties closely matching a simple hollow waveguide, weakly influenced by the surrounding microstructure. The analysis gives a quantitative determination of the wavelength dependent confinement loss of these modes and illustrates a mechanism not photonic band gap in origin by which colouration can be observed in such fibres. Finally, highly multimode MOFs (also called `air-clad' fibres) that have much wider light acceptance angles than conventional fibres are studied. An original and accurate method is presented for determining the numerical aperture of such fibres using leaky modes. The dependence on length, wavelength and various microstructure dimensions are evaluated for the first time for a class of fibres. These results show excellent agreement with published measurements on similar fibres and verify that bridge thicknesses much smaller than the wavelength are required for exceptionally high numerical apertures. The influence of multiple layers of holes on the numerical aperture and capture efficiency are then presented. It shows that a substantial increase in both these parameters can be achieved for some bridge thicknesses. Simple heuristic expressions for these quantities are given, which are based on the physical insight provided by the full numerical models. The work is then supported by the first fabrication attempts of large-core polymer MOFs with thin supporting bridges. These fibres exhibit relatively high numerical apertures and show good agreement with theoretical expectations over a very wide scaled-wavelength range.

Microstructured optical fibres (MOFs), also commonly called photonic crystal fibres or holey fibres, describe a type of optical fibre in which continuous channels of (typically) air run their entire length. These `holes' serve to both confine electromagnetic waves within the core of the fibre and to tailor its transmission properties. In order to understand and quantify both of these functions, a new computational algorithm was developed and implemented. It solves for the eigenvalues of Maxwell's wave equations in the two-dimensional waveguide cross-section, with radiating boundary conditions imposed outside the microstructure. This yields the leaky modes supported by the fibre. The boundary conditions are achieved exactly using a novel refinement scheme called the Adjustable Boundary Condition (ABC) method. Two implementations are programmed and their computational efficiencies are compared. Both use an azimuthal Fourier decomposition, but radially, a finite difference scheme is shown to be more efficient than a basis function expansion. The properties of the ABC method are then predicted theoretically using an original approach. It shows that the method is highly efficient, robust, automated and generally applicable to any implementation or to other radiating problems. A theoretical framework for the properties of modes in MOFs is also presented. It includes the use of the Bloch-Floquet theorem to provide a simpler and more efficient way to exploit microstructure symmetry. A new, but brief study of the modal birefringence properties in straight and spun fibres is also included. The theoretical and numerical tools are then applied to the study of polymer MOFs. Three types of fibres are numerically studied, fabricated and characterised. Each is of contemporary interest. Firstly, fabrication of the first MOFs with uniformly oriented elliptical holes is presented. A high degree of hole ellipticity is achieved using a simple technique relying on hole deformation during fibre draw. Both form and stress-optic birefringence are characterized over a broad scaled-wavelength range, which shows excellent agreement with numerical modelling. Secondly, an analysis of leaky modes in real air core MOFs, fabricated specifically for photonic band gap guidance, is then used to identify alternative guiding mechanisms. The supported leaky modes exhibit properties closely matching a simple hollow waveguide, weakly influenced by the surrounding microstructure. The analysis gives a quantitative determination of the wavelength dependent confinement loss of these modes and illustrates a mechanism not photonic band gap in origin by which colouration can be observed in such fibres. Finally, highly multimode MOFs (also called `air-clad' fibres) that have much wider light acceptance angles than conventional fibres are studied. An original and accurate method is presented for determining the numerical aperture of such fibres using leaky modes. The dependence on length, wavelength and various microstructure dimensions are evaluated for the first time for a class of fibres. These results show excellent agreement with published measurements on similar fibres and verify that bridge thicknesses much smaller than the wavelength are required for exceptionally high numerical apertures. The influence of multiple layers of holes on the numerical aperture and capture efficiency are then presented. It shows that a substantial increase in both these parameters can be achieved for some bridge thicknesses. Simple heuristic expressions for these quantities are given, which are based on the physical insight provided by the full numerical models. The work is then supported by the first fabrication attempts of large-core polymer MOFs with thin supporting bridges. These fibres exhibit relatively high numerical apertures and show good agreement with theoretical expectations over a very wide scaled-wavelength range.