A full-vectorial imaginary-distance beam propagation method based on a finite element scheme is newly formulated and is effectively applied to investigating the problem of leakage due to a finite ...number of arrays of air holes in photonic-crystal holey fibers (HFs). In order to treat arbitrarily shaped air holes and to avoid spurious solutions, a curvilinear edge/nodal hybrid element is introduced. Furthermore, in order to evaluate propagation characteristics of not only bound modes but leaky modes in HFs, an anisotropic perfectly matched layer is also employed as a boundary condition at computational window edges. It is confirmed from numerical results that the propagation loss increases rapidly with increasing wavelength, especially for HFs with one ring of smaller air holes, and that the propagation loss is drastically reduced by adding one more ring of air holes to the cladding region.
A new structure of single-polarization single-mode (SPSM) photonic crystal fiber (PCF) is proposed and analyzed by using a full-vector finite element method with anisotropic perfectly matched layers. ...From the numerical results it is confirmed that the proposed fiber is low-loss SPSM-PCF within the wavelengths ranging from 1.48 to 1.6 μm, where only the slow-axis mode exists and the confinement loss is less than 0.1 dB/km.
In order to control dispersion and dispersion slope of indexguiding photonic crystal fibers (PCFs), a new controlling technique of chromatic dispersion in PCF is reported. Moreover, our technique is ...applied to design PCF with both ultra-low dispersion and ultra-flattened dispersion in wide wavelength range. A full-vector finite element method with anisotropic perfectly matched layers is used to analyze the dispersion properties and the confinement losses in a PCF with finite number of air holes. It is shown from numerical results that it is possible to design a fourring PCF with flattened dispersion of 0 +/- 0.5 ps/(km.nm) from 1.19 m to 1.69 m wavelength range and a five-ring PCF with flattened dispersion of 0 +/- 0.4 ps/(km.nm) from 1.23 m to 1.72 m wavelength range.
A multiplexer-demultiplexer (MUX-DEMUX) based on PC waveguide couplers is proposed, and its wavelength demultiplexing properties are theoretically investigated. First, a two-channel MUX-DEMUX is ...designed and characterized, and then, by cascading, two stages of photonic crystal (PC) waveguide couplers with different coupling coefficients are constructed. The device sizes are expected to be drastically reduced from a scale of a few tens of micrometers to a scale of a few hundreds of micrometers in a MUX-DEMUX.
Recent progress on numerical modeling methods for photonic crystal fibers (PCFs) such as the effective index approach, basis-function expansion approach, and numerical approach is described. An ...index-guiding PCF with an array of air holes surrounding the silica core region has special characteristics compared with conventional single-mode fibers (SMFs). Using a full modal vector model, the fundamental characteristics of PCFs such as cutoff wavelength, confinement loss, modal birefringence, and chromatic dispersion are numerically investigated.
A novel design of polarization splitter in three-core photonic crystal fibers (PCFs) has been proposed. The three-core PCF consists of two given identical cores with two-fold symmetry separated by a ...core with high birefringence. The polarization splitter is based on the phenomenon of resonant tunneling. Numerical simulations with a full vectorial beam propagation method demonstrate that it is possible to obtain a 1.9-mm-long splitter with the extinction ratio better than -20 dB and a bandwidth of 37nm.
A rigorous full-vector finite element method is effectively applied to evaluating the effective area Aeff and the mode field diameter (MFD) of holey fibers (HFs) with finite cross sections. The ...effective modal spot size (a half of MFD), weff, is defined with the help of the second moment of the optical intensity distribution. The influence of hole diameter, hole pitch, operating wavelength, and number of rings of air holes on Aeff and weff is investigated in detail. As a result, it is shown that Aeff and weff are almost independent of the number of hole rings and that the relation Aeff = piweff 2, which is frequently utilized in the conventional optical fibers, does not always hold, especially in smaller air-filling fraction and/or longer wavelength regions. In addition, we find that for HFs with large air holes operating at longer wavelengths, the mode profiles of the two linearly polarized fundamental modes are significantly different from each other, even though they are degenerate. Using the values of Aeff and weff obtained here, the beam divergence and the nonlinear phase shift are calculated and are compared with the earlier experimental results.
We study the dispersion and leakage properties for the recently reported low-loss photonic band-gap fiber by Smith et al. Nature 424, 657 (2003). We find that surface modes have a significant impact ...on both the dispersion and leakage properties of the fundamental mode. Our dispersion results are in qualitative agreement with the dispersion profile reported recently by Ouzounov et al. Science 301, 1702 (2003) though our results suggest that the observed long-wavelength anomalous dispersion is due to an avoided crossing (with surface modes) rather than band-bending caused by the photonic band-gap boundary of the cladding.
A powerful algorithm based on a finite element method (FEM) is newly formulated for the analysis of waveguide discontinuities. In an earlier approach, FEM was applied to the finite region with ...discontinuities, and a mode expansion technique was applied to the uniform waveguides that are connected to the input and output ports of finite region. Although, in the present approach, the uniform waveguides are replaced by perfectly matched layer (PML) boundary conditions, it is possible to treat periodically varying waveguide structures such as photonic crystal (PC) waveguides. A combined method of beam propagation method (BPM) and FEM is also shown in such a form that a mode expansion technique is not required. To show the validity and usefulness of the present approach, numerical examples for optical gratings, circuit components based on PC waveguides and optical directional couplers are presented.
A unified approach using curvilinear hybrid edge/nodal elements with triangular shape is, for the first time, described for the study of guided-wave problems. Not only the lowest order (fundamental) ...but the higher order elements are systematically constructed. The advantage of curvilinear elements lies in the fact that they can model curved boundaries with more accuracy and lesser number of degrees of freedom than rectilinear elements. The vector basis functions derived here are also applicable to rectilinear cases. To show the validity and usefulness of the present approach, computed results are illustrated for rib waveguides with straight boundaries and circular waveguides with large refractive-index differences.
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