Finite element analysis of photonic crystal fibers

A finite-element-based vectorial optical mode solver, furnished with Bayliss-Gunzburger-Turkel-like transparent boundary conditions, is used to rigorously analyze photonic crystal fibers (PCFs). Both the real and imaginary part of the modal indices can be computed in a relatively small computational domain. The leakage loss, the dispersion properties, the vectorial character, as well as the degeneracy of modes of the fibers can be studied through the finite element results. Results for PCFs with either circular or non-circular microstructured holes, solidor air-core will be presented, including the air-core air-silica Bragg fiber. Using the mode solver, the single-modeness of a commercial endlessly single-mode PCF was also investigated

Modelling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions

Finite element vectorial optical mode solver is used to analyze microstructured waveguides in a relatively small computational domain. The presentation will consider the computational method, as well as the applications of it on a number of waveguides with 2-D cross section where microstructures are employed

A finite element characterization of a commercial endlessly single-mode photonic crystal fiber: is it really single mode?

One of interesting properties of photonic crystal fibers (PCFs) is their possibility to be single-moded over a wide wavelength range, down to UV, while still having a reasonably large modal profile. Such properties are attractive for applications like optical sensing, interferometry, and transport of white light. PCFs, which is designed specially for such property are known as the endlessly single-mode (ESM-) PCFs [1].\ud However, the ESM property requires the holey cladding of a PCF to have a small air-filling factor. Such a requirement indeed creates problems for PCF manufacturers, as it does not go in harmony with other equally important properties of the PCF. A small air filling factor implies large leakage loss. So, the characteristics of commercially available ESM-PCFs, in fact come out from compromises between the desirable endlessly-single-modeness and the low leakage loss properties. Hence, depending on the type of applications, the term ESM itself could mislead its users, if the endlessly single modeness is presumed without proper precautions.\ud In this work, using a vectorial finite-element leaky mode solver published recently [2], several dominant leaky modes of a commercial ESM-PCF [3] were investigated. Although the leakage loss of the fundamental mode is already 6 orders lower (on a dB/unit-length scale) than that of the nearest higher order modes, the leakage losses of these higher order modes are still quite low, which might still be significant, especially for short wavelength and short fiber-length applications. In addition to the ordinary-fiber-like hybrid core modes, the existence and significance of unusual modes like cladding-resonance modes and core-cladding-resonance modes were also numerically observed. Based on the loss discrimination between the most dominant and the nearest higher order mode, we set-up a criterion for the single-modeness. Using that measure, we verified the single-modeness of the corresponding ESM-PCF and found that the endlessly single-modeness is valid only for a relatively long fiber, typical of local area network applications. This finding implies that applications employing short fiber-length, working in short wavelength regimes, should be prepared for significant effects of the higher order modes, e.g. by employing a mode stripper to suppress their effects. We suggest that ESM-PCF for short fiber-length applications need to be designed differently from those for long fiber-length applications.\ud \ud References\ud [1]. T.A. Birks, J.C. Knight, and P.S.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., Vol. 22, No. 13, pp. 961-963, 1997.\ud [2]. H.P. Uranus and H.J.W.M. Hoekstra, “Modelling of microstructured waveguides using a finite-element based vectorial mode solver with transparent boundary conditions,” Opt. Express, Vol. 12, No. 12, pp. 2795-2809, 2004.\ud [3]. www.crystal-fibre.com/datasheets/ESM%20-%2012%20-%2001.pdf\u

Simple high-order Galerkin finite element scheme for the investigation of both guided and leaky modes in axially anisotropic planar waveguides

A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with diagonal permitivity tensor. Schemes up to 8th-order of accuracy in the effective index are demonstrated

Modes of an endlessly single-mode photonic crystal fiber: a finite element investigation

Using a finite-element mode solver, the modes of a commercial endlessly single-mode photonic crystal fiber (ESM-PCF) were investigated. Based on the loss discrimination between the dominant and the nearest higher order mode, we set-up a criterion for the single-modeness. Using that measure, we verified the single-modeness of the corresponding ESM-PCF and found that the endlessly single-modeness are valid only for relatively long fiber-length applications. Based on this, we suggest that ESM-PCF for short fiber-length applications should be designed differently from those for long fiber-length applications

Scaling relations for galaxy clusters: properties and evolution

Well-calibrated scaling relations between the observable properties and the total masses of clusters of galaxies are important for understanding the physical processes that give rise to these relations. They are also a critical ingredient for studies that aim to constrain cosmological parameters using galaxy clusters. For this reason much effort has been spent during the last decade to better understand and interpret relations of the properties of the intra-cluster medium. Improved X-ray data have expanded the mass range down to galaxy groups, whereas SZ surveys have openened a new observational window on the intracluster medium. In addition,continued progress in the performance of cosmological simulations has allowed a better understanding of the physical processes and selection effects affecting the observed scaling relations. Here we review the recent literature on various scaling relations, focussing on the latest observational measurements and the progress in our understanding of the deviations from self similarity.Comment: 38 pages. Review paper. Accepted for publication in Space Science Reviews (eds: S. Ettori, M. Meneghetti). This is a product of the work done by an international team at the International Space Science Institute (ISSI) in Bern on "Astrophysics and Cosmology with Galaxy Clusters: the X-ray and Lensing View