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

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

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

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

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