Jan-Philipp Roth, Thomas Kühler and Elmar Griese
For the realization of optical waveguide components, needed for photonic integrated circuits, multimode-interference based (MMI-based) devices are an excellent component class for…
Abstract
Purpose
For the realization of optical waveguide components, needed for photonic integrated circuits, multimode-interference based (MMI-based) devices are an excellent component class for the realization of low loss optical splitters. A promising approach to the manufacturing of these components is their embedding in thin glass sheets by ion-exchange diffusion processes, which has not yet been extensively studied. This study aims to significantly enhance the modeling of the diffusion process to support manufacturing of graded-index, MMI-based optical splitters.
Design/methodology/approach
The methods of design and analysis of MMI-based components are based on a step-index refractive index profile. In this work, fundamental correlations between the properties of the manufacturing ion-exchange process and the characteristics of the graded-index, MMI-based components are established. The refractive index profile is calculated with a proprietary solver based on the finite element method. Any further investigation with respect to parameter influence is based on the beam propagation method, specifically a finite difference based, semi-vectorial, wide-angle beam propagation algorithm. The influence of the parameters of the self-imaging effect is investigated. On this basis, different approaches for efficient power splitting with graded-index, MMI-based waveguide components are evaluated.
Findings
Easy approximations – mostly linear – can be found to model the dependencies of the investigated parameters. The resulting graded-index splitters are characterized by their low excess and insertion loss.
Originality/value
These findings are the first step in the direction of the semi-analytical modeling of the respective waveguide components to reduce the numerical effort.
Details
Keywords
Ich habe genug (I have enough) BWV 82 is one of the best known, most regularly performed and consistently recorded of J.S. Bach's approximately 200 extant sacred cantatas.1 In the…
Abstract
Ich habe genug (I have enough) BWV 82 is one of the best known, most regularly performed and consistently recorded of J.S. Bach's approximately 200 extant sacred cantatas.1 In the text, by an anonymous author, the narrator repeatedly expresses their readiness to die, in faith that they will be received by their saviour in eternal life. The whole cantata expresses a fearless ‘longing for death’ (Schweitzer, 1911/1966, p. 114), coupled with a serene contentment. Bach's setting of this text for religious purposes not only supports the sentiments expressed by the narrator but colours, illuminates, vitalises and elevates it in ways that startle the ear, quicken the spirit and stir the imagination. In the third and final aria of the cantata, Bach employs an almost-jaunty dance rhythm to accompany the narrator's anticipatory delight in their own death, liberated from worldly and bodily suffering. After identifying some of the ingenious ways Bach animates the text, I offer some speculations and elaborations as to how and why this work has had such an enduring presence in the Western musical canon, for believers and non-believers alike.