Out-of-plane coupling structures for optical printed circuit boards

We present an integrated total internal reflection mirror and pluggable coupler that can be used for out-of-plane coupling in an optical PCB. The coupling efficiency of both mirror configurations is measured and compared

Embedded 45° micro-mirror for out-of-plane coupling in optical PCBs

We present an embedded 45° micro-mirror that can be used to couple light out-of-plane of the optical layer. The discrete micro-mirror is inserted in a micro-cavity into the optical layer. Loss measurements at receiver side show a mirror loss as low as 0.35dB

Pairing and duality of algebraic quantum groupoids

Algebraic quantum groupoids have been developed by two of the authors (AVD and SHW) of this note in a series of papers. Regular multiplier Hopf algebroids are obtained also by two authors (TT and AVD). Integral theory and duality for those have been studied by one author here (TT). Finally, again two authors of us (TT and AVD) have investigated the relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. In the paper 'Weak multiplier Hopf algebras III. Integrals and duality' (by AVD and SHW), one of the main results is that the dual of an algebraic quantum groupoid, admits a dual of the same type. In the paper 'On duality of algebraic quantum groupoids' (by TT), a result of the same nature is obtained for regular multiplier Hopf algebroids with a single faithful integral. The duality of regular weak multiplier Hopf algebras with a single integral can be obtained from the duality of regular multiplier Hopf algebroids. That is however not the obvious way to obtain this result. It is more difficult and less natural than the direct way. We will discuss this statement further in the paper. Nevertheless, it is interesting to investigate the relation between the two approaches to duality in greater detail. This is what we do in this paper. We build further on the intimate relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. We now add the presence of integrals. That seems to be done best in a framework of dual pairs. It is in fact more general than the duality of these objects coming with integrals

Towards Low Cost Coupling Structures for Short-Distance Optical Interconnections

The performance of short distance optical interconnections in general relies very strongly on coupling structures, since they will determine the overall efficiency of the system to a large extent. Different configurations can be considered and a variety of manufacturing technologies can be used. We present two different discrete and two different integrated coupling components which can be used to deflect the light beam over 90 degrees and can play a crucial role when integrating optical interconnections in printed circuit boards. The fabrication process of the different coupling structures is discussed and experimental results are shown. The main characteristics of the coupling structures are given. The main advantages and disadvantages of the different components are discussed

Comment on: a two-stage fourth-order “almost” P-stable method for oscillatory problems

AbstractIn Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118) a fourth-order “almost” P-stable method for y″=f(x,y) is proposed. We claim that it is possible to retrieve this combination of multistep methods by means of the theory of parameterized Runge-Kutta-Nyström (RKN) methods and moreover to generalize the method discussed by Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118)

Opto-PCB: Three demonstrators for optical interconnections

We report on a research project targeting optical waveguide integrated PCBs conducted within the European FP6 Network of Excellence on Micro-Optics NEMO. For three identified feature requests we have built three specific demonstrators respectively addressing the integration of active components, the fabrication of peripheral fibre ribbons and the integration of multiple layers of waveguides on the board