Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement

Single mode silicon photonic wire waveguides allow low-loss sharp micro-bends, which enables compact photonic devices and circuits. The circuit compactness is achieved at the cost of loss induced by micro-bends, which can seriously affect the device performance. The bend loss strongly depends on the bend radius, polarization, waveguide dimension and profile. In this paper, we present the effect of waveguide profile on the bend loss. We present waveguide profile improvement with optimized etch chemistry and the role of etch chemistry in adapting the etch profile of silicon is investigated. We experimentally demonstrate that by making the waveguide sidewalls vertical, the bend loss can be reduced up to 25% without affecting the propagation loss of the photonic wires. The bend loss of a 2 μm bend has been reduced from 0.039dB/90° bend to 0.028dB/90° bend by changing the sidewall angle from 81° to 90°, respectively. The propagation loss of 2.7 ± 0.1dB/cm and 3 ± 0.09dB/cm was observed for sloped and vertical photonic wires respectively was obtained.     

Ultrafast and bias-free all-optical wavelength conversion using III-V-on-silicon technology

Using a 7.5 μm diameter disk fabricated with III-V-on-silicon fabrication technology, we demonstrate bias-free all-optical wavelength conversion for non-return-to-zero on-off keyed pseudorandom bit sequence (PRBS) data at the speed of 10 Gbits/s with an extinction ratio of more than 12 dB. The working principle of such a wavelength converter is based on free-carrier-induced refractive index modulation in a pump-probe configuration. We believe it to be the first bias-free on-chip demonstration of all-optical wavelength conversion using PRBS data. All-optical gating measurements in the pump-probe configuration with the same device have revealed that it is possible to achieve wavelength conversion beyond 20 Gbits/s.     

Scheduling a triple round robin tournament with minitournaments for the Finnish national youth ice hockey league

This paper presents a method to schedule a triple round robin tournament, which involves minitournaments, each hosted by one team. A key issue is that at the end of the season the number of home games should be balanced over the teams, despite the fact that in minitournament matches only the host team plays at home. This format is played in the Finnish national ice hockey league for players under the age of 20 years, where the problem is further complicated by many other constraints, for example, preassigned matches resulting from away tours that should limit the distances travelled by the teams. To obtain a schedule for this league, we sequentially solve four distinct combinatorial problems. This method allows us to construct a schedule for the 2009–2010 season, which is superior to the official schedule: it has no hard constraint violations, and outperforms the official schedule on three of five soft constraints.     

Breaks, cuts, and patterns

We generalize the concept of a break by considering pairs of arbitrary rounds. We show that a set of home-away patterns minimizing the number of generalized breaks cannot be found in polynomial time, unless P=NP. When all teams have the same break set, the decision version becomes easy; optimizing remains NP-hard.     

H-fields and their Liouville extensions

We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending , as well as the field of logarithmic-exponential series over are H-fields. We study Liouville extensions in the category of H-fields, as a step towards a model theory of H-fields. The main result is that an H-field has at most two Liouville closures. Received: 15 November 1999 / in final form: 19 December 2000 / Published online: 1 February 2002     

A note on the projecton of Gibbs measures

We give an example of a projection which maps two Gibbs measures for the same interaction into Gibbs measures for different interactions. As a corollary we find a case where by decimation a non-Gibbsian measure is transformed into a Gibbs measure.     

Independence of inadmissible strategies and best reply stability: a direct proof

Hillas (1990) introduced a definition of strategic stability based on perturbations of the best reply correspondence that satisfies all of the requirements given by Kohlberg and Mertens (1986). Hillas et al. (2001) point out though that the proofs of the iterated dominance and forward induction properties were not correct. They also provide a proof of the IIS property, a stronger version of both iterated dominance and forward induction, using the results of that paper. In this note we provide a direct proof of the IIS property.Received February 2002     

Kinetics of orientation of a side-chain liquid–crystal polymer as measured by a high-temperature SQUID-magnetometer

A superconducting quantum interference device (SQUID) magnetometer suitable for measurements of the magnetic susceptibility up to 600 K has been used to follow the kinetics of realignment in the nematic phase of a side-chain liquid–crystal polymer. Experiments are performed using monodomain and polydomain samples. Results obtained in monodomain samples are in quantitative agreement with the prediction of the continuum theory up to an angle of approximately 60°. Experiments conducted at higher starting angles give clear indication of backflow effects. Data obtained from experiments on polydomain samples have been compared with model calculations using the data on the monodomain samples. This comparison leads to the conclusion that in this case backflow effects play an important role, too. All results show that SQUID magnetometry allows monitoring of the kinetics of realignment with highest precision. © 1992 John Wiley & Sons, Inc.