Interval-valued algebras and fuzzy logics

In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter

On the first place antitonicity in QL-implications

To obtain a demanded fuzzy implication in fuzzy systems, a number of desired properties have been proposed, among which the first place antitonicity, the second place isotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, R- and QL-implications all satisfy the second place isotonicity and the boundary conditions. However, not all the QL-implications satisfy the first place antitonicity as S- and R-implications do. In this paper we study the QL-implications satisfying the first place antitonicity. First we establish the relationship between the first place antitonicity and other required properties of QL-implications. Second we work on the conditions under which a QL-implication generated by different combinations of a t-conorm S, a t-norm T and a strong fuzzy negation N satisfy the first place antitonicity, especially in the cases that both S and T are continuous. We further investigate the interrelationships between S- and R-implications generated by left-continuous t-norms on one hand and QL-implications satisfying the first place antitonicity on the other

III-V-on-silicon photonic integrated circuits for communication and sensing applications

We review the integration of III-V semiconductors on silicon photonic integrated circuits as a way of realizing fully integrated silicon photonic transceivers and short-wave infrared spectroscopic sensors

Hybrid integrated mode-locked laser diodes with a silicon nitride extended cavity

Integrated semiconductor mode-locked lasers have shown promise in many applications and are readily fabricated using generic InP photonic integration platforms. However, the passive waveguides offered in such platforms have relatively high linear and nonlinear losses that limit the performance of these lasers. By extending such lasers with, for example, an external cavity the performance can be increased considerably. In this paper, we demonstrate for the first time that a high-performance mode-locked laser can be achieved with a butt-coupling integration technique using chip scale silicon nitride waveguides. A platform-independent SiN/SU8 coupler design is used to couple between the silicon nitride external cavity and the III/V active chip. Mode-locked lasers at 2.18 GHz and 15.5 GHz repetition rates are demonstrated with Lorentzian RF linewidths several orders of magnitude smaller than what has been demonstrated on monolithic InP platforms. The RF linewidth was 31 Hz for the 2.18 GHz laser.Comment: Submitted to Optics Expres

A III-V-on-Si ultra-dense comb laser

Optical frequency combs emerge as a promising technology that enables highly sensitive, near-real-time spectroscopy with a high resolution. The currently available comb generators are mostly based on bulky and high-cost femtosecond lasers for dense comb generation (line spacing in the range of 100 MHz to 1 GHz). However, their integrated and low-cost counterparts, which are integrated semiconductor mode-locked lasers, are limited by their large comb spacing, small number of lines and broad optical linewidth. In this study, we report a demonstration of a III-V-on-Si comb laser that can function as a compact, low-cost frequency comb generator after frequency stabilization. The use of low-loss passive silicon waveguides enables the integration of a long laser cavity, which enables the laser to be locked in the passive mode at a record-low 1 GHz repetition rate. The 12-nm 10-dB output optical spectrum and the notably small optical mode spacing results in a dense optical comb that consists of over 1400 equally spaced optical lines. The sub-kHz 10-dB radio frequency linewidth and the narrow longitudinal mode linewidth (<400 kHz) indicate notably stable mode-locking. Such integrated dense comb lasers are very promising, for example, for high-resolution and real-time spectroscopy applications