On non-abelian extensions of 3-Lie algebras

In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed.Comment: 17 page

Integrated Phase-locked Laser Diodes at 1.55μm

Two types of integrated phased locked laser diodes operating at 1.55 μm were demonstrated, using either a distributed feedback laser seeding source or a self-locking multi-mode interference array. Both exhibited far field patterns that reflected mutual coherence between the light from the output waveguides

1.55 µm AlGaInAs/InP sampled grating laser diodes for mode-locking at THz frequencies

We report mode locking in lasers integrated with semiconductor optical amplifiers, using either conventional or phase shifted sampled grating distributed Bragg reflectors(DBRs). For a conventional sampled grating with a continuous grating coupling coefficient of ~80 cm-1, mode-locking was observed at a fundamental frequency of 628 GHz and second harmonic of 1.20 THz. The peak output power was up to 142 mW. In the phase shifted sampled grating design, the grating is present along the entire length of the reflector with π-phase shift steps within each sampled section. The effective coupling coefficient is therefore increased substantially. Although the continuous grating coupling coefficient for the phase shifted gratings was reduced to ~23 cm-1 because of a different fabrication technology, the lasers demonstrated mode locking at fundamental repetition frequencies of 620 GHz and 1 THz, with a much lower level of amplified spontaneous emission seen in the output spectra than from conventional sampled grating devices. Although high pulse reproducibility and controllability over a wide operation range was seen for both types of grating, the π-phase-shifted gratings already demonstrate fundamental mode-locking to 1 THz. The integrated semiconductor optical amplifier makes sampled grating DBR lasers ideal pump sources for generating THz signals through photomixing

THz Repetition Frequency Mode-Locked Laser Using Novel Sampled Gratings

Conventional sampled grating distributed-Bragg-gratings (C-SGDBRs) are widely used in tunable DBR lasers [1], and more recently have been used to precisely control the wavelength spacing in arrays of DBR lasers for use in WDM systems [2], and as the reflectors in THz repetition frequency (Fr) semiconductor mode locked lasers (SMLLs) [3]. However, the effective coupling coefficient, κ, of a C-SGDBR (Fig. 1(a)) is necessarily reduced substantially from that of a uniform grating because much of the sampled grating period has no grating. Here, for the first time, we apply a combination of π-phase shifted gratings, previously demonstrated in fiber lasers [4], with the C-SGDBR technique to THz repetition frequency SMLLs. Using a single electron beam lithography (EBL) step we have demonstrated a 620 GHz side-wall SGDBR MLL with an increased effective κ