Strings propagating in the (2+1)-dimensional black hole anti-de Sitter spacetime.
We study the string propagation in the 2+1 black hole anti de Sitter background (2+1 BH-ADS). We find the first and second order fluctuations around the string center of mass and obtain the expression for the string mass. The string motion is stable, all fluctuations oscillate with real frequencies and are bounded, even at $r=0.$ We compare with the string motion in the ordinary black hole anti de Sitter spacetime, and in the black string background, where string instabilities develop and the fluctuations blow up at $r=0.$ We find the exact general solution for the circular string motion in all these backgrounds, it is given closely and completely in terms of elliptic functions. For the non-rotating black hole backgrounds the circular strings have a maximal bounded size $r_m,$ they contract and collapse into $r=0.$ No indefinitely growing strings, neither multi-string solutions are present in these backgrounds. In rotating spacetimes, both the 2+1 BH-ADS and the ordinary Kerr-ADS, the presence of angular momentum prevents the string from collapsing into $r=0.$ The circular string motion is also completely solved in the black hole de Sitter spacetime and in the black string background (dual of the 2+1 BH-ADS spacetime), in which expanding unbounded strings and multi-string solutions appear.
Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions
The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b 1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. The world-sheet time $\tau$ is an infinite-valued function of the string physical time, each branch yields a different string. This has no analogue in flat spacetime. We compute the string energy $E$ as a function of the string proper size $S$, and analyze it for the expanding and oscillating strings. For expanding strings $(\dot{S}>0)$: $E\neq 0$ even at $S=0$, $E$ decreases for small $S$ and increases $\propto\hspace*{-1mm}S$ for large $S$. For an oscillating string $(0\leq S\leq S_{max})$, the average energy $ $ over one oscillation period is expressed as a function of $S_{max}$ as a complete elliptic integral of the third kind.
Coherent pulsed injection seeding of two gain-switched semiconductor lasers
High-power, narrow-spectrum, short pulses at a wavelength near 830 nm are needed for optical logic applications. The authors report the generation of two coherent trains of pulses by pulsed injection seeding of two gain-switched semiconductor lasers with one mode-locked master oscillator. The available power was doubled and both lasers emit in nearly identical spectral lines. Short pulses (30-50 ps) are generated at a repetition rate of 1.9 GHz. The spectrum is reduced to a single mode cluster and shows a 1.7 AA wide chirp suitable for pulse compression. The peak power is 0.1 W for each pulse train. The capability of this technique for coherent power combining is demonstrated.<<ETX>>