Noise in optical amplifiers

This article presents an application of a recently published probablistic model for traveling wave optical amplification. Both optical signal and amplified spontaneous emission (ASE) noise are modeled as bunches of photons traveling along the amplifying region with size varying according to simple random rules. The results of the theory enable one to obtain a complete and accurate characterization of the signal and noise counting at the amplifier output. On the basis of the above statistics, we find a realistic evaluation of the limits imposed by both quantum and ASE noise on the performances of a receiver including an optical amplifier at a preamplifier stage.     

Heterocycles from ylides. Part VIII Reactivity of 2-arylmethylenebenzofuran-3-ones with stabilized sulphur ylides

2-Arylmethylenebenzofuran-3-ones react with carbonyl stabilized sulphur ylides yielding spiro-[cyclopropane-1,2′-benzofuran-3′-ones], whose structure and stereochemistry were assigned on the basis of spectroscopic data and chemical behaviour.     

Aromatization of aliphatic compounds—II: On the aromatization of some alkyl substituted cyclohexenones

2,3,5-Trimethyl-4-oxo-cyclohex-2-en acetic acid 5 treated with PyHCl aromatizes to the corresponding 2,3,5-trimethyl-benzene acetic acid 9 through a mechanism different from that leading to arylacetic acids from 2-oxo-cyclohex-3-en acetic acids 3. 2,3,4,6-Tetrakyl cyclohexenone 11, lacking the 2-carboxymethyl group, also aromatizes to tetralkyl benzene 13.     

Addition reactions of heterocycles. VI. Reactions of 1,2-dimethylpyrrole and 1-methyl-2-carbomethoxypyrrole with nitrilimines

Addition reactions of 1,2-dimethylpyrrole and 1-methyl-2-carbomethoxypyrrole with C-acetyl-N-phenylnitrilimine, have been investigated. 1,2-Dimethylpyrrole gives three different types of adducts: i.e. bis-cycloadducts (Vc) and (VIc), spirocycloadduct (IX), and non cyclic bis-adduct (XII). On the other hand, 1-methyl-2-carbomethoxypyrrole gives the bis-cycloadduct (VIb) only. Compound XII arises probably through a double 1,3-addition reaction, whereas the formation of cycloadducts Vc, VIc, and IX depends on the substituents present at C₂ of the pyrrole ring and consequentially on the intermediary occurence of mono-cycloadduct (IIIc), its methylenic tautomer VII, VIc, and XL The behaviour of the cycloadducts towards heating or acidic treatment showed a termal cleavage of the pyrazoline ring and acidic cleavage of the pyrrolidine ring.     

FIR Laser Lines from CH3OD: A Review

The methanol isotopic species CH₃OD has also proved to be an efficient and powerful medium to generate radiation in the far infrared (FIR) region. After the critical review of 1994, six papers have been published dealing with new FIR laser lines from this molecule. As a consequence of the use of wide tunability waveguide CO₂ lasers as well as a new pulsed CO₂ laser operating at hot and sequential bands, as of optical pumping sources, the total number of the FIR laser lines increased from 122 in 1994 to 227 today. In this communication we present an updated and complete catalogue of FIR laser lines generated from CH₃OD. Information on wavelength, offset, relative polarization, intensity, and optimum operation pressure is generally available.     

Rigorous bounds of the Lyapunov exponents of the one-dimensional random Ising model

We find analytic upper and lower bounds of the Lyapunov exponents of the product of random matrices related to the one-dimensional disordered Ising model, using a deterministic map which transforms the original system into a new one with smaller average couplings and magnetic fields. The iteration of the map gives bounds which estimate the Lyapunov exponents with increasing accuracy. We prove, in fact, that both the upper and the lower bounds converge to the Lyapunov exponents in the limit of infinite iterations of the map. A formal expression of the Lyapunov exponents is thus obtained in terms of the limit of a sequence. Our results allow us to introduce a new numerical procedure for the computation of the Lyapunov exponents which has a precision higher than Monte Carlo simulations.