Two-photon resonant three-photon ionization with ultrashort pulses

The problem of two-photon resonant three-photon ionization is analysed for the case of ultrashort ionizing pulses. An analytic solution to the problem is obtained and discussed. A simple experiment is proposed which would demonstrate the effect of optical nutation on the photoelectron flux.     

The role of the interactive Kerr effect in two-photon optical multistability

We show that bistable behaviour in a two-photon resonant system within a cavity may be attributed to interactive mode-pulling via the two-photon optical Kerr effect and also to absorptive bleaching (atomic saturation). The interactive Kerr process may be regarded as giving rise to a new category of optical bistability. Moreover, a mechanism for the recently-predicted tristability can be found in terms of simultaneous competition between the interactive Kerr effect and bleaching.     

Incompatibility of polarization-division multiplexing with wavelength-division multiplexing in soliton-transmission systems

In a recent experiment it was demonstrated that polarization-division multiplexing was incompatible with wavelength-division multiplexing. We discuss a theoretical model that explains this result.     

Structure-function correlations in Iron(II) tris(pyrazolyl)borate spin-state crossover complexes

Iron(II) poly(pyrazolyl)borate complexes have been investigated to determine the impact of substituent effects, intramolecular ligand distortions, and intermolecular supramolecular structures on the spin-state crossover (SCO) behavior. The molecular structure of Fe[HB(3,4,5-Me3pz)3]2 (pz = pyrazolyl ring), a complex known to remain high spin when the temperature is lowered, reveals that this complex has an intramolecular ring-twist distortion that is not observed in analogous complexes that do exhibit a SCO at low temperatures, thus indicating that this distortion greatly influences the properties of these complexes. The structure of Fe[B(3-(cy)Prpz)4]2.(CH3OH) ((cy)Pr = cyclopropyl ring) at 294 K has two independent molecules in the unit cell, both of which are high spin; only one of these high-spin iron(II) sites, the site with the lesser ring-twist distortion, is observed to be low-spin iron(II) in the 90 K structure. A careful evaluation of the supramolecular structures of these complexes and several similar complexes reported previously revealed no strong correlation between the supramolecular packing forces and their SCO behavior. Magnetic and M?ssbauer spectral measurements on Fe[B(3-(cy)Prpz)4]2 and Fe[HB(3-(cy)Prpz)3]2 indicate that both complexes exhibit a partial SCO from fully high-spin iron(II) at higher temperatures, respectively, to a 50:50 high-spin/low-spin mixture of iron(II) below 100 K. These results may be understood, in the former case, by the differences in ring-twisting and, in the latter case, by a phase transition; in all complexes in which a phase transition is observed, this change dominates the SCO behavior. A comparison of the M?ssbauer spectral properties of these two complexes and of Fe[HB(3-Mepz)3]2 with that of other complexes reveals correlations between the M?ssbauer-effect isomer shift and the average Fe-N bond distance and between the quadrupole splitting and the average FeN-NB intraligand dihedral torsion angles and the distortion of the average N-Fe-N intraligand bond angles.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Statistical properties in the chaotic regime of the Maxwell-Bloch equations

The statistical properties of the electric field solution of the Maxwell-Bloch equations describing a single mode, homogeneously broadened laser in the mean field limit are investigated in the strange attractor regime. The electric field distribution sis calculated and it is found that the low order intensity moments are somewhat higher than those for thermal-chaotic light whilst the higher order moments are substantially lower. The field and intensity correlation functions are also calculated and found to exhibit radically different behaviour. The results are interpreted in terms of iterative map which is dederived using multiple time-scale perturbation theory. It is shown that a simple random phasor model is compatible with the numerical data.     

Solitons in fibers with polarization mode dispersion

Evaluating the relative time displacement of the two orthogonally polarized components of a pulse propagating down a birefringent optical fiber is considered. A method that provides analytical expressions for this time displacement is described and generalizes analytical results already published.