Ring resonators with N × M couplers

Multiple-zero multiple-pole optical filter transfer functions may be implemented more efficiently in an integrated optics architecture if higher order N × M optical couplers are utilized. For example, a coherent ring resonator made from two 3×3 couplers offers some advantages over the three mirror Fabry-Perot etalon, which is its analog. To this end we develop the formalism for obtaining the transfer functions and scattering matrices of ring resonators made from two N × M couplers. We then present a methodology for analyzing serial and parallel systems of N × M optical coupler ring resonators.     

Theq-calculus for genericq andq a root of unity

Theq-calculus for genericq is developed and related to the deformed oscillator of parameterq ^1/2. By passing with care to the limit in whichq is a root of unity, one uncovers the full algebraic structure ofZ _n -graded fractional supersymmetry and its natural representation.Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996.This paper describes research supported in part by E.P.S.R.C and P.P.A.R.C. (UK) and by the C.I.C.Y.T (Spain). J.C.P.B. wishes to acknowledge an FPI grant from the CSIC and the Spanish Ministry of Education and Science.     

Identification and quantitation of phenylalanine, tyrosine and dihydroxyphenylalanine in the thoracic nervous system of the locust, Schistocerca gregaria, by gas chromatography-negative-ion chemical ionisation mass spectrometry

Phenylalanine, tyrosine and dihydroxyphenylalanine (DOPA) were identified unambiguously and quantitatively determined in single ventral thoracic nerve cords from the locust, Schistocerca gregaria, by gas chromatography-negative-ion chemical ionisation mass spectrometry. Deuterium-labelled analogues of each compound were added to a single ventral thoracic nerve cord in hydrochloric acid; the tissue was homogenised and the suspension centrifuged. The remaining hydrochloric acid was eliminated azeotropically by repeated additions of acetonitrile followed by evaporation under a stream of nitrogen and the resultant residue derivatised by reaction with hexafluoroisopropanol and pentafluoropropionic anhydride. Under negative-ion chemical ionisation conditions, the hexafluoroisopropanol-pentafluoropropionyl derivatives produced characteristic ions which were sufficiently abundant to be suitable for selected-ion monitoring. This method is highly specific and gave a limit of detection below the nanogram level. The amounts of phenylalanine, tyrosine and DOPA in a single ventral thoracic nerve cord were, respectively, 194 +/- 81, 347 +/- 88 and 11 +/- 11 ng per tissue.     

Self-Assembly and X-Ray Crystal Structures of Novel Sn(IV)Porphyrin Phenolates

A series of complexes of the type [Sn(TTP)L₂] have been prepared by the condensation of [Sn(TTP)OH₂] (TTP = meso-tetratolylporphyrin) with a range of substituted phenols. The resulting complexes were characterised using ¹H NMR and single crystal X-ray diffraction techniques. In each case, the condensation of the phenols with the Sn(IV)porphyrin in CDCl₃ solution is slow (h) but essentially quantitative. The slow kinetics of the formation of the diaxial phenolate complexes allows for the identification, by ¹H NMR spectroscopy, of three independent complexes within this process, namely an outer-sphere (H-bonded) complex as well as two independent phenolate complexes. The rate of condensation is in the order phenol 4-methoxyphenol > 4-nitrophenol and suggests a steric rather than pKa dependency.     

A comparison of phototautomerism in different sites of free-base porphin (H2P) in n-alkane crystals

Selective laser-induced phototautomerism of free-base porphin in different n-alkanes (n-hexane, n-heptane, n-octane, nnonane, n-decane, n-undecane and n-dodecane) has been used to identify tautomer splittings in a number of sites in polycrystalline samples at 2 K. Pairs or lines arising from the two molecular orientations in each site can be reversibly transformed into each other. In the odd n-alkanes the occupation of different sites was not dependent on the rate at which the samples were frozen, but in the even n-alkanes metastable sites were only occupied following rapid quenching.