The connection between Mueller and Jones matrices of polarization optics

A necessary and sufficient condition for the 4 × 4 Mueller matrix to be derivable from the 2 × 2 Jones matrix is obtained. This condition allows one to determine if a given Mueller matrix describes a totally polarized system or a partially polarized (depolarizing) system. The result of Barakat is analysed in the light of this condition. A recently reported experimentally measured Mueller matrix is examined using this condition and is shown to represent a partially polarized system.

Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.

Systematic crystallographic investigation of hydrogen-bonded networks involving monohydrogen tartrate-amine complexes: Potential materials for nonlinear optics

Crystal structures of six binary salts involving aromatic amines as cations and hydrogen tartrates as anions are presented. The materials are 2,6-xylidinium-L-monohydrogen tartrate monohydrate, C12H18O6.5N, P22(1)2(1), a = 7.283(2) Angstrom, b = 17.030(2) Angstrom, c = 22.196(2) Angstrom, Z = 8; 2,6-xylidinium-D-dibenzoyl monohydrogen tartrate, C26H25O8N, P2(1), a = 7.906(1) Angstrom, b = 24.757(1) Angstrom, c = 13.166(1) Angstrom, beta = 105.01(1)degrees, Z = 4; 2,3-xylidinium-D-dibenzoyl monohydrogen tartrate monohydrate, C26H26O8.5N, P2(1), a = 7.837(1) Angstrom, b = 24.488(1) Angstrom, c = 13.763(1) Angstrom, beta = 105.69(1)degrees, Z = 4; 2-toluidinium-D-dibenzoyl monohydrogen tartrate, C25H23O8N, P2(1)2(1)2(1), a = 13.553(2) Angstrom, b = 15.869(3) Angstrom, c = 22.123(2) Angstrom, Z = 8; 3-toluidinium-D-dibenzoyl monohydrogen tartrate (1:1), C25H23O8N, P1, a = 7.916(3) Angstrom, b = 11.467(6) Angstrom, c = 14.203(8) Angstrom, alpha = 96.44(4)degrees, beta = 98.20(5)degrees, = 110.55(5)degrees, Z = 2; 3-toluidinium-D-dibenzoyl tartrate dihydrate (1:2), C32H36O10N, P1, a = 7.828(3) Angstrom, b = 8.233(1) Angstrom, c = 24.888(8) Angstrom, alpha = 93.98 degrees, beta = 94.58(3)degrees, = 89.99(2)degrees, Z = 2. An analysis of the hydrogen-bonding schemes in terms of crystal packing, stoichiometric variations, and substitutional variations in these materials provides insights to design hydrogen-bonded networks directed toward the engineering of crystalline nonlinear optical materials.

A New Method For The Generation Of 5,6-Quinolinedione 5-Methide .5. Synthesis Of Polycyclic Heteroaromatics

Reaction of 6-acetoxy-5-bromomethylquinoline (1c) and 2-bromomethyl-4-(2'-pyridyl)phenyl acetate (2b) with tetrachlorocatechol in acetone in the presence of anhydrous potassium carbonate resulted in the formation of diastereomeric products 3c, 3d, 4e and 4f.

2,4-Dichloro-6-methoxyquinoline

The title compound, C10H7Cl2NO, features a planar molecule, excluding the methyl H atoms [maximum deviation = 0.0385 (1) angstrom]. The crystal packing is stabilized by pi-pi stacking interactions across inversion centres [centroid-to-centroid distance = 3.736 (3) angstrom].

1,3-Dimethyl-2,6-diphenylpiperidin-4-one

In the title moleclue, C19H21NO, the 4-piperidone ring adopts a chair conformation in which the two benzene rings and the methyl group attached to C atoms all have equatorial orientations. In the crystal structure, centrosymmetric dimers are formed through weak intermolecular C-H center dot center dot center dot O hydrogen bonds [the dihedral angle between the aromatic rings is 58.51 (5)degrees].

Twist phase in Gaussian-beam optics

The recently discovered twist phase is studied in the context of the full ten-parameter family of partially coherent general anisotropic Gaussian Schell-model beams. It is shown that the nonnegativity requirement on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transverse coherence area of the beam. The twist phase as a two-point function is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an otherwise untwisted beam is shown to result in a linear transformation in the ray phase space of the Wigner distribution. Though this transformation preserves the four-dimensional phase-space volume, it is not symplectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interior of the set.

Unusual photodimerization of 7-fluoro-4-methylcoumarin and 6-fluoro-4-methylcoumarin in the solid state

Photodimerization of 7-fluoro-4-methylcoumarin 1 is topochemical while 6-fluoro-4-methylcoumarin 2 does not lead to the expected product based on the topochemical principles. Compound 1 yield an anti-MT photodimer with a lower dimer conversion while compound 2 results in a syn-HH photodimer. The packing features of 1, 2 and 2a (the photodimer of 2) have been unequivocally established by single crystal X-ray diffraction studies. The rationale for the significant lower dimer conversion in 1 is provided. The defect induced dimerization reaction in 2 as a function of temperature is analyzed which verifies that the reaction proceeds with an induction period. The details of the interactions involving fluorine are analyzed.

Colossal dielectric behavior of semiconducting $Sr_{2}TiMnO_{6}$ ceramics

Manganitelike double perovskite Sr2TiMnO6 (STMO) ceramics fabricated from the powders synthesized via the solid-state reaction route, exhibited dielectric constants as high as similar to 10(5) in the low frequency range (100 Hz-10 kHz) at room temperature. The Maxwell-Wagner type of relaxation mechanism was found to be more appropriate to rationalize such high dielectric constant values akin to that observed in materials such as KxTiyNi(1-x-y)O and CaCu3Ti4O12. The dielectric measurements carried out on the samples with different thicknesses and electrode materials reflected the influence of extrinsic effects. The impedance studies (100 Hz-10 MHz) in the 180-300 K temperature range revealed the presence of two dielectric relaxations corresponding to the grain boundary and the electrode. The dielectric response of the grain boundary was found to be weakly dependent on the dc bias field (up to 11 V/cm). However, owing to the electrode polarization, the applied ac/dc field had significant effect on the low frequency dielectric response. At low temperatures (100-180 K), the dc conductivity of STMO followed a variable range hopping behavior. Above 180 K, it followed the Arrhenius behavior because of the thermally activated conduction process. The bulk conductivity relaxation owing to the localized hopping of charge carriers obeyed the typical universal dielectric response.

Bridged systems via radical cyclization reactions. Stereospecific synthesis of chiral tricyclo[6.2.1.0(1,5)]undecanes

The application of radical-mediated cyclizations and annulations in organic synthesis has grown in importance steadily over the years to reach the present status where they are now routinely used in the strategy-level planning.2 The presence of a quaternary carbon atom is frequently encountered in terpenoid natural products, and it often creates a synthetic challenge when two or more quaternary carbon atoms are present in a contiguous manner.3 Even though creation of a quaternary carbon atom by employing a tertiary radical is very facile, creation of a quaternary carbon atom (or a spiro carbon atom) via radical addition onto a fully substituted olefinic carbon atom is not that common but of synthetic importance. For example, the primary radical derived from the bromide 1 failed to cyclize to generate the two vicinal quaternary carbon atoms and resulted in only the reduced product 2.4 The tricyclic carbon framework tricyclo[6.2.1.01,5]undecane (3) is present in a number of sesquiterpenoids e.g. zizzanes, prelacinanes, etc.5

DC-SIGN and alpha 2,6-sialylated IgG Fc interaction is dispensable for the anti-inflammatory activity of IVIg on human dendritic cells

Intravenous immunoglobulin (IVIg) is widely used to treat autoimmune diseases. Several mutually nonexclusive mechanisms are proposed to explain the beneficial effects of IVIg in patients (1, 2). Lately, Ravetch and colleagues (3) demonstrate that anti-inflammatory activity of IVIg is mediated mainly by antibodies that contain terminal _2,6-sialic acid linkages at the Asn297-linked glycan of Fc region.

Imaging in turbid media using quasi-ballistic photons

We study by means of experiments and Monte Carlo simulations, the scattering of light in random media, to determine the distance up to which photons travel along almost undeviated paths within a scattering medium, and are therefore capable of casting a shadow of an opaque inclusion embedded within the medium. Such photons are isolated by polarisation discrimination wherein the plane of linear polarisation of the input light is continuously rotated and the polarisation preserving component of the emerging light is extracted by means of a Fourier transform. This technique is a software implementation of lock-in detection. We find that images may be recovered to a depth far in excess of that predicted by the diffusion theory of photon propagation. To understand our experimental results, we perform Monte Carlo simulations to model the random walk behaviour of the multiply scattered photons. We present a. new definition of a diffusing photon in terms of the memory of its initial direction of propagation, which we then quantify in terms of an angular correlation function. This redefinition yields the penetration depth of the polarisation preserving photons. Based on these results, we have formulated a model to understand shadow formation in a turbid medium, the predictions of which are in good agreement with our experimental results.

3,3,6,6-Tetramethyl-9-phenyl-3,4,5,6-tetrahydro-9H-xanthene-1,8(2H,7H)-dione

In the title compound, C23H26O3, the three six-membered rings of the xanthene system are non-planar, having total puckering amplitudes, QT, of 0.443 (2), 0.202 (2) and 0.449 (2) Å. The central ring adopts a boat conformation and the outer rings adopt sofa conformations. The crystal structure is stabilized by van der Waals interactions.

A thermal molecular migration in the solid-state - structures of isomeric 5-amino-4-(2,6-dichlorophenyl)-1-(2-nitrophenyl)-1h-1,2,3-triazole (yellow form i) and 4-(2,6-dichlorophenyl)-5-(2-nitroanilino)-2h-1,2,3-triazole (red form-ii), c14h9cl2n5o2

Yellow form (I): Mr= 350.09, monoclinic, P2Jn, Z--4, a=9.525(1), b=14.762(1), c= 11.268(1),/t, fl= 107.82 (1) o , V= 1508.3 A 3 , Din(flotation in aqueous KI)= 1.539 (2), D x= 1.541 (2) g cm -3, #(Cu Ka, 2 = 1.5418 A) = 40.58 cm -~, F(000) = 712, T= 293 K, R = 8.8% for 2054 significant refections. Red form (II): Mr= 350.09, triclinic, Pi, Z=2, a=9.796(2), b= 10.750 (2), c= 7.421 (1)A, a= 95.29 (2), fl= 0108-2701/84/111901-05501.50 70.18 (1), y = 92-.76 (2) °, V= 731.9 A 3, Din(flotation in KI) = 1.585 (3), D x = 1.588 (3) g cm -3, ~t(Cu Ka, 2 = 1.5418/~) = 40.58 cm -1, F(000) = 356, T=293 K, R = 5.8% for 1866 significant reflections. There are no unusual bond distances or angles. The triazole and two phenyl rings are planar. On the basis of packing considerations the possibility of intermolecular interactions playing a role in the reactivity of the starting material is ruled out.

Structure of the Monosodium Salt of D-Glucose 6-Hydrogenphosphate

Na+.C6HI209 P-, Mr=282.1, monoclinic, e2~, a=5-762(1), b=7.163(2), c=12.313(1)A, fl= 99.97 (1) °, U= 500.5 A 3, Z= 2, D m = 1.86, D x = 1.87 Mg m -s, Cu Ka, 2 = 1.5418 A, /a = 3-3 mm -1, F(000) = 292, T= 300 K, final R for 922 observed reflections is 0-042. The phosphate ester bond, P-O(6), is 1.575 (5)A, slightly shorter than the P~O bond in monopotassium phosphoenolpyruvate [1.612 (6) A] [Hosur & Viswamitra (1981). Acta Cryst. B37, 839-843]. The pyranose sugar ring takes a 4C 1 chair conformation. The conformation about the exocyclic C(5)-C(6) bond is gauche-trans. The endocyclic C-O bonds in the glucose ring are nearly equal with C(5)-O(5) = 1.435 (8) and C(1)-O(5) = 1.436 (9) A. The sodium ion has seven near neighbours within a distance of 2.9 A. The crystal structure is stabilized by hydrogen bonds between the O atoms of symmetryrelated molecules.