Solutions of the thin phase grating diffraction equation

An integral solution and a Bessel function solution of the thin phase grating difference-differential equation that describes diffraction by a thin arbitrarily-shaped periodic grating are presented and discussed.     

Tuning, attenuating, and switching by controlled flexure of long-period fiber gratings

Azimuthal variations in the refractive index that are inherent in CO(2) -laser-induced long-period fiber gratings (LPFG's) coupled to small controlled flexure of the LPFG produce a wide variety of transmission characteristics as a function of LPFG curvature. The particularly useful cases of (1) wavelength tuning at a constant attenuation and (2) variable attenuation (switching) at a constant wavelength are demonstrated by flexing of LPFG's that have been appropriately axially rotationally oriented relative to the plane of curvature.     

Donor-Acceptor Complexes in Copolymerization. XXXVII. Alternating Diene-Dienophile Copolymers. 5. Formation of Conjugated Diene-Maleic Anhydride Copolymers through Retrograde Dissociation of Furan-Maleic Anhydride Diels-Alder Adduct

Abstract

The equimolar, alternating copolymer of isoprene, as well as other conjugated dienes, and maleic anhydride is formed by the radical catalyzed reaction of the conjugated diene with maleic anhydride in the presence of furan as well as with the furan-maleic anhydride Diels-Alder adduct. The retrograde dissociation of the cyclic adduct above 60°C regenerates furan and maleic anhydride which in the presence of isoprene forms the isoprene-maleic anhydride ground state complex. The latter yields the corresponding cyclic adduct in the absence of a radical catalyst and undergoes excitation and homopolymerization in the presence of a catalyst.     

Donor-Acceptor Complexes in Copolymerization. XXXVI. Alternating Diene-Dienophile Copolymers. 4. Copolymerization of Furan and 2-Methylfuran with Maleic Anhydride

Abstract

The copolymerization of furan and 2-methylfuran with maleic anhydride in the presence of a radical catalyst yields equimolar, alternating copolymers in which the furan units have a 2,5-linkage (NMR and IR). The copolymerization appears to have a floor temperature of about 40°C. The furan-maleic anhydride Diels-Alder adduct polymerizes in solution in the presence of a radical catalyst at temperatures above 60°C to yield the identical copolymer as is obtained from the monomers. The adduct undergoes a retrograde reaction above 60°C to regenerate the monomers which then copolymerize through excitation of the ground state comonomer charge transfer complex.     

Donor-Acceptor Complexes in Copolymerization. XVII. NMR Analyses of Random and Alternating Styrene–α-Chloroacrylonitrile Copolymers

The NMR spectra of random and equimolar alternating copolymers of styrene with a-chloroacrylonitrile were studied. The monomer sequence distribution in the random copolymers, prepared in the presence of free radical catalysts, as determined from NMR analyses, was in accordance with the values expected from the r₁ and r₂ values derived from the conventional copolymerization theory. The alternating structure of the copolymer prepared by complexation with AlEt_1-5 Cl_1-5 was confirmed. The equimolar random copolymer, prepared by free radical initiation, was shown to contain essentially alternating sequences.     

Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses

In this paper, we report results of n₂ measurements of new chalcogenide glasses in the Ge-Sb-S-Se system using a modified Z-Scan technique. Measurements were made with picosecond pulses emitted by a 10 Hz Q-switched mode-locked Nd-YAG laser at 1064 nm under conditions suitable to characterize ultrafast nonlinearities. The nonlinear index increases up to 500 times the n₂ of fused silica with an increase in the Ge/Se ratio and a decrease with an increase of the Ge/Sb ratio. We confirmed, using Raman spectroscopy, that the nonlinear refractive index depends on the number of Ge-S(Se) and Sb-S(Se) bonds in the glass network. Sulfide glasses were shown to have a nonlinear FOM near or <1, at 1064 nm.     

Size‐Specific Interactions Between Single‐ and Double‐Stranded Oligonucleotides and Cationic Water‐Soluble Oligofluorenes

An improved synthetic approach was developed for the synthesis of 1,4‐bis[9′,9′‐bis(6″‐(N,N,N‐trimethylammonium)‐hexyl)‐fluoren‐2′‐yl]benzene tetrabromide ( 1a ), 1,4‐bis[9′,9′;9″,9″‐tetra(6″′‐(N,N,N‐trimethylammonium)‐hexyl)‐7′,2″‐bisfluoren‐2′‐yl] benzene octabromide ( 1b ) and 1,4‐bis[9′,9′;9″,9″;9″′,9″′‐hexakis(6″″‐(N,N,N‐trimethylammonium)‐hexyl)‐7′,2″,7″,2″′‐trifluoren‐2′‐yl] benzene dodecabromide ( 1c ). These molecules provide a size‐specific series of water‐soluble oligofluorene molecules with increasing numbers of repeat units to model the interactions between cationic conjugated polymers and DNA. Fluorescence quenching and energy‐transfer measurements were performed with 1a – c and single‐stranded (ss) DNA and double‐stranded (ds) DNA, with and without fluorescein (Fl). These studies show that, on a per‐negative‐charge basis, ssDNA quenches the emission of 1a – c more effectively than dsDNA. Furthermore, we show that the energy‐transfer ratios dsDNA–Fl/ssDNA–Fl are dependent on the number of repeat units in 1a – c .     

Electric field, permittivity, and strain distributions induced by interdigitated electrodes on electrooptic waveguides

Integrated optical interdigitated-electrode devices are used to diffract light and to launch acoustic waves. The electric field and the permittivity and strain tensors induced by a voltage applied to periodic interdigitated electrodes of finite thickness on the surface of an anisotropic electrooptic crystalline waveguide are calculated rigorously. A buffer layer between the electrodes and the waveguide is included in the analysis.     

Bound and quasibound state calculations for biased/unbiasedsemiconductor quantum heterostructures

A complex transcendental equation valid for a wide range of electron energies for semiconductor quantum heterostructures under unbiased or biased conditions is derived. Its complex roots have as real parts the structure eigenenergy levels, and their imaginary parts are directly related to the lifetime of the corresponding eigenenergies. A numerical method is presented that is capable of extracting all these complex eigenenergies. The method is based on the argument principle theorem from complex number theory. Therefore, all the energy levels and lifetimes of bound and quasibound states can be determined. Energy levels and lifetimes can also be calculated in the presence of scattering events when these are modeled with an energy broadening imaginary potential. Extensive comparisons between this numerical method and other currently used techniques are included, proving the generality and the accuracy of this new method