Enhanced complete photonic band gap in the optimized planar diamond structure

The diamond photonic crystal with dielectric rods has been modified to enlarge the fundamental band gap. By planarizing the diamond structure and reducing the thickness of the hexagonal meshes, the band gap can be increased substantially. The band gap is 29% for a refractive index contrast of 3.6. The modified structure is amenable to fabrication at optical and infrared wavelengths using state-of-the-art silicon-processing methods. Transfer matrix calculations demonstrate a large attenuation within the band gap.     

Differential operators and immersions of a Riemann surface into a Grassmannian

We consider equivariant holomorphic immersions of a universal cover of a compact Riemann surface X into a Grassmannian satisfying a nondegeneracy condition. The equivariance condition says that there is a homomorphism ρ of the Galois group to that takes the natural action of the Galois group on to the action of the Galois group on defined using ρ. We prove that the space of such embeddings are in bijective correspondence with the space of all holomorphic differential operators of order two on a rank n vector bundle over X with the property that the symbol of the operator is an isomorphism.     

Quantization and contact structure on manifolds with projective structure

We consider complex manifolds with a class of holomorphic coordinate functions satisfying the condition that each transition function is given by the standard action on of some element in . We show that such a manifold has a natural contact structure. Given any contact manifold, one can associate with it a symplectic manifold. It is shown that the symplectic manifolds arising from complex manifolds with special coordinate functions of the above type admit a canonical quantization.     

Analysis of BPSK homodyne receivers based on modified balanced optical phase-locked loop in the presence of non-negligible loop propagation delay

Optical homodyne receivers based on modified balanced optical phase-locked loop is analyzed taking into account loop propagation delay. This modified loop contains all the components of a standard BOPLL in conjunction of an additional phase modulator. This modified loop offers a much improved tracking performance and also shows good improvements in the reduction performance over previously reported methods, like, relaxed line-width requirement and improved lock-in range. This study for the first time shows the imperfect-phase-recovery-induced power penalty as a function of laser line-width with the optimum phase deviations in the presence of non-negligible loop propagation delay. It is found that in order to maintain a 10⁻¹⁰ BER system performance with ξ = 1, R = 1 A/W, P_R = −53 dBm, Δυ = 1 MHz, phase modulator sensitivity K_PM = 10 rad/V and 10° phase deviation between the two transmitted bits, the loop delay must be kept below 3 ns. Further, the required line-width with the non-negligible loop delay time is evaluated and found to be (2.1 × 10⁻³)/τ, where τ (s) is the loop delay. This number corresponds to BER = 10⁻¹⁰, imperfect phase recovery power penalty of 1 dB and phase modulator sensitivity K_PM = 20 rad/V.     

Wobbling phenomena with logarithmic law nonlinear Schrödinger equations for incoherent spatial Gaussons

We apply the equivalence particle principle to several nonlinear Schrödinger equations (NLSEs) that model the propagation of a spatial beam with logarithmic law nonlinearity. Using this principle, expressions for acceleration, spatial frequency, spatial period and other variables for a spatial soliton can be derived from the solution of the homogenous NLSE with logarithmic law nonlinearity. These results agree well with numerical simulations of the perturbed NLSE. We show that if the expression of the acceleration is bounded this means the spatial soliton propagates with a swing effect.     

X-ray studies of the structure of thermotropic copolyesters

This paper describes x-ray analysis of the structure of a group of wholly aromatic thermotropic liquid crystalline copolyesters, focusing on two systems: condensation copolymers of 4-hydroxy-benzoic acid (HBA) and 2-hydroxy–6-naphthoic acid; and of HBA, 2,6-dihydroxy-naphthalene, and terephthalic acid. The fiber diagrams of these copolymers contain a series of aperiodic meridional maxima that shift in position with the monomer ratio. We have shown that these characteristics are predicted by a structure consisting of an array of chains of completely random monomer sequence. The positions of the maxima are predicted by a simple model in which the monomers are represented by points, separated from their neighbors by the appropriate monomer lengths. Use of atomic models for the monomers leads to prediction of both the positions and the intensities of the maxima. Calculations for nonrandom sequence distribution show that all but minimal blockiness can be ruled out. From the breath of the meridional maximum at d = 2.1 Å it is possible to estimate the correlation or persistence length for the stiff chain conformation in the solid state.     

On symmetries,reductions, conservation laws and conserved quantities of optical solitons with inter-modal dispersion

This paper studies the compressional dispersive Alfvén (CDA) waves where Noether symmetries will be calculated from which the corresponding conservation laws will be obtained via Noether's theorem. Furthermore, one case of double reduction is performed via the association of a conserved vector with a Noether symmetry (with zero gauge). The conserved quantities of optical solitons in the presence of intermodal dispersion that is governed by the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. The invariance-multiplier method is adopted to carry out the analysis, from which the conserved densities are then retrieved. Finally, the conserved quantities are obtained using the 1-soliton solution of the governing equation.     

Statistical Dynamics of Solitons in Optical Fibers

The soliton perturbation theory is used to study and analyze the stochastic perturbation of optical solitons in addition to deterministic perturbations of optical solitons that are governed by the nonlinear Schro¨dinger's equation. The Langevin equations are derived and analyzed. The deterministic perturbations that are considered here are of both Hamiltonian as well as of non-Hamiltonian type.     

Semi-Analytical Simulation of Titanium-Indiffused Lithium Niobate–Integrated Optic Directional Couplers Consisting of Curved Waveguides

Integrated optic directional couplers consisting of curved waveguides are simulated analytically by solving the Riccati equation. The coupling coefficient between the curved waveguides with a parabolically varying gap and the condition of total power transfer between the waveguides are derived. In order to compute the overall coupling coefficient and hence the power distribution along the waveguides for Ti:LiNbO ₃ curved waveguide directional couplers, the coupling coefficient for straight waveguide couplers is computed for different gaps using the effective-index-based matrix method (EIMM). Finally, the power distribution in the curved waveguides along the length is computed. The method is mostly analytical except the effective-index method and is computationally simple.     

Experimental gravity induced coexistence curve of methyl fluoride near the critical point

Abstract

The top part of the coexistence curve of methyl fluoride in the critical region has been determined first by direct observation of the disappearance of the meniscus of the fluid situated in a high-pressure light scattering cell and subsequently from the measured maximum depolarization ratio of an appreciable number of isochores close to the critical point. The experimental data obtained from direct observations yield a coexistence curve which nearly coincides with that found recently from pVT measurements. However, the data obtained from light scattering experiments describe a gravity induced coexistence curve which lies above the previous one and which shows a minimum at the critical point. The complete experimental data have been used to evaluate the critical parameters p_c, ρ_c and T_c and the critical exponent β.