Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x-y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method.     

Mode dispersion characteristics of graded-index optical waveguides

A method to compute the propagating modes of graded index waveguides with an arbitrary refractive index distribution is proposed, based on the variational method applied to the integral wave equation. The method is applied to two refractive index distributions: a Gaussian index distribution and a complementary error-function index distribution. The results are compared with the predictions of perturbation analysis and are experimentally verified by measuring the mode spectrum of a Ti-diffused LiNbO₃ waveguide.     

Resonant coupling into hybrid 3D micro-resonator devices on organic/biomolecular film/glass photonic structures

We have designed and realized an integrated photonic family of micro-resonators (MR) on multilayer SU8/lipidic film/glass materials. Such a family involves hybrid 3D-MR structures composed of spherical glass-MR arranged upon organic pair-SU8-waveguides, an efficient coupling being ensured with a Langmuir-Blodgett Dipalmitoylphosphatidylcholine (DPPC-lipid from Avanti Polar^®) film whose thickness is ranging from 12 to 48 nm. We have characterized such add/drop filters, respectively, in intensity and spectral measurements, and experimentally achieved an evanescent resonant-photonic-coupling between the 3D-MR and the 4-ports structure through the DPPC-gap. Spectral resonances have been measured for 4-whispering gallery-modes (WGM) into such 3D-structures, respectively, characterized with a 0.97 nm free spectral range (FSR) and a high quality Q-factor up to 4.10⁴.     

Periodic sub-micrometric structures using a 3D laser interference pattern

A method to obtain three-dimensional sub-micrometric periodic structures is presented. The experimental set-up consists in a pulsed UV laser beam source (λ = 355 nm) coming into an interferometer in order to generate four beams converging inside a chamber. According to the directions, to the relative intensities and to the polarizations of these four beams, a 3D interference pattern can be obtained inside the overlapping volume of these four beams; the characteristics of the four laser beams have been optimized in order to obtain a maximal contrast of intensity. In order to visualize the interference pattern, its contrast and its stability at each laser pulse, a video camera coupled to an oil immersion microscope objective has been installed above the interferometer. By suppressing the central beam, it is also possible to generate a bidimensional interference pattern which defines an hexagonal structure in the (1 1 1) plane with a period of 377 nm.This optical set-up has been used to obtain 3D sub-micrometric periodic structures in negative photoresists. Experiments consist in a one- or multi-pulse irradiation of the photoresist followed by a development procedure which leads to a sub-micrometric face-centred cubic structure cut in a (1 1 1) plane with a cell parameter of 650 nm. The optimization of the experimental conditions is presented for two kinds of photoresists; the role of the substrate according to its reflectivity at the laser wavelength and its influence on the interference pattern is also discussed.     

Spin waves propagation in Fibonacci quasiperiodic metamagnet superlattices

In this work we present a fractal analysis of the spin wave modes propagating in a Fibonacci quasiperiodic metamagnetic superlattices consisting of a ferromagnetic material (layer A being Fe) and a metamagnetic material (layer B being FeBr₂). The spin wave modes are obtained in the exchange regime, using the transfer matrix technique. Our numerical results show that the power law for this system is independent of the dimensionless in-plane wavevector kxa$k_{x}a$, and that the spectrum present a multifractal characteristic, exhibiting several scale invariant windows for a fixed value of the in-plane wavevector. The results reported here can be experimentally observed by light scattering techniques.     

NORMAL MODES OF A NON-LINEAR CLAMPED-CLAMPED BEAM

Non-linear modal analysis approach based on invariant manifold method proposed earlier by Shaw and Pierre (Journal of Sound and Vibration164, 85-124) is utilized here to obtain the non-linear normal modes of a clamped-clamped beam for large amplitude displacements. The results obtained for the fundamental normal mode are compared with the corresponding reported experimental and theoretical studies. The effects of modal coupling are examined in greater detail. The limitation of the present method for analyzing non-linear behavior is highlighted.     

Relaxation modes of point defect pairs in ionic crystals: Approximate solutions for the threeshell model

A perturbation technique is used to obtain first-order expressions for the relaxation frequencies for the relaxation modes of the three-shell model of pairs of coupled defects moving on the same fcc lattice (e.g. divalent cation-cation vacancy in the rocksalt structure) or on interpenetrating fcc lattices (vacancy pairs in the rocksalt structure, or interstitial anion—excess valency cation in the fluorite structure). For the dielectrically-active T_lu modes, expressions are given for the relaxation intensities in the zero-order approximation. These results are then used to discuss experimental data for NaCl and KCl containing divalent cations and for alkaline earth fluorides containing trivalent rare earth ions.     

Characterization of laser waveguides in Nd:CNGG crystals formed by low fluence carbon ion implantation

We report on Nd:CNGG active planar waveguides produced by 6.0 MeV carbon ion implantation at fluence from 1 × 10¹⁴ ions/cm² to 8 × 10¹⁴ ions/cm². The refractive index profiles, which were reconstructed according to the measured dark mode spectroscopy, showed that the refractive indices had negative changes in the surface region, forming typical barrier waveguide. The width of waveguide structure induced by carbon ion implantation is ∼3.8 μm. The typical barrier-shaped distribution may be mainly due to the nuclear energy deposition of the incident ions into the substrate. By performing a modal analysis on the observed TE modes, it was found that the TE₀ and TE₁ modes can be well-confined inside the waveguide.     

Analysis and design of grating couplers

Based on an accurate perturbation analysis of the guiding properties of dielectric gratings, simple design criteria are developed for grating couplers which transfer the energy of a beam into or out of an optical waveguide. Gratings having arbitrary groove shapes are considered and explicit formulae are given for the leakage parameters of gratings with symmetric profiles. The results cover TE_v and TM_v modes and they apply to both shallow and deep grating grooves. The variation of the leakage parameter α in rectangular gratings is examined in detail; these rectangular gratings are then used as basic configurations for predicting the characteristics of other grating profiles. Particular attention is given to trapezoidal and triangular profiles and gratings with asymmetric profiles are also discussed.     

Excess entropy for a vacancy in a crystal

The following topics are discussed: (1) Within the harmonic theory a general expression is given for excess entropy of a localized detect in any crystal with cyclic boundary conditions and in the small perturbation limit. For a single vacancy defect Stripp and Kirkwood's formula is obtained, ΔS/k_B = d/2,d being the dimension of the space. For other localized defects the perturbation formula requires calculation of the unperturbed Green's matrix. (2) It is argued that the effect of free surface boundary conditions, as well as other surface changes, leaves ΔS effectively invariant. (3) Using the vacancy perturbation result for ΔS and Lawson's formula, a value for the vacancy formation volume is obtained only in terms of known measured parameters; this result is compared to experimental and other calculated values of ΔV_f. (4) If localized vibrational modes are present due to the vacancy, what effect these might have on ΔS, and, from this, what materials might be candidates for observing localized modes.     

Losses in diffused optical waveguides

It has been shown that the attenuation characteristics of TE modes in diffused waveguides are different from those of a conventional slab. A simple semiempirical analysis is performed on the base of a ray-optics picture assuming a parabolic index distribution. Analytical expressions for surface scattering and volume loss are derived. The analysis precisely describes the modal loss behaviour of Ag⁺ ion-exchanged waveguides in glass (new results) and Nb diffused waveguides in LiTaO₃ (data reported by other authors).     

Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides

The propagation of electromagnetic energy via coupled surface plasmon polariton modes in a metal-insulator-metal heterostructure is analyzed analytically for a core material exhibiting optical gain. It is shown that a sufficiently large gain can completely compensate for the absorption losses due to energy dissipation in the metallic boundaries, enabling long-range transport with a confinement below the diffraction limit for on-chip switching and sensing applications. For a free-space wavelength of 1500 nm, lossless propagation in a gold-semiconductor-gold waveguide with a core size of 50 nm is predicted for a gain coefficient γ = 4830 cm⁻¹, comparable to that of semiconductor gain media. The gain requirements decrease with the use of low-index nanocrystal-doped glasses or polymers as core materials.     

Reduced depth polarizer for integrated optics

Taking advantage of the different cut-off thickness of the two fundamental modes in an optical waveguide, a polarizing structure has been realized. It consists of a narrow stripe (∼100 μm) of reduced diffusion depth in an ion-exchanged waveguide. The TE₀-mode passes the polarizer with negligible losses, whereas the TM₀-mode is forced to couple out into the substrate. The extinction ratio is better than −16 dB.     

Study of optical waveguide of barium sodium niobate films on potassium titanyl phosphate

Barium sodium niobate (BSN) optical waveguide films were grown on potassium titanyl phosphate (KTP) substrate by pulsed laser deposition (PLD). X-ray diffraction (XRD), scanning electron microscopy (SEM), X-ray pole spectroscopy, and X-ray photoelectron spectroscopy (XPS) showed that the as-grown BSN films are epitaxially smooth, fine-particled and show small constituent deviation. Both m lines of the waveguided TE and TM modes were recorded. Lattice match between the BSN(110) and both the KTP(001) and KTP(100) planes is examined with mismatch less than 3%. Effective refractive indices as a function of incident wavelength and order of the waveguided modes are studied. A phase matching relationship of k ⁽¹⁾−2k ⁽⁰⁾=0 is established between the first-order and fundamental modes in the BSN/KTP waveguided system. Effective thicknesses for TE and TM modes were obtained to be equal to 0.76 and 0.72 μm, respectively, larger than the thickness of the as-grown BSN film of 0.60 μm. A constituent ratio of Ba:Na:Nb in the BSN film measured was equal to 2:0.82:5.14, slightly deviating from the stoichiometric ratio of 2:1:5, which is attributed to higher relative asymptotic velocity for Nb species and higher evaporation pressure for Na species. Finally, the main factors affecting quality of the as-grown BSN films are also discussed. Received: 26 March 1999 / Accepted: 30 March 1999 / Published online: 19 August 1999     

Multiple polarization of geodesic curvature induced modes

Dispersion relations for geodesic acoustic modes are derived by using the Grad hydrodynamic equations thereby reconciling long known but not previously explained discrepancy between the results of kinetic and fluid calculations. Extended fluid theory allows a simple analysis of mode polarization and coupling. A new type of electromagnetic modes induced by geodesic compressibility is predicted. These modes are related to Alfvén and geodesic acoustic modes. While a standard geodesic acoustic mode involves poloidally and toroidally symmetric perturbations of electrostatic potential (m=n=0) and the first poloidal side-bands of plasma pressure, new modes involve side-bands of the electrostatic and vector potential as well as pressure perturbations at zeroth and second harmonics. It is shown that there exist two different values of the adiabatic constant depending on the mode polarization. Both standard (electrostatic) geodesic acoustic modes and new electromagnetic modes involve finite perturbations of parallel viscosity, which modify an effective adiabatic (compressibility) index for a toroidal plasma.     

Advection of a passive vector field by the Gaussian velocity field with finite correlations in time

Using the field theoretic renormalization group technique the model of a passive vector field advected by an incompressible turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation). The turbulent environment is given by statistical fluctuations of the velocity field that has a Gaussian distribution with zero mean and defined noise with finite correlations in time. Two-loop analysis of all possible scaling regimes in general d-dimensional space is done in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∝ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that the scaling regimes of the present model of vector advection have essentially different properties than the scaling regimes of the corresponding model of passively advected scalar quantity. The results demonstrate the fact that within the present model of passively advected vector field the internal tensor structure of the advected field can have nontrivial impact on the diffusion processes deep inside in the inertial interval of given turbulent flow.     

Raman spectra of the orthorhombic semiconductor compound Cu2SnTe3

The optical phonon spectrum of the semiconductor Cu₂SnTe₃, that crystallizes in the orthorhombic structure with space group Imm2 (), have been studied by measuring unpolarized Raman scattering between 10 and 300 K. The experimental frequencies of the phonon modes observed were compared to those calculated by using simplified lattice dynamical models reported in the literature. From combined analysis of these results together with the factor group analysis of the zone-center vibrational modes, valuable information about these modes was obtained and their possible symmetry was assigned. A₁ modes at 71, 123, 167, 176 and 190 cm⁻¹; A₂ modes 115 and 131 cm⁻¹; B₁ modes at 76, 142 and 152 cm⁻¹; B₂ modes at 89, 100 and 206 cm⁻¹; a overtone at 246 cm⁻¹, and combinations at 218, 270 and 292 cm⁻¹; have been observed in this compound.     

Advection of passive magnetic field by the Gaussian velocity field with finite correlations in time and spatial parity violation

Using the field theoretic renormalization group technique the model of passively advected weak magnetic field by an incompressible isotropic helical turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation) in the framework of an extended Kazantsev-Kraichnan model of kinematic magnetohydrodynamics. Statistical fluctuations of the velocity field are taken in the form of a Gaussian distribution with zero mean and defined noise with finite correlations in time. The two-loop analysis of all possible scaling regimes is done and the influence of helicity on the stability of scaling regimes is discussed and shown in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∞ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that in non-helical case the scaling regimes of the present vector model are completely identical and have also the same properties as those obtained in the corresponding model of passively advected scalar field. Besides, it is also shown that when the turbulent environment under consideration is helical then the properties of the scaling regimes in models of passively advected scalar and vector (magnetic) fields are essentially different. The results demonstrate the importance of the presence of a symmetry breaking in a given turbulent environment for investigation of the influence of an internal tensor structure of the advected field on the inertial range scaling properties of the model under consideration and will be used in the analysis of the influence of helicity on the anomalous scaling of correlation functions of passively advected magnetic field.     

Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure

It has recently been predicted that a conical singularity (=Dirac point) in the band structure of a photonic crystal produces an unusual 1/L scaling of the photon flux transmitted through a slab of thickness L. This inverse-linear scaling is unusual, because it is characteristic of radiative transport via diffusion modes through a disordered medium - while here it appears for propagation of Bloch modes in an ideal crystal without any disorder. We present a quantitative numerical test of the predicted scaling, by calculating the scattering of transverse-electric (TE) modes by a two-dimensional triangular lattice of dielectric rods in air. We verify the 1/L scaling and show that the slope differs by less than 10% from the value predicted for maximal coupling of the Bloch modes in the photonic crystal to the plane waves in free space.     

Invariant exchange perturbation theory for multicenter systems and its application to the calculation of magnetic chains in manganites

The formalism of exchange perturbation theory is presented with regard to the general principles of constructing an antisymmetric vector with the use of the Young diagrams and tableaux in which the coordinate and spin parts are not separated. The form of the energy and wave function corrections coincides with earlier obtained expressions, which are reduced in the present paper to a simpler form of a symmetry-adapted perturbation operator, which preserves all intercenter exchange contributions. The exchange perturbation theory (EPT) formalism itself is presented in the standard form of invariant perturbation theory that takes into account intercenter electron permutations between overlapping nonorthogonal states. As an example of application of the formalism of invariant perturbation theory, we consider the magnetic properties of perovskite manganites La_1/3Ca_2/3MnO₃ that are associated with the charge and spin ordering in magnetic chains of manganese. We try to interpret the experimental results obtained from the study of the effect of doping the above alloys by the model of superexchange interaction in manganite chains that is constructed on the basis of the exchange perturbation theory (EPT) formalism. The model proposed makes it possible to carry out a quantitative analysis of the effect of substitution of manganese atoms by doping elements with different electron configurations on the electronic structure and short-range order in a magnetic chain of manganites.