Nonlinear planar waveguides with gracled-index core: power series solution

Abstact Solutions are presented for a class of nonlinear, planar waveguides with graded-index linear film and nonlinear cladding and/or substrate. The solutions are based on a powerseries expansion for the field in the core and, for several interesting examples, can be expressed explicitly - without the need to solve any eigenvalue equation. For more general problems, the solution can be described in a form that is directly analogous to that for the asymmetric step-index waveguide. Some interesting differences between the mocles of the step-and graded-index waveguides are illustrated.     

Asymmetric planar luminescent waveguide based on amorphous silicon carbide with polarized radiation in leaky modes

Plasma-enhanced chemical vapor deposition is used to fabricate asymmetric planar luminescent waveguides (APWs) based on amorphous silicon-carbide films with submicron thickness on quartz substrates. Narrow peaks of linearly (P and S) polarized radiation related to the emission in the APW leaky modes are detected in the APW emission spectra from the end surface of a substrate under excitation of photoluminescence. The dependence of the spectral positions of peaks on the angle at which the radiation is emitted from the end surface and the film thickness is analyzed. At grazing angles of emission, the radiation wavelength is almost independent of the angle. It is demonstrated that the difference between the wavelengths of the P- and S-polarized peaks in the PL spectra decreases with an increase in the waveguide thickness. The waveguide works as an optical microcavity for leaky modes. The amplitude of the S-polarized peak is higher than the amplitude of the P-polarized peak due to the fact that the Q factor for the S-polarized leaky modes is greater than the Q factor for the P-polarized leaky mode. The luminescent APWs can be used to generate optical beams with radial and azimuthal polarizations.     

Transmission properties of asymmetric slab waveguides with left-handed materials

A new dielectric slab waveguide with a left-handed material (LHM) cover and substrate is proposed. The dispersion relations and normalized effective thickness of the asymmetric LHM slab waveguide are investigated, in view of the normalized parameters. A number of unusual properties are found, for example, the fundamental and first-order modes do not exist and higher-order modes have double degeneracy. The propagation modes are absent at the low normalized frequency, and the cutoff frequencies of some LHM slab waveguide modes decrease with increase in the asymmetry measure. Unlike traditional slab waveguides, the V –H curves of the LHM slab waveguides are in one-to-one correspondence. Both TE and TM modes are discussed; in addition, the dispersion relations and normalized effective thicknesses of the TM modes are discussed in detail, when the difference in refractive indices of the film and the substrate is small. The results show that the region of mode coexistence taking place near the cutoff frequency becomes narrower with increase in the difference in refractive indices of the film and the substrate. The influence of this difference on the normalized effective thickness curves is different, and becomes smaller and smaller with increase in the value of the asymmetry measure, if different values of the refractive indices are employed.     

Field transformation in a multimode optical waveguide with random irregularities of the film surface

A self-consistent mathematical model for the transformation of the average intensity of the mode spectrum I(z) of a waveguide field in a multimode planar optical waveguide with a step profile and rough surface is developed. This model is based on the matrix model for multiple scattering of modes in an optical waveguide. The elements of the intermode scattering matrix are found, which describe the process of mutual transfer of the energy of modes along a waveguide and their transformation into radiation modes. The transformation of the I(z) modes in waveguides with large-and small-scale inhomogeneities is investigated. It is shown that the largest qualitative differences in the noted dependences manifest themselves only in the initial portions of the optical waveguide. The length z of these portions is much smaller than the characteristic scale length L _k at which the fundamental energy of the kth mode excited in the optical waveguide is renewed. The effect of self-filtration of the mode spectrum I(z) is described, as a result of which a stable (normalized), independent of distance z, distribution I* is formed. It is established that irregularities of the optical waveguide boundaries exert a depolarizing effect on a guided light beam. The specific features of the normalization of the radiative dissipation of a group of modes I_i(z) in an optical waveguide are investigated. It is ascertained that, in the case of small-scale irregularities, the attenuation coefficient is described by a nonlinear monotonic dependence α(z), which asymptotically converges to the value α*, characteristic of the normalized field I*. When the optical-waveguide film has large irregularities, the dependence α(z) is characterized by a pronounced maximum due to the formation of alternative channels of radiative dissipation of the energy of waveguide modes.     

Slow light effect with high group index and wideband by saddle-like mode in PC-CROW

Slow light with high group index and wideband is achieved in photonic crystal coupled-resonator optical waveguides (PC-CROWs). According to the eye-shaped scatterers and various microcavities, saddle-like curves between the normalized frequency f and wave number k can be obtained by adjusting the parameters of the scatterers, parameters of the coupling microcavities, and positions of the scatterers. Slow light with decent flat band and group index can then be achieved by optimizing the parameters. Simulations prove that the maximal value of the group index is > 10⁴, and the normalized delay bandwidth product within a new varying range of n _g > 10² or n _g > 10³ can be a new and effective criterion of evaluation for the slow light in PC-CROWs.     

Optical microscopy of quasi-periodic structures induced upon excitation of waveguide TE and TM modes under irradiation of AgCl-Ag films by a laser beam

This paper reports on the results of analyzing the conditions under which quasi-periodic structures induced in AgCl-Ag photosensitive films by a linearly polarized Gaussian laser beam (λ=633 nm) can be clearly observed with the use of an optical microscope. It is shown that quasi-periodic structures with vectors K ∥ E (where E is the vector of polarization of the inducing beam) and periods d > λ are effectively formed upon excitation of waveguide TM₀ modes at a large angle of incidence (φ=70°) and the p polarization of the inducing beam. Exposure of the film on a 60° glass prism to a p-polarized beam incident on the sample at an angle φ=60° from the side of the glass leads to the effective formation of primary gratings with vectors K⊥E (due to the excitation of waveguide TM₀ modes) and secondary oblique gratings. The specific features of the quasi-periodic structures and the correlation between the primary and secondary gratings are revealed and analyzed.     

Analyze and calculation of coupling coefficient based on evanescence field for plasmonic directional coupler structure

We obtain the calculation of coupling coefficient of plasmonic directional coupler made up of two monolayer waveguides separated in the range of 200 nm for TM mode and we assume each waveguides acts as a perturbation to other waveguide but does not affect the waveguide mode. We simulation the transfer distance respect to normalized frequency in two directions, x and z, values transfer distance a limitation of a bandwidth is suitable for designing of integrated optical circuits and construction of couplers and switches.     

Molecular dynamics study of the growth of a metal nanoparticle array by solid dewetting

We investigated the effect of the substrate and the ambient temperature on the growth of a metal nanoparticle array (nanoarray) on a solid-patterned substrate by dewetting a Au liquid film using an atomic simulation technique. The patterned substrate was constructed by introducing different interaction potentials for two atom groups (C₁ and C₂) in the graphene-like substrate. The C₁ group had a stronger interaction between the Au film and the substrate and was composed of regularly distributed circular disks with radius R and distance D between the centers of neighboring disks. Our simulation results demonstrate that R and D have a strikingly different influence on the growth of the nanoparticle arrays. The degree of order of the nanoarray increases first before it reaches a peak and then decreases for increasing R at fixed D. However, the degree of order increases monotonously when D is increased and reaches a saturated value beyond a critical value of D for a fixed R. Interestingly, a labyrinth-like structure appeared during the dewetting process of the metal film. The simulation results also indicated that the temperature was an important factor in controlling the properties of the nanoarray. An appropriate temperature leads to an optimized nanoarray with a uniform grain size and well-ordered particle distribution. These results are important for understanding the dewetting behaviors of metal films on solid substrates and understanding the growth of highly ordered metal nanoarrays using a solid-patterned substrate method.     

Characteristics of surface acoustic waves in (11$$\bar 2$$ 0)ZnO film/ R-sapphire substrate structures

(11\(\bar 2\)0)ZnO film/R-sapphire substrate structure is promising for high frequency acoustic wave devices. The propagation characteristics of SAWs, including the Rayleigh waves along [0001] direction and Love waves along [1ī00] direction, are investigated by using 3 dimensional finite element method (3D-FEM). The phase velocity (v _p), electromechanical coupling coefficient (k ²), temperature coefficient of frequency (TCF) and reflection coefficient (r) of Rayleigh wave and Love wave devices are theoretically analyzed. Furthermore, the influences of ZnO films with different crystal orientation on SAW properties are also investigated. The results show that the 1st Rayleigh wave has an exceedingly large k ² of 4.95% in (90°, 90°, 0°) (11\(\bar 2\)0)ZnO film/R-sapphire substrate associated with a phase velocity of 5300 m/s; and the 0th Love wave in (0°, 90°, 0°) (11\(\bar 2\)0)ZnO film/R-sapphire substrate has a maximum k ² of 3.86% associated with a phase velocity of 3400 m/s. And (11\(\bar 2\)0)ZnO film/R-sapphire substrate structures can be used to design temperature-compensated and wide-band SAW devices. All of the results indicate that the performances of SAW devices can be optimized by suitably selecting ZnO films with different thickness and crystal orientations deposited on R-sapphire substrates.     

Minimization of losses and calculation of the optical properties of Bragg fiber waveguides with a hollow core

A numerical method for solving the inverse problem of determining the geometry of the multilayer shell of a Bragg waveguide that has the lowest waveguide losses for a given mode has been developed with the use of the genetic algorithm. For the calculated designs of waveguides, the distribution of the coordinates of the boundaries of shell layers has been found to be aperiodic under the condition r ₁ ≤ λ due to the axial symmetry of the problem. Waveguide losses for the TE ₀₁, TM ₀₁, and HE ₁₁ modes satisfy the conditions \(\alpha _{TM_{01} } > \alpha _{HE_{11} } > \alpha _{TE_{01} } \). It follows from the dependence of n _eff obtained for these modes on the core radius and number of shell layers that any change in the structure of the waveguide leads to the violation of the optimal propagation regime for these modes. A Bragg fiber waveguide with a hollow core that is designed for the TE ₀₁ mode and directs light in the single-mode regime is presented. The main fraction of losses in this waveguide is attributed to material absorption.     

Slow light engineering in a photonic crystal slab waveguide through optofluidic infiltration and geometric modulation

In this paper, a new type of flat-band slow light structure with high group index (n _g) and large normalized delay-bandwidth product (NDBP) in a silicon on insulator (SOI) based photonic crystal (PC) slab waveguide with a triangular lattice of circular holes is demonstrated. The dispersion engineering is performed by infiltrating optical fluids with different refractive indices n _f in the first row and shifting the second row of air holes adjacent to the PC waveguide (PCW) in the longitudinal direction. In the optimized case, a high NDBP of 0.32 with a group index of 54.55 and a bandwidth of 9.13 nm could be obtained. Furthermore, an ultra-low group velocity dispersion (GVD) in the range of 10^–20 s²/m is achieved in all of the structures. These results are obtained by numerical simulations based on three-dimensional (3D) plane wave expansion (PWE) method.     

Formation of textured Ni(200) and Ni(111) films by magnetron sputtering

The effect of the working gas pressure (P ≈ 1.33–0.09 Pa) and the substrate temperature (T_s ≈ 77–550 K) on the texture and the microstructure of nickel films deposited by magnetron sputtering onto SiO₂/Si substrates is studied. Ni(200) films with a transition type of microstructure are shown to form at growth parameters P ≈ 0.13–0.09 Pa and T_s ≈ 300–550 K, which ensure a high migration ability of nickel adatoms on a substrate. This transition type is characterized by a change of the film structure from quasi-homogeneous to quasi-columnar when a film reaches a critical thickness. Ni(111) films with a columnar microstructure and high porosity form at a low migration ability, which takes place at P ≈ 1.33–0.3 Pa or upon cooling a substrate to T_s ≈ 77 K.     

Effective refractive index of a quasi-two-dimensional polydomain film of a conjugated polymer

The relation between the effective ordinary refractive index n* = (n _o n _e )^1/2 of a quasi-two-dimensional polydomain uniaxial film of a conjugated polymer F8BT in the visible transparency region and the refractive indices (n _o,e ) of uniaxial domains with the optical axes randomly oriented in the plane of the film has been confirmed experimentally. The permissible interval of variations in n* has been established and a strong spectral dispersion of this interval near the long-wavelength electronic absorption band of the film has been demonstrated.     

Calculation of effective index for different dielectric waveguides structures made of PVCi/PMATRIFE polymers at telecom-wavelength \lambda =1.55\,\upmu m

In this paper, a number of polymeric waveguide structures have been analyzed by using two distinct techniques which are: effective index method (EIM) and numerical simulation based on finite difference method (FDM). The main aim of this investigation is the calculation of effective indexes (EI) of the following structures: rib, ridge and buried channel waveguides at telecom wavelength $\lambda =1.55\,\upmu \hbox {m}$ for different dimensions of waveguide cores varying from 1.5–4  $\upmu \hbox {m}$ . Moreover, other optical propagation characteristics such as: confinement factor, normalized and propagation constant have been studied in TE polarisation. Otherwise the effect of the structure parameters and dimensions on the dispersion characteristics has been investigated. On the other hand, the optical field distribution has been computed using commercial software named OlympIOs. The polymers applied in the design of waveguide structures are the PVCi (n = 1,562 $\lambda = {1.55}\,\upmu $ m) used as core layer and the PMATRIFE (n = 1,409 $\lambda = 1.55\,\upmu $ m) used as substrate or cladding layer. The results obtained using EIM and simulation based on FDM show that effective index and field confinement factor of TE fundamental mode increase monotonously with the increasing dimension of core. The obtained results are in good agreement with published data based on other numerical methods.     

A spectroscopic prism coupler for measuring the refractive indices and thicknesses of dielectric films

A spectroscopic prism coupler is created for measuring refractive indices n_f and thicknesses H_f of dielectric films. The operating principle of the device is based on the simultaneous resonance excitation of several waveguide modes in a film by a focused TE or TM polarized light beam in the geometry of frustrated total internal reflection. Calculations of n_f and H_f are performed using measured angular positions θ_m of dark m-lines in the cross section of the specularly reflected beam. Using obtained angles θ_m, we can calculate effective refractive indices β_m of modes. By solving a set of nonlinear dispersion equations for the modes of a planar waveguide, we can calculate refractive index n_f and thickness H_f of a film. The proposed prism coupler has no moving parts and allows us to measure the optical parameters of films 0.5–10 μm thick in the 400–1100 nm range of wavelengths. The device can also be used as a spectroscopic refractometer for measuring the refractive indices of bulk media. The device is used to measure refractive index and thickness of a SiO film and the refractive index of TF4 glass.     

A nonlinear dynamic effect of formation of photo-induced periodic structures in waveguiding As<Subscript>2</Subscript>S<Subscript>3</Subscript>-Ag thin films

A nonlinear effect of spatiotemporal transformations of a focused linearly polarized Gaussian beam of a He-Ne laser obliquely incident (S and P polarizations) upon an As₂S₃-Ag film containing a small amount of chlorine and deposited onto a glass substrate is found and interpreted. The effect consists in the appearance, in the process of exposure, of beams diffracted and anisotropically scattered by periodic structures arising due to excitation of the waveguide TE₀ and TM₀ modes in the film. The diffraction measurements of the effective refractive indices for the TE₀ and TM₀ modes make it possible to calculate the refractive index and the thickness of the film from dispersion equations. Along with slow evolution of the diffraction and scattering patterns, we have found a persistent optical turbulence in the fringes of scattering from the structures related to excitation of the TE₀ modes. It is suggested that the turbulence is an indication of existence of reversible processes in the mechanism of photosensitivity.     

Structure and Surface Morphology of Cd<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se Epitaxial Films

Cd_1–xMn _x Se (х = 0.03) epitaxial films are produced by the molecular beam condensation method in a vacuum chamber with a residual pressure of 10^–4 Pa on mica and glass substrates. It is established that at room temperature and at a substrate temperature of T = 573 K films of polycrystalline structure grow on the mica substrates, but films of both polycrystalline and amorphous structure grow on the glass substrates. It is shown that the polycrystalline Cd_1–xMn _x Se (х = 0.03) films, unlike the bulk crystals, have a sphalerite-type structure with a lattice parameter of a = 6.05 Å. Increasing the substrate temperature to 673 K leads to epitaxial growth with the direction [111]. Dark aggregates, observed on the film surface, are removed using a source of compensating Se vapors during the growth process. The optimal conditions for the production of structurally perfect epitaxial films are defined.     

Anti-Kählerian Geometry on Lie Groups

Let G be a Lie group of even dimension and let (g, J) be a left invariant anti-Kähler structure on G. In this article we study anti-Kähler structures considering the distinguished cases where the complex structure J is abelian or bi-invariant. We find that if G admits a left invariant anti-Kähler structure (g, J) where J is abelian then the Lie algebra of G is unimodular and (G, g) is a flat pseudo-Riemannian manifold. For the second case, we see that for any left invariant metric g for which J is an anti-isometry we obtain that the triple (G, g, J) is an anti-Kähler manifold. Besides, given a left invariant anti-Hermitian structure on G we associate a covariant 3-tensor ?? on its Lie algebra and prove that such structure is anti-Kähler if and only if ?? is a skew-symmetric and pure tensor. From this tensor we classify the real 4-dimensional Lie algebras for which the corresponding Lie group has a left invariant anti-Kähler structure and study the moduli spaces of such structures (up to group isomorphisms that preserve the anti-Kähler structures).     

Effect of bias voltage polarity of a substrate on the texture,microstructure, and magnetic properties of Ni films prepared by magnetron sputtering

The influence of the bias voltage polarity U_s on microstructure, crystallographic texture and magnetic properties has been investigated for Ni films with a thickness of ≈15–420 nm, which are obtained via magnetron sputtering at a working gas pressure P corresponding to the collision-deficient flight mode of atoms of the sputtered target between the target and the substrate. The Ni(111)-textured films have been shown to form at U_s ≈–100 V, whose microstructure and magnetic parameters are almost unchanged with a thickness. In contrast, the Ni(200) films are formed at U_s ≈ +100 V, whose magnetic properties and micro-structure depend significantly on the thickness d that manifests in a critical thickness d* ≈ 150 nm, when the structure of the film becomes inhomogeneous in the thickness, the remagnetization loops are changed from rectangular to supercritical with the formation of the band domain structure.     

Magnetic properties of arrays of cobalt nanoparticles on the CaF<Subscript>2</Subscript>(110)/Si(001) surface

The Co/CaF₂/Si(001) heterostructures with the corrugated (110) surface of the CaF₂ buffer layer have been grown by molecular beam epitaxy. The structures are nanoparticle arrays of single-crystal Co, mostly of the cubic fcc modification. The behavior of the magnetic hysteresis loops as a function of the density of coverage of the substrate by cobalt islands, the island size, and the temperature is studied using the magnetooptical technique. At low coverage densities, where the effective cobalt film thickness d _eff is less than the critical value d _eff ^c , the magnetic structure of the films at T = 294 K can be visualized as an ensemble of superparamagnetic, weakly interacting nanoparticles and is characterized by small values of the coercive field H _c and the remanent magnetization M _rem. A decrease in the temperature leads to a strong increase in H _c and M _rem, which is associated with the transition of the islands to the blocked state. The blocking temperature of the structures is T _b ～ 280 K. The magnetic anisotropy parameter K and the saturation magnetization M _s of the islands depend on the growth temperature of cobalt T _Co. An increase in the coverage density above the critical thickness d _iff ^c at T = 294 K brings about a strong increase in H _c and M _rem and the appearance of a hysteresis loop anisotropy originating from the corrugated structure of the CaF₂ buffer layer. The experimental results are compared with the model of an ensemble of noninteracting superparamagnetic particles.