Number Of Propagating Modes Research Articles

Original Solution of Coupled Nonlinear Schrödinger Equations for Simulation of Ultrashort Optical Pulse Propagation in a Birefringent Fiber

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system, different from the generally accepted approach based on the method of splitting according to physical processes. A combined explicit/implicit finite-difference integration scheme based on the implicit Crank–Nicolson finite-difference scheme is proposed and substantiated. It allows the integration of a nonlinear system of equations with a choice of nonlinear terms from the previous integration step. The main advantages of the proposed method are: its absolute stability through the use of an implicit finite-difference integration scheme and an integrated mechanism for refining the numerical solution at each step; integration with automatic step selection; performance gains (or resolutions) up to three or more orders of magnitude due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step, as is required in the method of splitting according to physical processes. An additional advantage of the proposed method is the ability to calculate the interaction with an arbitrary number of propagation modes in the fiber.

Modeling of Nonlinear Propagation in Space-Division Multiplexed Fiber-Optic Transmission

In recent years, space-division multiplexed (SDM) transmission in multimode and multicore fiber structures has been attracting growing interest as a mean of scaling the capacity of the optical transport network. As in the case of standard systems based on the single-mode fibers, the ultimate limit to the achievable transmission rate is set by the nonlinearity of the fiber, and hence, the accurate modeling of nonlinear propagation in SDM fibers is a critical task. A key feature of long multimode fiber structures that are relevant for communications is the existence of random coupling between modes. This coupling has a major effect on the properties of nonlinear propagation, and in its presence, the coupled nonlinear Schrodinger equations, which are characterized by a very large number of propagation constants, reduce to the much simpler form of the coupled generalized Manakov equations. These equations shed light on the relevant aspects of signal propagation dynamics, and facilitate the establishment of an intuitive physical picture. Another key feature of SDM fibers is the existence of modal dispersion that introduces frequency dependence into the mode mixing process and modifies the effects of nonlinear propagation. In this paper, we review all of the above mentioned phenomena, and in addition, we assess the way in which the information capacity of SDM fibers is expected to scale with the number of propagation modes. Finally, we extend the Manakov formalism so as to account for the noninstantaneous Raman contribution to the nonlinear response of silica.

Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part I: Clean inner surface

The dynamics of the inner surface of an infinitely long circular‐cylindrical cavity in an isotropic elastic medium is studied in the whole range of the Poisson's ratio including negative values characteristic of auxetic materials. The existence of the unique long‐lived propagation mode (true surface wave, TSW) has been confirmed on the clean surface with the following properties: (i) existence of a low frequency cut‐off for all the azimuthal indices n except for n = 1 (flexural mode), (ii) polarization tending to that of the Rayleigh wave in the short wavelength limit, (iii) Airy phases (inflection points of dispersion curves) for n < 6 that shift towards short wave region when the Poisson's ratio becomes negative. A number of propagation modes with complex frequencies, i.e., with finite life times (surface leaky waves, pseudo surface waves) are found. The torsional leaky mode transforms into the skimming shear‐horizontal wave (Love wave) in the short wavelength limit. An axial–radial leaky mode, similar to the Rayleigh wave but with reverse elliptical polarization turns out a physical solution except for extremely short wavelengths. A strong radial component of the longitudinal resonance occurs at wavelengths comparable to the cavity's radius especially in the incompressible limit.

Holistic random encoding for imaging through multimode fibers.

The input numerical aperture (NA) of multimode fiber (MMF) can be effectively increased by placing turbid media at the input end of the MMF. This provides the potential for high-resolution imaging through the MMF. While the input NA is increased, the number of propagation modes in the MMF and hence the output NA remains the same. This makes the image reconstruction process underdetermined and may limit the quality of the image reconstruction. In this paper, we aim to improve the signal to noise ratio (SNR) of the image reconstruction in imaging through MMF. We notice that turbid media placed in the input of the MMF transforms the incoming waves into a better format for information transmission and information extraction. We call this transformation as holistic random (HR) encoding of turbid media. By exploiting the HR encoding, we make a considerable improvement on the SNR of the image reconstruction. For efficient utilization of the HR encoding, we employ sparse representation (SR), a relatively new signal reconstruction framework when it is provided with a HR encoded signal. This study shows for the first time to our knowledge the benefit of utilizing the HR encoding of turbid media for recovery in the optically underdetermined systems where the output NA of it is smaller than the input NA for imaging through MMF.

Electric Field Induced by the Spin Current in a Semiconductor Dresselhaus Nanowire

Using a new spin current definition the spin current and spin-current-induced electric field in a weak semiconductor Dresselhaus spin-orbit coupling nanowire (quantum wire) have been investigated theoretically. It is found that two nonzero linear spin current density elements take on oscillation peaks at the center of nanowire and their strengths can be changed by the number of propagation modes and Dresselhaus constant, respectively. Moreover, the spin-current-induced electric field has been calculated and its strength is measurable with today's technology which can be used to spin current detection. Our consequences also show that the strengths of spin current and spin-current-induced electric field for the Dresselhaus case are smaller than that for the Rashba case.

SPIN TRANSPORT FOR A QUANTUM WIRE WITH WEAK DRESSELHAUS SPIN-ORBIT COUPLING

We investigate theoretically the electron transport properties of a quantum wire (QW) non-adiabatically connected to two normal leads with weak Dresselhaus spin-orbit coupling (DSOC). Using the scattering matrix method and Landauer–Büttiker formula within the effective free-electron approximation, we have calculated the spin-dependent conductances G↑/↓ and spin polarization Pz of a hard-wall potential confined QW. It is demonstrated that regardless of the existence of DSOC G↑/↓ and Pz present oscillation structures near the subband edges of QW, and the number of quantized conductance plateaus is determined by the number of propagation modes in two leads. Moreover, the DSOC induces splitting of spin-up and spin-down conductance plateaus as well as the existence of spin polarization (Pz ≠ 0), and the enhancement of Dresselhaus strength destroys the conductance plateaus for the wide QW case. The above results indicate that the spin-dependent conductances and Pz are strongly dependent on the Dresselhaus strength which is the physical basis for spin transistor.

Highly dispersive scattering centre analysis using an enhanced parametric model

The existing dispersive scattering centre (DSC) models characterise high frequency backscatter of targets for range profile analysis. These models fail to analyse the inherent non-point scatterers such as highly dispersive waveguide geometries with a large number of propagation modes. Here, a parametric model is proposed that represents such misbehaved DSC as a sum of few equivalent point scatterers using an auxiliary correcting dispersion factor that gets around modal analysis. A population-based maximum likelihood algorithm is utilised to estimate the unknown parameters. The high-spatial resolution PRONY method is utilised for initialisation of some parameters. Measurements and method of moment solutions of some canonical and non-canonical dispersive targets are used in the authors’ parameter estimation. Comparisons are made with the inverse fast Fourier transform (IFFT) results.

Femtosecond laser fabricated fiber Bragg grating in microfiber for refractive index sensing

Fiber Bragg grating (FBG) is fabricated in the microfiber by the use of femtosecond laser pulse irradiation. Such a grating can be directly exposed to the surrounding medium without etching or thinning treatment of the fiber, thus possessing high refractive index (RI) sensitivity while maintaining superior reliability. The grating in the microfiber may have a number of propagation modes in its transmission spectrum, depending on the fiber diameter, and the higher order of mode has larger RI sensitivity. The RI sensitivity also depends on the fiber diameter and a smaller diameter corresponds to a large sensitivity. The maximum sensitivity obtained is approximately 231.4 nm per refractive index unit at the refractive index value of approximately 1.44 when the fiber diameter is approximately 2 microm. The FBG fabricated in the microfiber has high potential in various types of optical fiber sensor applications.

SPIN CURRENT INDUCED ELECTRIC FIELD IN A RASHBA QUANTUM WIRE

We investigate theoretically the spin current and spin current induced electric field in a weak Rashba spin-orbit coupling quantum wire (QW) using a definition for spin current by means of scattering matrix. It is found that there exists two non-zero linear spin current density elements which have oscillation peaks at the center of QW and their strengths can be changed by the number of propagation modes and Rashba constant, respectively. Moreover, the spin current induced electric field has also been calculated and its strength is measurable with present technology with which can be used to detect spin current.

Interferometric studies on the influence of temperature on the optical and dispersion parameters of GRIN optical fibre

Opto-thermal device attached to automate Fizeau interferometer is used to investigate the influence of temperature on opto-thermal properties of multimode graded-index (GRIN) optical fibre in the range from 27 to 54 °C. The effect of temperature on the refractive index profile of fibre is studied. The optical parameters and the opto-thermal coefficient of this fibre are determined. Also the variation of oscillation and dispersion energies, zero dispersion wavelengths, coupling efficiency, normalised frequency, number of propagation modes with the temperature and the material dispersion with the wavelength at different temperatures are calculated. Microinterferograms are given for illustration.

Linear magnetohydrodynamic waves in a finely stratified plasma

In a number of astrophysical systems, the magnetic field, instead of varying over a scale comparable with the ''natural'' scale of the object (e.g., tens of thousands of kilometers in the case of the solar convective zone), varies over lengths that are orders of magnitude less than this (e.g., over distances down to 100 km in the case of the magnetic filaments detected in the upper part of the solar convective zone and probably present in much deeper layers). Therefore, the study of the propagation of magnetohydrodynamic (MHD) waves in plasmas with fine magnetic nonuniformities is of considerable general importance for astrophysics. We have developed a general formalism that allows one to treat the propagation of large-scale MHD waves in a finely stratified medium. We demonstrate that the presence of a fine structure of the plasma may produce considerable modifications of the modes existing in a uniform plasma, with a number of propagation modes that may even increase. We also show that the slow MHD mode may experience a collisionless damping, which causes the wave energy to be converted into the energy of the peristaltic modes of the plasma ''resonant'' layers. (c) 2000 The American Physical Society.

Multiple ocean layering models and mode trapping in sublayers for high frequency propagation

It is possible for sublayers in a layered ocean to have pronounced effects on the propagating modes in the water column. For example, atypical effects occur for sound speeds less than the overlaying water column or some overlying sublayers. In some cases one predicts the concentration of a large energy flux in that layer even at model eigenvalues that prohibit propagation in the water column while supporting propagating modes in the sublayer. Since some data suggest the possibility of underlying gaseous regions that support low sound speeds, this is a practical problem. This allows for the possibility that for a layer thick enough to absorb energy before arriving in a higher speed sublayer, the number of propagation modes in the water column can be reduced with increasing frequency. Since this is a frequency-dependent effect [effective (absorbing) thickness of layers is inversely proportional to wavelength or directly proportional to frequency], absorption into the overlying sublayers becomes more pronounced with increased frequency thus reducing the possibility of ‘‘tunnelling’’ which leads to a reduction in propagating modes in the water column. This effect is the converse of the usual case for ocean bottom layering and can be directly measured. Some interesting effects are studied and compared with available data using the high frequency mode model SWAMP. [Work sponsored by the Office of Naval Research.]