Second-harmonic Generation in Glass Fibres

Abstract

Experiments on frequency doubling of 1064 nm and 1053 nm radiation with non-phase-matched and (close to) phase-matched germania-doped silica fibres are reported. The greatest conversion efficiencies are obtained with non-phase-matched fibres that are single-mode at the second-harmonic wavelength, in which phase-matching is thought to arise from a self-written grating. Competition between grating self-writing and self-erasure in these fibres in the absence of an external seed is also reported. Phase-matched fibres allow the formation of the nonlinearity to be studied independently of the phase matching. The nonlinearity is optically induced by exposing the fibre to short-wavelength visible radiation. An enhancement of 10⁴ to 10⁵ in conversion efficiency between the fundamental and the phase-matched LP₃₁ second-harmonic mode over the intrinsic background second harmonic has been observed. We also report on the occurrence of phase-matched second-harmonic generation (SHG) and non-phase-matched SHG in the same fibre.     

Dynamics of self-similar sub-10-fs-pulses in an inhomogeneous highly nonlinear fibre amplifier

ABSTRACT

We study the propagation of ultrashort pulses of width around sub-10 femtosecond in an inhomogeneous highly nonlinear single-mode fibre within the framework of a generalized higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms and spatially inhomogeneous coefficients. Additional effects to the cubic model include the distributed third-order dispersion, self-steepening, self-frequency shift due to stimulated Raman scattering, quintic nonKerr nonlinearity, derivative non-Kerr nonlinear terms, and gain or loss. The exact self-similar brightand dark-solitary-wave solutions of the governing equation are derived via a transformation connected with the constant-coefficient higher-order nonlinear Schrödinger equation with non-Kerr nonlinearity. The constraint relations among the optical fibre parameters for the existence of these self-similar structures are also discussed. Based on these exact solutions, we investigate the dynamical behaviours of self-similar localized pulses in a periodic distributed fibre system for different parameters.     

Design of an As2Se3-based photonic quasi-crystal fiber with highly nonlinear and dual zero-dispersion wavelengths

We propose an As₂Se₃-based highly nonlinear photonic quasi-crystal fiber with dual zero-dispersion wavelengths (ZDWs). Using a full-vector finite element method, the proposed fiber is optimized to obtain high nonlinear coefficient, low confinement loss and two zero-dispersion points by optimizing the structure parameters. Numerical results demonstrate that the proposed photonic quasi-crystal fiber (PQF) has dual ZDWs and the nonlinear coefficient up to 2600 W^?1 km^?1 within the wavelength range from 2 to 5.5 μm. Due to the introduction of the large air holes in the third ring of the proposed fiber, the ability of confining the fundamental mode field can be improved effectively and thus the low confinement loss can be obtained. The proposed PQF with high nonlinearity and dual ZDWs will have a number of potential applications in four-wave mixing, super-continuum generation, and higher-order dispersion effects.     

Steady-state analysis of a saturable nonlinear amplifying fibre loop resonator

Abstract

The steady-state response is analysed for a saturable nonlinear amplifying fibre loop resonator. With the amplification, the bistable region represented by the saturation coefficient of the nonlinear refractive index and by the feedback gain of the fibre loop is found to be highly enlarged when compared with the conventional passive loop resonator.     

Fraunhofer and Fresnel field distributions from the LP01 mode in a micro-sized hollow optical fibre

Abstract

The electric field distribution of a LP₀₁ mode and properties of the evanescent-wave field in a micro-sized hollow optical fibre under the weakly guiding approximation are analysed. The far- and near-field distributions of the output beam from the LP₀₁ mode and its propagation characteristics in free space are calculated numerically from Fraunhofer and Fresnel diffraction theory. We also derive an analytical expression of the far-field distribution of the LP₀₁ mode and discuss its applicable conditions. Our study shows that the output beam of the LP₀₁ mode in the hollow fibre is a dark hollow divergent beam whose near-field divergent angle is slightly smaller than the far-field divergent angle. The dark spot size (DSS) of the beam in the near field is about equal to the beam radius r ₀, whereas the DSS in the far field is smaller than its beam radius. We analyse the dependences of the far-field divergent angle of the output beam from the LP₀₁ mode on various fibre parameters and briefly discuss potential applications of the dark hollow beam in atomic physics and atomic optics.     

Optical solitons in some SIT type equations

Abstract

In this paper, we consider the SIT type equations with group velocity dispersion, Kerr nonlinearity, higher order dispersion, self-steepening and pumping effects and analyse the dynamics of ultra short pulse propagation in nonlinear resonant fibre. The nature of the pulse propagation is governed by the nonlinear Schrödinger-Maxwell Bloch (NLS-MB) type equations. Considering the isospectral and non-isospectral eigen value parameter, we generate the soliton solutions through the Bäcklund transformation method.     

In-fibre LP11–LP21 mode conversion using force-induced long-period fibre gratings with polarization controllers

ABSTRACT

Mode conversion between higher-order modes is attained in a step-index four mode fibre using an in-line polarization controller followed by a force-induced long period fibre grating. By adjusting the field orientation of the LP₁₁ mode to the antisymmetric fibre grating, the LP₁₁ mode is converted to the LP₂₁ mode with a spatially periodic force of 50 N along the fibre length of 50?mm. The mode conversion is evaluated by observing the far-field and near-field patterns of the fibre output and by comparing the transmitted optical power with and without the additional two-mode fibre. The phase-matching grating period is required of the accuracy of roughly ±5?μm and the radiation loss during the mode conversion is as low as 0.01?dB.     

Coherent Brillouin scattering in noncentrosymmetric semiconductors: bound and free charge carriers contribution

With the aid of a hydrodynamic model for semiconductor plasmas, an analytical investigation of coherent Brillouin scattering (CBS) has been made in noncentrosymmetric (NCS) semiconductor plasmas both under the presence and in the absence of an externally applied magnetic field. Using the coupled mode approach, the nonlinear induced polarization and third-order nonlinear optical susceptibility, due to bound and free charge carrier nonlinearity, are obtained. The analysis further deals with the qualitative behavior of the threshold pump electric field E _T for onset of CBS and the resulting gain coefficient (steady-state as well as transient, [g _B]_SS,TR) in NCS semiconductor plasmas. Numerical estimates are made for InSb crystal at 77 K duly irradiated by a pulsed 10.6 μm CO₂ laser. The effects of piezoelectricity, doping concentration and magnetic field on both the E _T and [g _B]_SS,TR have been studied in detail. E _T required for onset of the CBS process is found to be lower when piezoelectricity is present and the doping level of the semiconductor is moderate than in other conditions. It is found that when the magnetic field is applied, the coherent backward Stokes wave can be amplified by a factor of 10² in NCS semiconducting crystals. The analysis also suggests the idea of pulse compression and the possibility of observing the phase conjugation reflection coefficient ～10⁶ which proves its potential for the fabrication of CBS-based phase conjugate mirrors.     

Analysis of Modulational Instability in Monomode Optical Fibres with High-order Nonlinearity

Abstract

The modulational instability (MI) in monomode optical fibres with fifth-order nonlinearity, fibre loss, higher-order dispersion, and the temporal variation of third-order nonlinearity is studied theoretically. The conditions for the existence of the MI and the maximal modulational growth are given and discussed in detail. The results obtained show that the key factor dominating the producing condition of the MI is the power P of the continuous wave initially launched into the optical fibres. If P falls into 3/10<P/P ₀ <1/2 where P ₀ is defined as characteristic power, the MI can be produced in the range of not only anomalous group velocity dispersion but also the normal in which the final evolution state of the modulated wave is dark soliton.     

Molecular design and synthesis of branched bichromophore-attached linear fluorinated polyimides for nonlinear optical applications

A branched structure bichromophore was developed to increase the nonlinearity of optical polymers. The branched bichromophore was incorporated into the polymer backbone to prepare a novel nonlinear optical (NLO) side-chain fluorinated polyimide with high optical nonlinearity and good thermal stability. The novel nonlinear optical side-chain fluorinated polyimide exhibits a large electro-optic (E-O) coefficient (γ₃₃) (34 pm/V at 1550 nm) which is larger than that of the conventional side-chain optical polyimide. This is mainly attributable to an increased chromophore concentration and high polarizing efficiency derived from the branched structure. The branched structure of the bichromophore is incorporated into a polymer backbone to result in a high chromophore concentration. Moreover, the three-dimensional (3D) architecture and large molecular size of the branched bichromophore can spatially shield from strong interchromophore electrostatic interactions to enhance the poling efficiency. The side-chain fluorinated polyimide exhibits excellent solubility in common organic solvents, good film-forming property, high glass-transition temperature (T _g) (190 °C) and thermal stability up to 235 °C.     

钛合金蠕变损伤的非线性Lamb波检测

金属材料在高温高压服役过程中会发生蠕变损伤,检测和评价金属材料的早期蠕变损伤具有重要工程意义。针对Ti60钛合金蠕变损伤采用非线性Lamb波进行检测,分别选择Lamb波S_1-S_2模式对和A_4-S_8模式对开展钛合金蠕变损伤试样的实验测量,并采用归一化非线性参数来表征钛合金的蠕变损伤状态。研究结果表,明两种模式对的归一化非线性参数随着材料蠕变损伤程度的加剧均表现出"上升-下降"的变化趋势,且A_4-S_8模式对归一化非线性参数变化率比S_1-S_2模式对更大,说明该模式对对Ti60钛合金蠕变损伤更为敏感。     

Third-order optical nonlinearity and figure of merit of CdS nanocrystals chemically stabilized in spin-processable polymeric films

We report figure of merit for sub-picosecond nonlinearity at 815 nm for nanocrystals of CdS dispersed in poly(methyl methacrylate) (PMMA). CdS nanocrystals were successfully transferred from the aqueous to the organic phase and stabilized in PMMA films using a new chemical route. We report a nonlinear Kerr coefficient n ₂ of –(8.4 ± 0.4) × 10^–14 cm²/W, and a one-photon figure of merit W = 1.2 for 3 wt% CdS-doped PMMA film. The results suggest the combined processibility and promising optical properties of such materials for use in transmission-mode optical switching and limiting devices based on ultrafast nonlinearity.     

Finite element characterization and parametric analysis of the nonlinear behaviour of an actual d 15 shear MFC

Nonlinear dependence between mechanical deformation and applied voltage has been experimentally observed on a recently manufactured lengthwise poled piezoelectric d ₁₅ shear macro-fibre composite (MFC) transducer. This work proposes a methodology to model this phenomenon by combining the nonlinear behaviour of the constituent piezoceramic fibre (electric field dependence of material properties) with a finite element homogenization technique to evaluate the resulting nonlinearity of the effective properties of the d ₁₅ MFC. Results show that the experimentally observed nonlinear behaviour of d ₁₅ MFC is reasonably well predicted by the proposed methodology indicating that this behaviour could be explained by an electric field dependence of the piezoceramic fibre material properties. Results also show that d ₁₅ and ${\epsilon_{11}^T}$ coefficients of the d ₁₅ MFC are not significantly reduced by the MFC packaging, while e ₁₅ and G ₁₃ coefficients are reduced by 90 %, compared to the piezoceramic fibre ones. A conducted parametric analysis indicates that the actuation performance of the d ₁₅ MFC transducer could be improved by increasing the active layer thickness.     

Nonlinear Refraction and Absorption in 4BCMU Planar Waveguides at 1·064 μm Wavelength

Abstract

We have measured the nonlinear refractive index, n ₂, and two-photon absorption coefficient, β, in 4BCMU planar waveguides at 1·064 μm wavelength using picosecond pulses. We use a beam propagation code, with n ₂ and β as fitting parameters, to make numerical comparison with the experimental data. Deduced values from this analysis are n₂ = ? 1·5 × 10^?13 cm²W^?1, confirming the negative sign of the nonlinearity at this wavelength, and β = 0·01 cm MW^?1.     

Phase conjugation in four-wave mixing of cw radiation under conditions of strong self-interaction

An experimental investigation is made of the influence of strong self-interaction of the reference waves on phase conjugation in four-wave mixing of cw radiation in a medium with a thermal nonlinearity. It is shown that the thermal lens formed by the Gaussian reference beams reduces the nonlinear reflection coefficient appreciably (several-fold) and causes a deterioration in the phase conjugation quality. Pis’ma Zh. Tekh. Fiz. 23, 60–63 (August 12, 1997)     

Output Characteristics of an Optical Fibre Ring Resonator Using a Planar or Nonplanar 3 × 3 Fibre Coupler: A Comparison

Abstract

A comparison is made between the output characteristics of type 1 optical fibre ring resonators with a different type of 3 × 3 fibre coupler, that is a planar or a nonplanar coupler. Three different nonplanar couplers are formed when the central fibre 1 of a loosely coupled planar 3 × 3 fibre coupler is displaced normally from the common plane. Such a 3 × 3 fibre coupler can be identified by the value of its relative coupling ratio m ₃. The dependence of the output intensities of the ring resonator on the coupling length kd and the relative coupling ratio m ₃ of the 3 × 3 fibre coupler is investigated. The former dependence can be used as a guide to obtain suitable output characteristics of a fibre ring resonator for a specific application, while the latter can be used to choose the right type of 3 × 3 fibre coupler to build a fibre ring resonator. It is found that the output characteristics of a fibre ring resonator with a 3 × 3 planar (m ₃ = 0) or an equilateral triangular (m ₃ = 1) fibre coupler are usually better than those of the others.     

Optical fibre Fabry–Perot relative humidity sensor based on HCPCF and chitosan film

Abstract

An optical fibre Fabry–Perot interferometer (FPI) sensor for relative humidity (RH) measurement is proposed. The FPI is formed by splicing a short section of hollow-core photonic crystal fibre(HCPCF) to single mode fibre and covering a chitosan film at the end of HCPCF. The refractive index of chitosan and film thickness will change with ambient RH, leading to the change in the reflected interference spectrum of FPI. RH response of the FPI sensor is analysed theoretically and demonstrated experimentally. It shows nonlinear response to RH values from 35 to 95%RH. The interference fringe shifts to shorter wavelength as RH increases with a maximum sensitivity of 0.28 nm/%RH at high RH level. And the fringe contrast also decreases as RH increases with an available maximum sensitivity of 0.5 dB/%RH. The sensor shows good stability and fast response time less than 1 min. With its advantages of compact structure, good performance, simple and safe fabrication, the proposed optical fibre FPI sensor has great potential for RH sensing.     

Calculation of Nonlinear Waves Guided by Optical Fibres Using the Resonance Technique

Abstract

A recently developed, simple, and easily programmable method based on a resonance technique for the analysis of nonlinear guided modes for planar geometry has been extended to include fibre configurations. We consider here nonlinear media of the general type (non-Kerr media) including the more complicated but realistic case of saturable media. In the present paper, as an example of the proposed methodology, the following configuration is treated: a circular optical fibre consisting of a linear core bounded by a nonlinear cladding medium. The numerical results obtained by the method, correspond to the ‘weak guidance’ approximation, including both field distribution and power calculations.     

Self-deflection of Three-dimensional Optical Beams by a Thin Nonlinear Layer with Saturable Dispersive and Absorptive Nonlinearity

Abstract

This paper describes self-deflection effects arising from the propagation of symmetric and asymmetric three-dimensional scalar optical beams through thin nonlinear layers. The model of nonlinearity used includes both saturation and absorption. In several cases, significant differences are observed between the present three-dimensional results and previous two-dimensional results based on the Kerr model of nonlinearity. Also, the existence of a large axial component of the self-deflected beam for a three-dimensional geometry against the absence of this component for a two-dimensional geometry is discussed.