Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber

We investigate the soliton dynamics in tapered parabolic index fibers via symbolic computation for a variety of dispersion profiles to inspect how a specific dispersion profile controls the optical soliton. By means of AKNS procedure, Lax pair is constructed for nonlinear Schrödinger equation with variable coefficients. Using obtained Lax pair, multi-soliton solutions are generated via Darboux transformation technique. Using multi-soliton solutions, soliton dynamics in tapered parabolic index fiber with the hyperbolic, Gaussian, exponential, and linear profiles are discussed. Results obtained in this study will be of certain potential application on construction of the nonlinear optical devices by soliton control. Results obtained in this study will be of certain value to the studies on the propagation and application of the soliton in the tapered parabolic index fiber and dispersion-managed fiber system.     

Investigation of evanescent coupling between tapered fiber and a multimode slab waveguide

A tapered fiber-slab waveguide coupler (TFSC) is proposed in this paper. Both the numerical analysis based on the beam propagation method and experiments are used for investigating the dependencies of TFSC transmission features on their geometric parameters. From the simulations and experimental results, the rules for fabricating a TFSC with low transmission loss and sharp resonant spectra by optimizing the configuration parameters are presented. The conclusions derived from our work may provide helpful references for optimally designing and fabricating TFSC-based devices, such as sensors, wavelength filters, and intensity modulators.     

Combinational system of a truncated ball lens and a hyperbolic lens for collimating a highly divergent source

We propose the use of a truncated ball lens in a collimating system to transform a spherical wave from a highly divergent source into a plane wave. The proposed scheme, which incorporates a hyperbolic lens, is discussed, and the overall system is found to have a large acceptance angle and to be free of spherical aberration. Diffraction and polarization effects are neglected, as well as skew rays.     

Dual wavelength erbium-doped fiber laser using a tapered fiber

A tapered fiber is fabricated by heating and stretching a piece of optical fiber after the polymer protective cladding has been removed. An equidistant comb-like transmission spectrum, with a spacing of 1.6?nm and an extinction ratio of more than 5?dB, was obtained by the tapered fiber due to the multibeam interferences of the cladding modes. The tapered fiber was applied in a ring erbium-doped fiber laser (EDFL) to generate dual-wavelength lasing oscillations. The EDFL operates at wavelengths of 1557.0?nm and 1558.6?nm with a stable peak power and a signal-to-noise ratio of more than 40?dB.     

Tunable Brillouin-erbium fiber laser incorporating a low-cost biconic tapered fiber

A new method of tuning a multi-wavelength Brillouin-erbium fiber laser (BEFL) within a Fabry–Perot cavity by incorporating a low-cost biconic tapered fiber is reported. The biconic tapered fiber was fabricated using a flame elongation technique and it was incorporated into the BEFL system to position the self-lasing cavity modes over a tuning range of 5.5 nm within the erbium-doped fiber gain profile. By injecting the Brillouin pump near to the tunable self-lasing cavity modes, it suppresses the modes and generates stable cascaded Brillouin–Stokes lines with more than 20 dB signal-to-noise ratio.     

Very low-loss passive fiber-to-chip coupling with tapered fibers

A novel passive fiber-to-chip coupling based on the use of fiber tapers embedded in a guiding structure is proposed. By beam-propagation calculations it is verified that this new coupling method exhibits a very low insertion loss. Major advantages of the proposed method compared with butt coupling are demonstrated by simulation results: first, tolerance requirements for the fibers, e.g., diameter variations and core eccentricity, and for fabrication of the alignment structure are reduced by at least 1 order of magnitude. Second, coupling to waveguides of nearly arbitrary dimensions and refractive indices seems to be possible. Experimental results on thermal drawing of fiber tapers are presented and used as input data for the simulations. A concept for fabrication of the new coupling method with the Lithographic Galvanik Abformung (LIGA) technique is presented.     

Optical coupling method utilizing a lensed fiber integrated with a long-period fiber grating

A novel optical coupling scheme that uses a lensed fiber integrated with a long-period fiber grating (LPFG) is proposed. Two experiments are performed to demonstrate the validity of such a scheme in single-mode-fiber-single-mode-fiber (SMF-to-SMF) and laser-diode-single-mode-fiber (LD-to-SMF) coupling setups. The measured results show that for an appropriate lens radius the addition of a LPFG will lead to a higher coupling efficiency over a longer range of working distance than without the LPFG. Coupling efficiencies of ~78% and 35% are achieved for corresponding working distances of ~250 and 110 mum, 1-dB longitudinal tolerances of ~40 and 26 mum, and 1-dB transverse tolerances of ~7.6 and 2.6 mum for SMF-to-SMF and LD-to-SMF, respectively.     

熔锥光纤与球微腔耦合系统的理论模拟

利用H. J. Shaw提出的单模光纤定向耦合器的分析方法并结合微球腔的特性,对熔锥光纤与球微腔系统的耦合特性进行了理论分析和数值模拟。研究表明,由于原本简并的球腔模式受腔体偏心率的影响而解除,系统吸收峰间距减小,Q值( 106 ~107 )比将腔体视为理想球时提高了三个数量级。这与已报道的实验结果相吻合。     

Coupling of a laser diode to single-mode fiber with an upside-down tapered lens end

We present in detail a simple analysis of the coupling efficiency and possible transverse and angular misalignment losses of a laser diode to single-mode, step-index fiber excitation with an upside-down tapered lens (UDTL) end, drawn by molding the end of a step-index fiber. The analysis employs our recently formulated ABCD matrix for an UDTL and has the advantage of simplicity compared with complicated methods involving cumbersome numerical integrations. Both the analysis and the results should be useful in designing coupling optics that use such lenses in the context of probable misalignments.     

Low-cost optical amplitude modulator based on a tapered single-mode optical fiber

A new, to our knowledge, modulator based on a tapered single-mode optical fiber is introduced. The electro-optic device consists of a tapered optical fiber placed on a resonator made of a piezoelectric material. An electrical signal applied to the piezoelectric material makes the taper bend, and that displacement produces a modulation in the intensity of the optical signal traveling through the fiber. This device is very easy to build and is low in cost. Because of its nature, this new device might be very useful in optical fiber sensors. Its performance is analyzed, and the results are discussed.     

Neutron transmission probability through a revolving slit for a continuous source and a divergent neutron beam

An analytical calculation for the transmission probability of neutrons travelling through a revolving slit is presented here. For the first time, two effects have been taken into account in the same approach, that is, on the one hand, the fact that the neutron beam might be divergent and, on the other hand, that neutrons from a continuous source can arrive at different times at the chopper. Furthermore, the neutron distribution at a given distance behind the chopper has been calculated and these theoretical results have been compared with simulated data obtained with the VITESS simulation program. The theoretical and the simulated curves are in good agreement.     

Scattering of a line source by a cylindrical parabolic impedance surface

The scattering of the radiated fields of a line source by a cylindrical parabolic reflector, which has impedance boundary conditions on its surface, is obtained by using the surface integrals of the modified theory of physical optics. The reflected geometrical optics and edge diffracted fields are evaluated by using the asymptotic methods. The scattered fields are plotted numerically for various parameters such as surface impedance and angles of the edges.     

Homogenization of a degenerate parabolic problem in a highly heterogeneous periodic medium

We consider the homogenization of a time-dependent heat transfer problem in a highly heterogeneous periodic medium made of two connected components having heat capacities c_α(x) and heat conductivities a_α(x), α=1,2 of order one, separated by a third material with thickness of the same order ε than the basic periodicity cell having heat capacity c₃(x) and conductivity λa₃(x) where a₃ is of order one and λ tends to zero with the size ε of the elementary cell. We assume only that c_i(x)?0, i=1,2,3 almost everywhere, such that the problem can be degenerate (parabolic-elliptic). We show that the critical value of the problem is and identify the homogenized problem depending on δ is zero, strictly positive finite or infinite.     

Accurate coupling coefficients for fiber couplers with weakly fused cross sections

For fused tapered fiber couplers with weakly fused cross sections, power coupling takes place between two touching tapered cladding cylinders embedded in the air, and the cylinders then become a strongly guiding structure. We provide accurate polarization-dependent coupling coefficients for such a structure, on the basis of a rigorous vectorial numerical calculation. Our results for the corresponding weakly guiding structure are compared with previous vector perturbation methods base on scalar fields. It is found that the scalar theories are not applicable to those cases with large normalized frequencies or with small fiber separations when the polarization-splitting effect is concerned.     

Microbend-induced mode coupling in a graded-index multimode fiber

We present a theoretical analysis of the mode coupling effects at a microbend along a graded-index (GI) multimode fiber (MMF). By matching the incident and excited mode fields at the microbend, we obtain the coupling coefficients among the guided modes at different microbending conditions. The theoretical results compare well with the experimental results from near-field measurements on a GI MMF subject to microbending. The usefulness of our theory is demonstrated with two applications: (i) an explanation of the operation principle of a wavelength-switchable fiber laser that contains a fiber Bragg grating in a GI MMF and (ii) quantification of the function of a microbend-based mode scrambler.     

Iterative computational identification of a space-wise dependent source in parabolic equation

Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems, tasks of recovering the dependence of the right-hand side on time and spatial variables can be treated as independent. These tasks relate to a class of linear inverse problems, which sufficiently simplifies their study. This work is devoted to finding the dependence of right-hand side of multidimensional parabolic equation on spatial variables using additional observations of the solution at the final point of time – the final overdetermination. More general problems are associated with some integral observation of the solution in time – the integral overdetermination. The first method of numerical solution of inverse problems is based on iterative solution of boundary value problem for time derivative with non-local acceleration. The second method is based on the known approach with iterative refinement of desired dependence of the right-hand side on spatial variables. Capabilities of proposed methods are illustrated by numerical examples for a two-dimensional problem of identifying the right-hand side of a parabolic equation. The standard finite-element approximation in space is used, whilst the time discretization is based on fully implicit two-level schemes.     

Single-mode fiber coupling efficiency with graded-index rod lenses

Losses are calculated for the single-mode graded-index- (GRIN-) lens coupler. The main advantage of this coupling system is large separation between fibers with small power loss. The excess loss of the GRIN-lens coupler is due primarily to the misalignments of the GRIN lenses and is most sensitive to angular tilt rather than lateral offset or end separation. The excess loss is calculated from the overlap of two differently sized or misaligned Gaussian beams. Experimental results show that this method is adequate for predicting losses that are due to misalignments of the GRIN lenses.     

Miniature tapered photonic crystal fiber interferometer with enhanced sensitivity by acid microdroplets etching

We fabricate a miniature tapered photonic crystal fiber (PCF) interferometer with enhanced sensitivity by acid microdroplets etching. This method is very simple and cost effective, avoiding elongating the PCF, moving and refixing the device during etching, and measuring. The refractive index sensing properties with different PCF diameters are investigated both theoretically and experimentally. The tapering velocity can be controlled by the microdroplet size and position. The sensitivity greatly increases (five times, 750?nm/RIU) and the size decreases after slightly tapering the PCF. The device keeps low temperature dependence before and after tapering. More uniformly and thinly tapered PCFs can be realized with higher sensitivity (～100 times) by optimizing the etching process.