Birefringent Optical Fiber Research Articles

Vector semirational rogue waves for the coupled nonlinear Schrödinger equations with the higher-order effects in the elliptically birefringent optical fiber

ABSTRACTUnder investigation in this paper are the coupled nonlinear Schrödinger equations with the higher-order effects arising from the elliptically birefringent optical fiber. We show the existence and properties of the analytic vector rational solutions and semirational rogue-wave solutions via the Darboux dressing transformation. Those solutions include the vector Peregrine solutions, bright- and dark-rogue-wave solutions, and breather-like pulses with rogue-wave solutions. We observe that the breather-like pulses may be generated because of the superposition of the dark and bright contributions in each of the two wave components. Peregrine and dark–bright solitons can separate when we decrease the value of . On the contrary, Peregrine and dark–bright solitons can combine without the Peregrine lump identifiable when we increase the value of .

A Fokas approach to the coupled modified nonlinear Schrödinger equation on the half‐line

In this work, we discuss the coupled modified nonlinear Schrödinger (CMNLS) equation, which describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. By use of the Fokas approach, the initial‐boundary value problem for the CMNLS equation related to a 3×3 matrix Lax pair on the half‐line is to be analyzed. Assuming that the solution {u(x,t),v(x,t)} of CMNLS equation exists, we will prove that it can be expressed in terms of the unique solution of a 3×3 matrix Riemann‐Hilbert problem formulated in the plane of the complex spectral parameter λ. Moreover, we also get that some spectral functions s(λ) and S(λ) are not independent of each other but meet a global relationship.

Effects of intermode nonlinearity and intramode nonlinearity on modulation instability in randomly birefringent two-mode optical fibers

We analyze in detail the effects of the intermode nonlinearity (IEMN) and intramode nonlinearity (IRMN) on modulation instability (MI) in randomly birefringent two-mode optical fibers (RB-TMFs). In the anomalous dispersion regime, the MI gain enhances significantly as the IEMN and IRMN coefficients increases. In the normal dispersion regime, MI can be generated without the differential mode group delay (DMGD) effect, as long as the IEMN coefficient between two distinct modes is above a critical value, or the IRMN coefficient inside a mode is below a critical value. This critical IEMN (IRMN) coefficient depends strongly on the given IRMN (IEMN) coefficient and DMGD for a given nonlinear RB-TMF structure, and is independent on the input total power, the power ratio distribution and the group velocity dispersion (GVD) ratio between the two modes. On the other hand, in contrast to the MI band arising from the pure effect of DMGD in the normal dispersion regime, where MI vanishes after a critical total power, the generated MI band under the combined effects of IEMN and IRMN without DMGD exists for any total power and enhances with the total power. The MI analysis is verified numerically by launching perturbed continuous waves (CWs) with wave propagation method.

Refractive index retrieving of polarization maintaining optical fibers

Abstract In this paper, the cross-section images, of two different types of polarization maintaining (PM) optical fibers, are employed to estimate the optical phase variation due to transverse optical rays passing through these optical fibers. An adaptive algorithm is proposed to recognize the different areas constituting the PM optical fibers cross-sections. These areas are scanned by a transverse beam to calculate the optical paths for given values of refractive indices. Consequently, the optical phases across the PM optical fibers could be recovered. PM optical fiber is immersed in a matching fluid and set in the object arm of Mach-Zehnder interferometer. The produced interferograms are analyzed to extract the optical phases caused by the PM optical fibers. The estimated optical phases could be optimized to be in good coincidence with experimentally extracted ones. This has been achieved through changing of the PM optical fibers refractive indices to retrieve the correct values. The correct refractive indices values are confirmed by getting the best fit between the estimated and the extracted optical phases. The presented approach is a promising one because it provides a quite direct and accurate information about refractive index, birefringence and beat length of PM optical fibers comparing with different techniques handle the same task.

Polarization state evolution in spun birefringent optical fibers

The evolution of the polarization state (PS) of radiation propagating in spun or twisted birefringent optical fibers is considered for a wide range of fiber parameters, and presented in a descriptive way using the Poincaré sphere. The effects of the bandwidth and the polarization state of input radiation, of the external magnetic field, and of the fiber bending on the polarization state evolution have been described for the most practical cases. An explanation of how the helical structure of the built-in linear birefringence in spun fibers provides the existence of the helical elliptically-polarized eigenmodes has been given. In spun fibers with a relatively large spin rate, the PS evolution is shown to change its azimuthal direction.

Bragg gratings multipusle inscription efficiency dependence on angular position of elliptical stress cladding in birefringent optical fibers

Subject of Research.The paper deals with mutlipulse inscription comparative results of the type IBragg gratings in the birefringent optical fiber with elliptical stress cladding and increased GeO2 concentration at different birefringence axes positions. Method. The gratings were inscribed by the phase mask method. The excimer laser Coherent COMPexPro 102F, working with the gas mixture KrF (248 nm), was used as the radiation source. The phase mask Ibsen Photonics with a period of1065.3 nm was used. Main Results.The results have shown that the multipusle inscription is more effective and has better dynamics when the plane containing the fiber axis and its slow birefringence axis is parallel to the writing radiation incidence plane containing the fiber axis. Practical Relevance. Theresearch results give the possibilityto make recommendations for the multipulse Bragg gratings inscription efficiency enhancement in the specialty birefringent fibers. The pre-inscription positioning of birefringence axes also makes it possible to reduce the polarization fading that is the noise source in phase interferometric sensors.

Lax pair and vector solitons for a variable-coefficient coherently-coupled nonlinear Schrödinger system in the nonlinear birefringent optical fiber

Nowadays, with respect to the nonlinear birefringent optical fibers, efforts have been put into investigating the coupled nonlinear Schrödinger (NLS) systems. In this paper, symbolic computation on a variable-coefficient coherently-coupled NLS system with the alternate signs of nonlinearities is performed. Under a variable-coefficient constraint , the system is shown to be integrable in the Lax sense with a Lax pair constructed, where t is the normalized time, is the strength of the four wave mixing terms, and is the strength of the anti-trapping parabolic potential. With an auxiliary function, bilinear forms, vector one- and two-soliton solutions are obtained. Figures are displayed to help us study the vector solitons: When is a constant, vector soliton propagates stably with the amplitude and velocity unvarying (vector soliton’s amplitude changes with the change of that constant, while its velocity can not be affected by that constant); When is a t-varying function, i.e. , amplitude and velocity of the vector soliton both vary with t increasing, while affects the vector soliton’s amplitude and velocity. With the different or , interactions between the amplitude- and velocity-unvarying vector two solitons and those between the amplitude- and velocity-varying vector two solitons are displayed, respectively. By virtue of the system and its complex-conjugate system, conservation laws for the vector solitons, including the total energy and momentum, are constructed.

FBGs written in specialty fiber for high pressure/high temperature measurement.

In this paper, we evaluate different thermal treatments in order to stabilize fiber Bragg gratings written by a femtosecond pulsed laser in specialty highly birefringent micro-structured optical fiber, targeting pressure monitoring at high pressure and high temperature environments. We have obtained a pressure sensitivity of 3.30 pm/bar up to 1400 bar and 290 °C. An effective thermal treatment has been experimentally implemented, yielding a nearly unchanged reflectivity at high temperature in combination with stable temperature and pressure readings: a standard deviation of 0.42 bar in the pressure reading was observed over 7 days at 280°C.

Visualization of fiber Bragg gratings of type II induced by radiation of an ArF excimer laser in an anisotropic single-mode optical fiber with an elliptical stress cladding

results in visualization of fiber Bragg gratings of type II recorded in birefringent single-mode optical fibers with an elliptical stress cladding with a high concentration of germanium dioxide are shown. Periodic structures of the induced refractive index are inscribed by a single pulse of an excimer laser with a working- gas mixture of ArF using the phase mask. Fiber Bragg gratings into anisotropic optical fiber were investigated by optical and scanning-probe microscopes. It is shown that single-pulse recording by ArF excimer laser creates in the fiber, both inside and on the surface of the quartz cladding, periodic structures, the spatial period of which corresponds to the period of the phase mask, optimized for the +1/–1 diffraction order.

The analysis of scattering interference pattern from the birefringent optical fiber with elliptical stress cladding

An experimental setup for observation of a scattering interference pattern from optical fibers is assembled. The dependence of scattering interference pattern from the anisotropic optical fiber with 4mol% of GeO2 in core on the stress applying ellipse position is studied experimentally. The anisotropic optical fiber with 4mol% of GeO2 in core was used for this study. The mathematical modeling and experimental data are in a good agreement. On its basis some recommendations for less time-consuming stressing ellipse orientation in specialty fibers used in fiber-optic interferometric sensors determination are made.

Thirring dipole solitons in birefringent optical fibers with spatio-temporal dispersion, four-wave mixing and non-Kerr law nonlinearities

In this paper, we investigate, for the first time, Thirring dipole solitons in birefringent optical fibers with Kerr and parabolic law nonlinearities in the presence of spatio-temporal dispersion and four-wave mixing terms. Based on a complex wave ansatz, we solved analytically tow variant of the vector coupled nonlinear Schrödinger equation. All the necessary parametric conditions for the existence of the Thirring dipole solitons are extracted.

Rogue waves in birefringent optical fibers: elliptical and isotropic fibers

Rogue waves in elliptically polarized birefringent optical fibers are analyzed within the framework of a ‘non-integrable’ coupled nonlinear Schrödinger (CNLS) system, which can be used to describe pulse propagation in elliptically birefringent optical fibers. The modulation instability (MI) analysis of this system reveals that, in general, this coupled system is more unstable than its scalar (isotropic) counterpart. In fact, numerical simulations indicate that the generation of rogue events is comparable to the isotropic case. This implies that there is no 1-1 correspondence between rogue wave generation and MI, in these media. The birefringence angle for which the maximum number of rogue events is identified and the nature of the rogue wave is described for the different cases. Although the CNLS system is non-integrable in certain cases these rogue waves are well approximated by the rational solutions of the scalar integrable nonlinear Schrödinger (NLS) equation, while in other cases solitons of the scalar integrable NLS equation are better approximations of these rogue events. In every case, the relative solution of the isotropic system is found to be well suited to describe these waves.

Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger equations in the birefringent optical fibers.

We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.

Exact Soliton Solutions for the (2+1)-Dimensional Coupled Higher-Order Nonlinear Schrödinger Equations in Birefringent Optical-Fiber Communication* *Supported by the National Natural Science Foundation of China under Grant No. 61671227 and the Natural Science Foundation of Shandong Province under Grant No. ZR2014AM018

In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higher-order nonlinear Schrödinger equations. In this paper, we will investigate the bright and dark soliton solutions of (2+1)-dimensional coupled higher-order nonlinear Schrödinger equations, with the aid of symbolic computation and the Hirota method. On the basis of soliton solutions, we test and discuss the interactions graphically between the solitons in the x-z, x-t, and z-t planes.

Experimental investigation of the thin fiber-optic hydrophone array based on fiber Bragg gratings

Abstract The paper presents the results of experimental investigations of the fiber optic hydrophone array consisting of six sensors, placed in one thin sensitive cable. Sensors were formed by pairs of Bragg gratings spaced 1.5 m apart and recorded in a birefringent optical fiber with the elliptical stressed coating. To form an extended sensor array the optical fiber was additionally covered with a silicone material RTV655 and protective coatings. Experimental investigations of the array showed that fiber-optic sensors pressure sensitivity increases as the acoustic frequency decreases at average value from −169.4 dB re rad/uPa at 495 Hz to −143.7 dB re rad/uPa at 40 Hz. The minimum detectable pressure was at average value from 53 mPa/√Hz at 495 Hz to 8.3 mPa/√Hz at 40 Hz. The obtained results might be used for developing and producing long thin hydroacoustic arrays for geophysical investigations and other hydroacoustic applications.

Critical blowup in coupled Parity-Time-symmetric nonlinear Schrödinger equations

In this article, we obtain suffcient conditions to obtain finite time blowup in a system of two coupled nonlinear Schrodinger (NLS) equations in the critical case. This system mainly considered here in dimension 2, couples one equation including gain and the other one including losses, constituting a generalization of the model of pulse propagation in birefringent optical fibers. In the spirit of the seminal work of Glassey, the proofs used the virial technique arguments.

On the Global Behavior of Solutions of a Coupled System of Nonlinear Schrödinger Equation

We mainly study a system of two coupled nonlinear Schrödinger equations where one equation includes gain and the other one includes losses. This model constitutes a generalization of the model of pulse propagation in birefringent optical fibers. We aim in this study at partially answering a question of some authors in [1]: “Is the H1‐norm of the solution globally bounded in the Manakov case, when ?” We found that in the Manakov case, and when , the solution stays in , and also that the H1‐norm of the solution cannot blow up in finite time. In the Manakov case, an estimate of the total energy is provided, which is different from that has been given in [1]. These results are corroborated by numerical results that have been obtained with a finite element solver well adapted for that purpose.

Darboux transformation and vector solitons for a variable-coefficient coherently coupled nonlinear Schrödinger system in nonlinear optics

Efforts have been put into investigating a variable-coefficient coherently coupled nonlinear Schrodinger system with the alternate signs of nonlinearities, describing the propagation of the waves in the nonlinear birefringent optical fiber. Via the Lax pair, Darboux transformation for the system is derived. Then, we derive the vector one- and two-soliton solutions. Figures are displayed to help us study the properties of the vector solitons: with the strength of the four-wave mixing terms γ(t) as a constant, the vector soliton propagates with the unvarying velocity and amplitude; with γ(t) being a time-dependent function, amplitude and velocity of the vector soliton keep varying during the propagation; bell- and M-shaped solitons can both be observed in q2 mode, while we just observe the bell-shaped soliton in q1 mode, where q1 and q2 are the two slowly varying envelopes of the propagating waves; head-on and overtaking interactions between the vector two solitons are both presented.

Birefringent optical fibers axial positioning technique for fiber Bragg gratings writing

An experimental setup for fiber Bragg gratings writing with preliminary optical fiber orientation has been described in this paper. The writing efficiency results of Bragg gratings of type I in birefringent optical fiber with an elliptical stress cladding at two extreme positions of the stress ellipse were presented. These results were compared to the similar data, received after the fiber Bragg gratings inscription in PANDA carried out in the same way.

Modulation instabilities in randomly birefringent two-mode optical fibers**Project supported by the Natural Science Foundation of Jiangsu Provincial Universities (Grant No. 14KJB140009), the National Natural Science Foundation of China (Grant No. 11447113), and the Startup Foundation for Introducing Talent of NUIST (Grant No. 2241131301064).

Modulation instabilities in the randomly birefringent two-mode optical fibers (RB-TMFs) are analyzed in detail by accounting the effects of the differential mode group delay (DMGD) and group velocity dispersion (GVD) ratio between the two modes, both of which are absent in the randomly birefringent single-mode optical fibers (RB-SMFs). New MI characteristics are found in both normal and anomalous dispersion regimes. For the normal dispersion, without DMGD, no MI exists. With DMGD, a completely new MI band is generated as long as the total power is smaller than a critical total power value, named by Pcr, which increases significantly with the increment of DMGD, and reduces dramatically as GVD ratio and power ratio between the two modes increases. For the anomalous dispersion, there is one MI band without DMGD. In the presence of DMGD, the MI gain is reduced generally. On the other hand, there also exists a critical total power (Pcr), which increases (decreases) distinctly with the increment of DMGD (GVD ratio of the two modes) but varies complicatedly with the power ratio between the two modes. Two MI bands are present for total power smaller than Pcr, and the dominant band can be switched between the low and high frequency bands by adjusting the power ratio between the two modes. The MI analysis in this paper is verified by numerical simulation.