Solitons and other solutions of the nonlinear fractional Zoomeron equation

In order to investigate the nonlinear fractional Zoomeron equation, we propose three methods, namely the Jacobi elliptic function rational expansion method, the exponential rational function method and the new Jacobi elliptic function expansion method. Many kinds of solutions are obtained and the existence of these solutions is determined. For some parameters, these solutions can degenerate to the envelope shock wave solutions and the envelope solitary wave solutions. A comparison of our new results with the well-known results is made. The methods used here can also be applicable to other nonlinear partial differential equations. The fractional derivatives in this work are described in the modified Riemann–Liouville sense.     

Adiabatic Berry phase in an atom-molecule conversion system

We investigate the Berry phase of adiabatic quantum evolution in the atom-molecule conversion system that is governed by a nonlinear Schrödinger equation. We find that the Berry phase consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule coupling. The total geometric phase can be still viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole. We also derive the classical Hannay angle of a geometric nature associated with the adiabatic evolution. It exactly equals minus Berry phase, indicating a novel connection between Berry phase and Hannay angle in contrast to the usual derivative form.     

Transient modal radiation of axisymmetric sources: Application to loudspeakers

The present study proposes a transient model of the acoustic radiation of axisymmetric structures. The pressure field is approximated by the Rayleigh integral corresponding to a monopole source distribution over the non-planar vibrating surface. The displacement field is expanded on the linear modes of the structure and a change of variables in the Rayleigh integral is then proposed in the case of a monotonic profile function to compute the Spatial Impulse Response associated to each mode of vibration efficiently. The results are compared to the formulation obtained in the case of planar and spherical sources. The method of calculation is then derived in the case of a typical loudspeaker profile (association of a truncated cone with a spherical cap). Finally, the present approach is used to estimate the nonlinear radiation pattern of a prototype loudspeaker and predictions are compared to measurements in anechoic room.     

A least square finite element formulation of the collimated irradiation in frequency domain for optical tomography applications

This paper presents an extension of the least square finite element formulation associated to the discrete ordinates method to solve collimated irradiation problems in frequency domain. The features of the method are shown with a separation of the intensity into its collimated and scattered parts for a better handling of discontinuities due to the boundary conditions of Dirichlet type used in optical tomography applications. Numerical tests are used to gauge the accuracy of the model in both isotropic and anisotropic scattering media, with and without frequency modulation. The results show that the method is accurate compared to some reference solutions.     

3,3′-Benzene-1,4-diylbis[1-(substituted)phenylprop-2-en-1-one] derivatives: A new class of materials for third-order nonlinear optical applications

We have investigated the third-order nonlinear optical parameters of Bischalcones embedded in DMF solution and in solid PMMA matrix, by Z-scan technique using nanosecond laser pulse trains at 532 nm. Z-scan results reveal that the Bischalcones exhibits negative nonlinear refractive index as high as 10⁻¹¹ esu. The molecular two-photon absorption cross-section of Bischalcones were of the order 10⁻⁴⁶ cm⁴ s/photon, which is nearly two orders of magnitude larger than that of Rhodamine 6G which is 10⁻⁴⁸ - 10⁻⁵⁰ cm⁴ s/photon. We found that, the two-photon absorption (TPA) is the dominating nonlinear process leading to nonlinear absorption in both the cases in solution and as well as in solid medium. Based on TPA process, the Bischalcones exhibit good optical power limiting of nanosecond laser pulses at the input wavelength. The nonlinear optical parameters found to increase on enhancing the strength of the electron donor groups indicating the dependence and importance of electron donor/acceptor units on third-order nonlinear optical susceptibility χ⁽³⁾.     

Distributed strain measurement using a tellurite glass fiber with Brillouin optical correlation-domain reflectometry

A tellurite glass fiber with a high Brillouin gain was employed for distributed strain measurement with Brillouin optical correlation-domain reflectometry (BOCDR). First, the spatial resolution of BOCDR was evaluated using the tellurite fiber. With the high Brillouin gain of the fiber, it was confirmed clearly in the experiment that the spatial resolution is limited by the Rayleigh scattering-induced noise. Then, the dependence of the Brillouin frequency shift (BFS) on strain in the tellurite fiber was investigated, showing a negative dependence with a coefficient of −0.023 MHz/με. Using this tellurite fiber, the distribution of the BFS around a 1-cm strain-applied section was successfully measured with BOCDR of a nominal spatial resolution of 6 mm.     

Periodic intensity variations on the pulse-train of a passively mode-locked fiber ring laser

We investigate the evolvement of the periodic intensity variations of the pulse-train in a fiber ring laser mode-locked by the nonlinear polarization rotation technique. It is found that the phenomenon of such intensity fluctuations is related to the orientation of the polarization controllers when the pump power is fixed. The numerical results show that the mechanism of the periodic intensity variations is caused by the interaction of the nonlinear polarization rotation and the passive polarizer in the cavity.     

Gray photorefractive polymeric optical spatial solitons

We show that gray spatial optical solitons are possible in biased photorefractive polymers under steady-state conditions. We find that for a given material parameter the absolute value of a gray photorefractive polymeric soliton's phase decreases with an increase in the beam's grayness, whereas it increases with the material parameter for a given beam's grayness and that the full width half maximum (FWHM) of the gray soliton beam's intensity increases with the beam's grayness when the normalized background intensity and the material parameter are fixed and decreases with an increase in the normalized background intensity when the material parameter is fixed. On the other hand, we also show that N coupled beam evolution equations in biased photorefractive polymers can exhibit multicomponent gray solitons. These multicomponent gray solitons can be obtained provided that the N coupled beams share the same polarization, wavelength, and are incoherent with one another. The characteristics and stability properties of these multicomponent gray solitons are also discussed in detail.     

Studies on multi-wavelength fiber Bragg grating laser strain sensor

A novel stable multi-wavelength fiber Bragg grating laser is achieved and its sensing characteristic with the strain is studied. The beat signals generated by the multi-wavelength fiber laser are measured under different strains. Four-wave mixing (FWM) is firstly observed in such a short-cavity fiber laser.     

High-speed transmission limitations due to Polarization Mode Dispersion

In this paper, the impacts of Polarization Mode Dispersion (PMD) on the performance of high-speed optical communication system have been reported at different bit rates. The two systems are modeled using older fibers with same PMD coefficient at different bit rates and third is with the new fiber with less PMD coefficient than that of the previous two. The attenuation, chromatic dispersion and non-linear effects have been disabled, so that all the variation of the results is due to PMD. The bit rate is varied from 2.5 to 40 Gbps and the length is varied from 1000 to 20,000 km. It is shown that the impact of PMD increases with the bit rate of system. It is also reported that the impact of PMD becomes intolerable at the bit rates of more than 40 Gbps. And also the PMD produces very minute impact on the system performance for same bit rate with the variation in the fiber length.