[Show abstract][Hide abstract]ABSTRACT: We address the efficiency of theoretical tools used in the development and optimization of mode-locked fiber lasers. Our discussion is based on the practical case of modeling the dynamics of a dispersion-managed fiber laser. One conventional approach uses discrete propagation equations, followed by the analysis of the numerical results through a collective coordinate projection. We compare the latter with our dynamical collective coordinate approach (DCCA), which combines both modeling and analysis in a compact form. We show that for single pulse dynamics, the DCCA allows a much quicker solution mapping in the space of cavity parameters than the conventional approach, along with a good accuracy. We also discuss the weaknesses of the DCCA, in particular when multiple pulsing bifurcations occur.
Full-text · Article · Jul 2016 · Journal of optics
[Show abstract][Hide abstract]ABSTRACT: We numerically study the vortex lattice
dynamics in presence of pseudorandom potential in rotating Bose-Einstein condensate. The rotating condensate displays highly ordered triangular vortex lattice. In presence of pseudorandom potential the vortex lattice gets distorted. The histogram of the distances between each pair of the vortices shows how the long-range order of the triangular vortex lattice is destroyed in presence of pseudorandom potential.
[Show abstract][Hide abstract]ABSTRACT: A theoretical investigation of the modulation instability (MI) in the three core triangular oppositely directed coupler with negative index material channel is presented. This class of couplers have an effective feedback mechanism due to the opposite directionality of the phase velocities in the negative and positive index channels. It is found that the MI in the nonlinear three core triangular oppositely directed coupler is significantly influenced by the ratio of the forward- to backward-propagating wave power and nonlinearity. Also, in the case of the normal dispersion regime a threshold-like behavior is observed, whereas this behavior is not identified in the anomalous dispersion regime. For the asymmetric case (), two pairs of instability bands are observed for both the nonlinear NIM and PIM channels, while a single pair of instability bands is noted for the symmetric case (h = 1). In the normal dispersion regime, the defocusing nonlinearity is found to suppress the MI by reducing both the gain and width of the instability band, whereas the MI is enhanced in the anomalous dispersion regime due to the defocusing nonlinearity. Thus we report new ways to generate and manipulate the MI and solitons in three-core triangular oppositely directed couplers with a particular emphasis on a negative-index material (NIM) channel.
No preview · Article · Mar 2016 · Journal of optics
[Show abstract][Hide abstract]ABSTRACT: A theoretical investigation on the influence of birefringence in the modulational instability (MI) spectra of an oppositely directed coupler (ODC) with a negative index material (NIM) channel is presented. We study the effect of birefringence on MI in linear and circular birefringent ODCs for both normal and anomalous dispersion regimes. It is found that besides the instability band due to nonlinear positive index material (PIM) and negative index material (NIM) channels, new symmetric instability regions are observed as a result of birefringent effects. Also defocusing nonlinearity suppresses the NIM band in the normal dispersion regime, but in the anomalous dispersion regime the defocusing nonlinearity enhances the gain of the NIM band. In contrast to the case of linear birefringence, in terms of MI gain from circular birefringence, only two birefringent bands dominate: the inherently PIM and NIM bands. This preponderance is attributed to the fact that the cross-phase modulation effect for the case of circular birefringence is stronger, thus allowing a better coupling between the beams, which results in the enhancement of the gain. Therefore, the manipulation of MI and solitons in an ODC is better performed when the birefringence is circular rather than linear. Here we report how to generate and manipulate MI and solitons in birefringent ODCs with a particular emphasis on a NIM channel.
[Show abstract][Hide abstract]ABSTRACT: We investigate a generalized coupled nonlinear Schrodinger (GCNLS) equation containing Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM) and Four Wave Mixing (FWM) describing the propagation of electromagnetic radiation through an optical fibre and generate the associated Lax-pair. We then construct bright solitons employing gauge transformation approach. The collisional dynamics of bright solitons indicates that it is not only possible to manipulate intensity (energy) between the two modes (optical beams), but also within a given mode unlike the Manakov model which does not have the same freedom. The freedom to manipulate intensity (energy) in a given mode or between two modes arises due to a suitable combination of SPM, XPM and FWM. While SPM and XPM are controlled by an arbitrary real parameter each, FWM is governed by two arbitrary complex parameters. The above model may have wider ramifications in nonlinear optics and Bose-Einstein Condensates (BECs).
Preview · Article · Feb 2016 · Communications in Nonlinear Science and Numerical Simulation
[Show abstract][Hide abstract]ABSTRACT: We study the vortex lattice dynamics in presence of single impurity as well
as random impurities or disorder. We show that in presence of a single impurity
the vortex lattice gets distorted and the distortion depends on the position of
the single impurity with respect to the positions of the vortices in the
impurity free Abrikosov vortex lattice and also the strength of the impurity
potential. We then show that a new type of giant hole with hidden vortices
inside it can be created in the vortex lattice by a cluster of impurities. In
presence of random impurity potential or disorder the vortex lattice melts. We
show that the vortex lattice also melts in presence of pseudorandom potential
generated by the superposition of two optical lattices. The absence of
long-range order in the melted vortex lattice is demonstrated from the
structure factor profile and the histogram of the distances between each pair
of the vortices.
[Show abstract][Hide abstract]ABSTRACT: A theoretical study of cross phase modulation (XPM) induced modulational instability (MI) in a semiconductor doped dispersion decreasing fiber (SD-DDF) is presented. The equation is suitably modeled to account for the saturable nonlinearity and dispersion decreasing nature of the fiber. Using linear stability analysis, the exact dispersion relation is obtained and MI analysis is performed. We exclusively analyze the influence of the walk-off effect in the instability spectra of an SD-DDF and an optimum walk-off parameter is identified. The contrasting nature of action of decreasing dispersion and saturating nonlinearity is emphasized, such that the former enhances and the latter suppresses bandwidth. Thus, a suitable combination of the two physical effects can enable one to realize the desired bandwidth profile. MI analysis in the normal dispersion regime is compared with the anomalous counterpart as well as the conventional single pump case and the results are tabulated. Also, our analytical results are compared through direct numerical simulation and the results are documented. Thus, we present a comprehensive study of XPM-MI in an SD-DDF and the influence of various physical effects on the MI dynamics.
[Show abstract][Hide abstract]ABSTRACT: We study modulation instability (MI) of flat states in two-component spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) in the framework of coupled Gross-Pitaevskii equations for two components of the pseudospinor wave function. The analysis is performed for equal densities of the components. Effects of the interaction parameters, Rabi coupling, and SOC on the MI are investigated. In particular, the results demonstrate that the SOC strongly alters the commonly known MI (immiscibility) condition, g122>g1g2, for the binary superfluid with coefficients g1,2 and g12 of the intra- and interspecies repulsive interactions. In fact, the binary BEC is always subject to the MI under the action of the SOC, which implies that the ground state of the system is plausibly represented by a striped phase.
Full-text · Article · Dec 2015 · Physical Review A
[Show abstract][Hide abstract]ABSTRACT: The localization characters of the first-order rogue wave (RW) solution $u$
of the Kundu-Eckhaus equation is studied in this paper.
We discover a full process of the evolution for the contour line with height
$c^2+d$ for the first-order RW $|u|^2$: A point at height $9c^2$ generates a
convex curve for $3c^2\leq d<8c^2$, whereas it becomes a concave curve for
$0<d<3c^2$, next it reduces to a hyperbola on asymptotic plane (i.e.
equivalently $d=0$), and the two branches of the hyperbola become two separate
convex curves when $-c^2<d<0$, and finally they reduce to two separate points
at $d=-c^2$. Using the contour line method, the length, width, and area of the
RW at height $c^2+d (0<d<8c^2)$ , i.e. above the asymptotic plane, are defined.
We study the evolutions of three above-mentioned localization characters on $d$
through analytical and visual methods.
[Show abstract][Hide abstract]ABSTRACT: We present a practical design of novel photonic crystal fibre (PCF) to investigate the nonlinear propagation of femtosecond pulses for the application of optical coherence tomography (OCT) based on supercontinuum generation (SCG) process. In addition, this paper contains a brief introduction of the physical phenomena of soliton and SCG. Typically, here we discuss how the ultrabroadband radiation in PCF can be generated by SCG through various nonlinear effects of the fibre. To accomplish the proposed aim, we put forth liquid core PCF (LCPCF) structure filled with chloroform for OCT measurements of the eye. From the proposed design, we observe that proposed LCPCFs with liquid material exhibit significant broadened wavelength spectrum with low input pulse energy over small propagation distances for the OCT application.
[Show abstract][Hide abstract]ABSTRACT: We study the stabilization properties of dipolar Bose-Einstein condensate by temporal modulation of short-range two-body interaction. Through both analytical and numerical methods, we analyze the mean-field Gross-Pitaevskii equation with short-range two-body and long-range, nonlocal, dipolar interaction terms. We derive the equation of motion and effective potential of the dipolar condensate by variational method. We show that there is an enhancement of the condensate stability due to the inclusion of dipolar interaction in addition to the two-body contact interaction. We also show that the stability of the dipolar condensate increases in the presence of time varying two-body contact interaction; the temporal modification of the contact interaction prevents the collapse of dipolar Bose-Einstein condensate. Finally we confirm the semi-analytical prediction through the direct numerical simulations of the governing equation.
Full-text · Article · Oct 2015 · Physical Review E
[Show abstract][Hide abstract]ABSTRACT: We investigate the nonlinear dynamics and steering performance of structurally asymmetric triple-core photonic crystal fiber (ATPCF) for the accomplishment of efficient all-optical logic gates. We study two kinds of ATPCF, one with planar and the other with triangular core setting. The effective mode indices are obtained through the finite element method. The dynamics and steering characteristics of ATPCF are numerically explored via coupled nonlinear Schrödinger equations. The extinction ratios for the various logic gate operations are determined in the presence of suitable control signal. ATPCFs are found to demonstrate efficient logic gate operation; in addition, they highlight the practical issue of geometrical tolerance in PCF design.
Full-text · Article · Aug 2015 · Journal of the Optical Society of America B
[Show abstract][Hide abstract]ABSTRACT: We study the amplitude perturbations of the cubic–quintic Gross–Piteavskii equation for weakly trapped Bose–Einstein condensates through a semiquantum procedure. After a quantization of the original problem, with the introduction of quantum degrees of freedom as the fluctuations around classical parameters, a new dynamical modulational instability condition is derived. Corrective terms bear quantum effects that play a crucial role over the reshape of instability domain and sometimes train all unstable modes into full stability. By making use of several indicators through direct numerical simulations of the subsequent set of equations of motion, we found that there are rooms of regular trajectories and those of totally chaotic ones that are strictly related to instability. These numerical results are in agreement with the analytical predictions regarding the stabilization of Bose–Einstein condensates.
[Show abstract][Hide abstract]ABSTRACT: We construct an analytical and explicit representation of the Darboux transformation (DT) for the Kundu– Eckhaus (KE) equation. Such solution and n-fold DT T n are given in terms of determinants whose entries are expressed by the initial eigenfunctions and 'seed' solutions. Furthermore, the formulae for the higher order rogue wave (RW) solutions of the KE equation are also obtained by using the Taylor expansion with the use of degenerate eigenvalues λ 2k−1 → λ 1 = − 1 2 a + βc 2 + ic, k = 1, 2, 3,. . ., all these parameters will be defined latter. These solutions have a parameter β, which denotes the strength of the non-Kerr (quintic) nonlinear and the self-frequency shift effects. We apply the contour line method to obtain analytical formulae of the length and width for the first-order RW solution of the KE equation, and then use it to study the impact of the β on the RW solution. We observe two interesting results on localization characters of β, such that if β is increasing from a/2: (i) the length of the RW solution is increasing as well, but the width is decreasing; (ii) there exist a significant rotation of the RW along the clockwise direction. We also observe the oppositely varying trend if β is increasing to a/2. We define an area of the RW solution and find that this area associated with c = 1 is invariant when a and β are changing.
Full-text · Article · Jul 2015 · Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences
[Show abstract][Hide abstract]ABSTRACT: We numerically solve the Gross-Pitaeveskii equation to study the Bose-Einstein condensate in the rotating harmonical tarp and co-rotating optical lattice. The effect of a pinning site or impurity shows that it is able to move the vortex lattice center to either left or right depending on the position of the impurity. Also, it is observed that the impurity at the random positions can destroy the vortex lattice and the resulting disordered lattice has more energy.
[Show abstract][Hide abstract]ABSTRACT: We study the transverse instability associated with higher-dimensional nonlinear systems. For this, a cubic-quintic-nonlinear system is considered wherein the coefficients of cubic and quintic terms are allowed to be of either focusing or defocusing nature. It is found that focusing-cubic and defocusing-quintic nonlinearity can suppress the transverse instability growth rate. The addition of guiding potentials can also suppress the instability growth rate for all kinds of solitons with the same propagation constant.
Full-text · Article · Jun 2015 · Journal of the Optical Society of America B
[Show abstract][Hide abstract]ABSTRACT: We consider a next-higher-order extension of the Chen–Lee–Liu equation, i.e., a higher-order Chen–Lee–Liu (HOCLL) equation with third-order dispersion and quintic nonlinearity terms. We construct the n-fold Darboux transformation (DT) of the HOCLL equation in terms of the n × n determinants. Comparing this with the nonlinear Schrödinger equation, the determinant representation T n of this equation is involved with the complicated integrals, although we eliminate these integrals in the final form of the DT, so that the DT of the HOCLL equation is unusual. We provide explicit expressions of multi-rogue wave (RW) solutions for the HOCLL equation. It is concluded that the rogue wave solutions are likely to be crucial when considering higher-order nonlinear effects.
[Show abstract][Hide abstract]ABSTRACT: We investigate the modulational instability (MI) induced Supercontinuum generation (SCG) in exponential saturable nonlinearity. The pump power (P) is observed to behave in a unique way such that unlike the conventional Kerr case, the effective nonlinearity of saturable nonlinear system does not monotonously increases with an increase in power. The supercontinuum is observed at the shortest distance of propagation at power equal to the saturation power (Ps), whereas for all combinations of powers (P Ps or P > Ps) spectral broadening occurs at longer distance.
No preview · Article · Apr 2015 · Journal of Physics Conference Series
[Show abstract][Hide abstract]ABSTRACT: We investigate the modulational instability (MI) of the optical beam propagating in the relaxing saturable nonlinear system. We identify and discuss the salient features of various functional forms of saturable nonlinear responses such as exponential, conventional and coupled type on the MI spectrum. Using Debye relaxation model, the relaxation of nonlinear response is effectively included along with the saturable nonlinear response (SNL). Using linear stability analysis, an explicit dispersion relation is determined for considering different functional forms of SNL. Firstly, we analyze the impact of SNL on the MI spectrum and found that the MI gain and bandwidth is maximum for exponential nonlinearity in comparison to other types of SNL's. Latter the relaxation of the nonlinearity is included, the inclusion of the finite value of the response time extends the range of the unstable frequencies literally down to infinite frequencies. In the regime of slow response, the MI inevitably suppressed regardless of the sign of the dispersion coefficient. To give insight into the MI phenomena, the maximum MI gain and the optimum modulation frequency is drawn as a function of the delay. Thus the MI dynamics in the system of relaxing saturable nonlinear media is emphasized and the significance of various functional forms of SNL are highlighted.
No preview · Article · Apr 2015 · Journal of Physics Conference Series
[Show abstract][Hide abstract]ABSTRACT: We harness the freedom in the celebrated gauge transformation approach to
generate dark solitons of coupled nonlinear Schr\"odinger (NLS) type equations.
The new approach which is purely algebraic could prove to be very useful,
particularly in the construction of vector dark solitons in the fields of
nonlinear optics, plasma physics and Bose-Einstein condensates. We have
employed this algebraic method to coupled Gross- Pitaevskii (GP) and NLS
equations and obtained dark solitons.
Full-text · Article · Mar 2015 · Romanian Reports in Physics