[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.
Journal of the Optical Society of America B 08/2015; 32(9):1920-1929. DOI:10.1364/JOSAB.32.001920 · 1.97 Impact Factor
[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.
Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 07/2015; 471(2180). DOI:10.1098/rspa.2015.0236 · 2.19 Impact Factor
[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.
Physica Scripta 05/2015; 90(5). DOI:10.1088/0031-8949/90/5/055207 · 1.13 Impact Factor
[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.
Journal of Physics Conference Series 04/2015; 605(1). DOI:10.1088/1742-6596/605/1/012031
[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.
Journal of Physics Conference Series 04/2015; 605(1). DOI:10.1088/1742-6596/605/1/012032
[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.
[Show abstract][Hide abstract] ABSTRACT: We explain how the modulational and oscillatory instabilities can be generated in Bose–Einstein condensates (BECs) with two- and three-body interactions trapped in a periodic optical lattice with driving harmonic potential. We solve a cubic–quintic Gross–Pitaevskii (GP) equation with external trapping potentials by using both analytical and numerical methods. Using the time-dependent variational approach, we derive and analyze the variational equations for the time evolution of the amplitude and phase of modulational perturbation, and effective potential of the system. Through the effective potential, we obtain the modulational instability condition of the BECs with two- and three-body interactions and shown the effects of the optical potential on the dynamics of the system. We perform direct numerical simulations to support our analytical results, and good agreement is observed.
Physics Letters A 02/2015; 379(4). DOI:10.1016/j.physleta.2013.12.047 · 1.68 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A variety of AS2S3 chalcogenide photonic crystal ﬁber coupler of special properties are proposed to study the role of birefringence in all optical coupling characteristics based on the projection operator method (POM). The equations of motion describing the dynamics of the individual pulse parameters through x- and y-polarized modes are arrived at by employing POM from the coupled nonlinear Schrödinger equations. From the pulse parameter dynamics, it is observed that the amplitudes of the polarization components are signiﬁcantly inﬂuenced by the pulse being introduced with different polarizing angle even at low input power level. Such a selective polarizing angles of the input pulse will provide efﬁcient control over the desired splitting ratio as well as the ability to decide the desired polarization component.
[Show abstract][Hide abstract] ABSTRACT: We investigate the modulation instability (MI) in a three-core oppositely-directed coupler with a
particular emphasis on a negative index material (NIM) channel. In order to give a comprehensive picture,
we consider the normal and the anomalous dispersion regimes. Special attention is paid to investigation
of the inﬂuence of system parameters such as the power and the coupling coeﬃcient on the MI. We also
analyze the impact of different nonlinear conﬁgurations of coupler channels on MI
Physics Letters A 01/2015; 379:223. · 1.68 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a novel asymmetric triple core photonic crystal fiber for the construction of NOR and OR logic gates by employing all optical control. Through extinction ratio calculated at apt control signal phase, the Boolean algebra for NOR and OR logic gates are demonstrated numerically.
International Conference on Fibre Optics and Photonics, IIT, Kharagpur India; 12/2014
[Show abstract][Hide abstract] ABSTRACT: A highly nonlinear CS2 filled liquid core PCF (LCPCF) is proposed to study the supercontinuum generation. It is observed that the novel design of LCPCF make suitable for highly scattering tissue optical coherence tomography applications.
International Conference on Fibre Optics and Photonics, IIT, Kharagpur India; 12/2014
[Show abstract][Hide abstract] ABSTRACT: We find self-trapped propagation of elliptical super-Gaussian beam in cubic–quintic nonlinear media. The soliton beam preserves its shape and size during propagation in Kerr media. Both defocusing and focusing quintic nonlinearities are considered. In a cubic (focusing)-quintic (defocusing) media breather like beam propagation with intriguing beam width oscillation is observed. The influence of beam ellipticity, super-Gaussian nature and quintic nonlinearity on self-trapping has been studied. A formula for critical power for self-focusing has been derived and it readily agrees with the results obtained by variational method. In Kerr and focusing quintic media beam collapse occurs quicker for higher order super-Gaussian beam. The critical power of self-focusing in defocusing (focusing) quintic medium prominently increases (decreases) with increasing strength of quintic nonlinearity. This variation rate is greater for higher order super Gaussian beam. A beam with greater ellipticity requires larger power for self-trapping.
[Show abstract][Hide abstract] ABSTRACT: We investigate the modulation instability in oppositely directed coupler in the presence of higher-order effects. Using linear stability analysis, we obtain an expression for instability gain. Special attention is paid to find out the influence of self-steepening effect and intrapulse Raman scattering on modulation instability. The study shows that in normal dispersion, regime instability gain exists even if perturbation frequency (Ω) is zero. But the instability gain at Ω=0 is zero, when the dispersion is anomalous. Moreover, self-steepening effect and intrapulse Raman scattering form new instability regions and, hence, provide a new way to generate solitons or ultrashort pulses. Further, efficient control of modulation instability by adjusting self-steepening effect and intrapulse Raman scattering also successfully demonstrated.
Physical Review E 10/2014; 90(4-1):042910. DOI:10.1103/PhysRevE.90.042910 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the vortex dynamics and vortex pinning effect in Bose-Einstein
condensate in a rotating double-well trap potential and co-rotating optical
lattice. We show that, in agreement with the experiment, the vortex number do
not diverge when the rotational frequency $\Omega \rightarrow 1$ if the trap
potential is of anisotropic double-well type. The critical rotational frequency
as obtained from numerical simulations agrees very well with the value $\sqrt
l/l$ for $l=4$ which supports the conjecture that surface modes with angular
momentum $l=4$ are excited when the rotating condensate is trapped in
double-well potential. The vortex lattice structure in a rotating triple-well
trap potential and its pinning shows very interesting features. We show the
existence and pinning of a new type of hidden vortices whose phase profile is
similar to that of the visible vortices.
Physical Review A 08/2014; 89(5). DOI:10.1103/PhysRevA.89.053625 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We have proposed a novel APCFCs for multi-frequency generation and its optical performance for generating new frequency components are studied numerically by using SSFM. For our study, we have considered two cases namely one with same GVD and different nonlinearity and the other with different GVD as well as nonlinearity. From the results obtained, we are able to demonstrate considerable new frequency generation within a shorter distance. In particular, APCFC with different nonlinearity as well as GVD exhibits the better new frequency generation. Hence, by preparing such APCFC of greater length one can realize a significantly broader frequency spectrum.
22nd National Laser Symposium, Manipal University, Manipal, Karnataka, India.; 08/2014
[Show abstract][Hide abstract] ABSTRACT: In this paper, we consider the complex modified Korteweg-de Vries (mKdV)
equation as a model of few-cycle optical pulses. Using the Lax pair, we
construct a generalized Darboux transformation and systematically generate the
first-, second- and third-order rogue wave solutions and analyze the nature of
evolution of higher-order rogue waves in detail. Based on detailed numerical
and analytical investigations, we classify the higher-order rogue waves with
respect to their intrinsic structure, namely, fundamental pattern, triangular
pattern, and ring pattern. We also present several new patterns of the rogue
wave according to the standard and non-standard decomposition. The results of
this paper explain the generalization of higher-order rogue waves in terms of
rational solutions. We apply the contour line method to obtain the analytical
formulas of the length and width of the first-order RW of the complex mKdV and
the NLS equations. In nonlinear optics, the higher-order rogue wave solutions
found here will be very useful to generate high-power few-cycle optical pulses
which will be applicable in the area of ultra-short pulse technology.
Physical Review E 05/2014; 89(6-1). DOI:10.1103/PhysRevE.89.062917 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the dynamics of spatially coupled Bose-Einstein condensates
and generate bright and dark solitons employing gauge transformation approach.
We observe that when bright/dark solitons evolve in time, the centre of localization of
the wave packet gets shifted to the left. We also notice that the spatial coupling stretches
the wave packet which can be used as a mechanism to stabilize the condensates. The
impact of spatial coupling is suitably exploited to generate an interference pattern in the
collision of bright-bright, dark-dark and dark-bright solitons.
[Show abstract][Hide abstract] ABSTRACT: We investigate the dynamical instability of Bose-Einstein condensates (BECs)
with higher-order interactions immersed in an optical lattice with weak driving
harmonic potential. For this, we compute both analytically and numerically a
modified Gross-Pitaevskii equation with higher-order nonlinearity and external
potentials generated by magnetic and optical fields. Using the time-dependent
variational approach, we derive the ordinary differential equations for the
time evolution of the amplitude and phase of modulational perturbation. Through
an effective potential, we obtain the modulational instability condition of
BECs and discuss the effect of the higher-order interaction in the dynamics of
the condensates in presence of optical potential. We perform direct numerical
simulations to support our analytical results, and good agreement is found.
Physical Review E 04/2014; 89(5-1). DOI:10.1103/PhysRevE.89.052917 · 2.29 Impact Factor