Cw States Research Articles

Phase engineering of chirped rogue waves in Bose–Einstein condensates with a variable scattering length in an expulsive potential

We consider a cubic Gross-Pitaevskii (GP) equation governing the dynamics of Bose-Einstein condensates (BECs) with time-dependent coefficients in front of the cubic term and inverted parabolic potential. Under a special condition imposed on the coefficients, a combination of phase-imprint and modified lens-type transformations converts the GP equation into the integrable Kundu-Eckhaus (KE) one with constant coefficients, which contains the quintic nonlinearity and the Raman-like term producing the self-frequency shift. The condition for the baseband modulational instability of CW states is derived, providing the possibility of generation of chirped rogue waves (RWs) in the underlying matter-wave (BEC) model. Using known RW solutions of the KE equation, we present explicit first- and second-order chirped RW states. The chirp of the first- and second-order RWs is independent of the phase imprint. Detailed solutions are presented for the following configurations: (i) the nonlinearity exponentially varying in time; (ii) time-periodic modulation of the nonlinearity; (iii) a stepwise time modulation of the strength of the expulsive potential. Singularities of the local chirp coincide with valleys of the corresponding RWs. The results demonstrate that the temporal modulation of the s-wave scattering length and strength of the inverted parabolic potential can be used to manipulate the evolution of rogue matter waves in BEC.

Soliton blockade in bidirectional microresonators.

We report a method to control, disrupt, and restore a regime of unidirectional soliton generation in a bidirectionally pumped ring microresonator. This control, i.e., the soliton blockade, is achieved by tuning the pump frequency of the counterrotating field. The blockade effect is correlated with the emergence of a dark-bright nonlinear resonance of cw states.

Modulation instabilities in nonlinear two-core optical fibers with fourth order dispersion

We study in detail the modulation instabilities (MIs) in nonlinear two-core optical fibers (TCFs) in the presence of fourth-order dispersion (FOD) by considering the symmetric and antisymmetric CW states. The analytical instability gain spectra with the FOD are shown explicitly. For the symmetric CW state, in the normal (anomalous) dispersion regime, the positive (negative) FOD reduces the original MI band, and the negative (positive) FOD can generate a completely new dominate MI band in the very high frequency range even with quite small amplitude of FOD for typical TCF parameters. For the antisymmetric CW state, in the normal dispersion regime, there is no MI without FOD. With the negative FOD, MI is generated at any given total powers. In the anomalous dispersion regime, being similar with the behaviors for symmetric CW state, the positive (negative) FOD effect is to reduce the original MI band, and the negative (positive) FOD can generate a completely new dominate MI band in the very high frequency range. We also verify our MI analysis by solving the coupled-mode equations numerically.

Effects of Ellipticity Angle on Modulation Instabilities in Birefringent Optical Fibers**Supported by the National Natural Science Foundation of China under Grant Nos. 11447113 and 11305031, Natural Science Foundation of Jiangsu Provincial Universities under Grant No. 14KJB140009, and the Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology under Grant No. 2241131301064

Previous studies on modulation instabilities (MIs) in birefringent optical fibers focus on the ordinary linearly and circularly ones. This paper reports an analysis of MIs in the general elliptically birefringent fibers with the emphasis on investigating the effects of ellipticity angle (0° ≤ θ ≤ 90°). Both symmetric and antisymmetric CW states are considered. In the anomalous dispersion regime, for the symmetric (antisymmetric) CW states, we show that MI gain increases dramatically (reduces first and then enhances greatly) as the increment of θ. In the normal dispersion regime, for the both CW states, the distinctive feature is that the gain of the MI bands reduces first, vanishes at θ = 45°, reappears across this ellipticity angle, and quickly increases after then.

Continuous-wave solutions in spinor Bose-Einstein condensates

We find analytic continuous wave (cw) solutions for spinor Bose-Einstein condenates (BECs) in a magnetic field that are more general than those published to date. For particles with spin F=1 in a homogeneous one-dimensional trap, there exist cw states in which the chemical potential and wavevectors of the different spin components are different from each other. We include linear and quadratic Zeeman splitting. Linear Zeeman splitting, if the magnetic field is constant and uniform, can be mathematically eliminated by a gauge transformation, but quadratic Zeeman effects modify the cw solutions in a way similar to non-zero differences in the wavenumbers between the different spin states. The solutions are stable fixed points within the continuous wave framework, and the coherent spin mixing frequencies are obtained.

Modulation instabilities in two-core optical fibers

Modulation instability (MI) of cw states of a two-core fiber, incorporating the effects of coupling-coefficient dispersion (CCD), is studied by solving a pair of generalized, linearly coupled nonlinear Schrodinger equations. CCD refers to the property that the coupling coefficient depends on the optical wavelength, and earlier studies of MI do not account for this physics. CCD does not seriously affect the symmetric/antisymmetric cw, but can drastically modify the MI of the asymmetric state. Generally, new MI frequency bands are produced, and CCD reduces (enhances) the original MI band in the anomalous (normal) dispersion regime. Another remarkable result is the existence of a critical value for the CCD, where the MI gain spectrum undergoes an abrupt change. In the anomalous dispersion regime, a new low-frequency MI band is generated. In the normal dispersion regime, an MI band vanishes, reappears, and then moves up in frequency on crossing this critical value. In both dispersion regimes, the relative magnitude of the low-frequency band and the high-frequency band depends strongly on the total input power. It is possible to switch the dominant MI frequency between a low frequency and a high frequency by tuning the total input power, providing a promising scheme to manipulate MI-related nonlinear effects in two-core fibers. The MI bands are independent of the third-order dispersion, but can be shifted significantly by self-steepening at a sufficiently high total input power. The evolution of MI from a cw input is also demonstrated with a wave propagation study.

Dark solitons in dynamical lattices with the cubic-quintic nonlinearity

Results of systematic studies of discrete dark solitons (DDSs) in the one-dimensional discrete nonlinear Schrödinger equation with the cubic-quintic on-site nonlinearity are reported. The model may be realized as an array of optical waveguides made of an appropriate non-Kerr material. First, regions free of the modulational instability are found for staggered and unstaggered cw states, which are then used as the background supporting DDS. Static solitons of both on-site and inter-site types are constructed. Eigenvalue spectra which determine the stability of DDSs against small perturbations are computed in a numerical form. For on-site solitons with the unstaggered background, the stability is also examined by dint of an analytical approximation, that represents the dark soliton by a single lattice site at which the field is different from cw states of two opposite signs that form the background of the DDS. Stability regions are identified for the DDSs of three types: unstaggered on-site, staggered on-site, and staggered inter-site; all unstaggered inter-site dark solitons are unstable. A remarkable feature of the model is coexistence of stable DDSs of the unstaggered and staggered types. The predicted stability is verified in direct simulations; it is found that unstable unstaggered DDSs decay, while unstable staggered ones tend to transform themselves into moving dark breathers. A possibility of setting DDS in motion is studied too. Analyzing the respective Peierls-Nabarro potential barrier, and using direct simulations, we infer that unstaggered DDSs cannot move, but their staggered counterparts can be readily set in motion.

Modulational Instabilities in the Dual-Core Nonlinear Optical Fiber

We describe modulational instability (MI) of the continuous-wave (cw) states in the dual-core nonlinear optical fiber with normal dispersion. We show that the asymmetric cw states (existing above the bifurcation point), as well as the symmetric ones (below the bifurcation point) exhibit MI at all values of the intensity (the instability of the symmetric cw states was known previously). Below the bifurcation, the MI's peak gain (with respect to the perturbation frequency, holding the intensity of the symmetric cw state constant) increases with intensity. Above the bifurcation – considering the asymmetric cw solution – the peak gain of this branch of the perturbation decreases with intensity; however, at the bifurcation point another branch goes unstable, its peak gain growing with intensity, and saturating at large intensities. The symmetric state's instability is non-oscillatory, while that of the asymmetric state is oscillatory. Direct simulations show that, in either case, MI eventually leads to full “optical turbulence,” both the initial symmetric and initial asymmetric cw states giving rise to statistically symmetric turbulent states, which have equal average intensities in each core. Thus, the transition to turbulence restores the spontaneously broken symmetry.

Dark and bright solitons in resonantly absorbing gratings.

We consider an optical medium consisting of a periodic refractive-index grating and a periodic set of thin layers of two-level systems resonantly interacting with the electromagnetic field. Recently, it has been shown that such a system gives rise to a vast variety of stable bright solitons. In this work, we demonstrate that the system has another very unusual property: stable bright solitons can coexist with stable continuous-wave (cw) states and stable dark solitons (DS's). Depending on the parameters' values, a DS frequency band coexists (without overlap) with one or two bright-soliton bands. Quiescent (standing) DS's are found in an analytical form, and moving ones are obtained numerically. Simulations show that a considerable part of the DS solutions are completely stable against arbitrary small perturbations. The fact that this system supports both stable bright and dark solitons for the same parameters values may find interesting applications in photonics.

Intracavity second-harmonic generation: The steady-state solutions

We study the steady states of a solid-state laser containing a birefringent frequency-doubling crystal such as a YAG-KTP laser and assess their stability in a systematic way. We show that as the pump power is increased, different scenarios arise: Hopf bifurcation to antiphased periodic regimes, mode hopping between different cw states, and finally breakup of the multimode states for a single- or two-mode cw regime involving homoclinic points.

Optical bistabilities, phase transitions, and Q-switch characteristics of an N_2O laser with a saturable NH_3 absorber

Results of a systematic investigation of an N(2)O laser with an internal NH(3) absorber are reported. Bistability between the cw and off as well as between the cw and Q-switched states is observed. The transitions in the former case resemble first-order phase transitions; whereas in the latter case first- and/or second-order transitions occur. The laser-power dependence of the bistability and Q-switched behavior is investigated in detail. In particular, fluctuations are found to be enhanced near the phase-transition points.

Dressed mode description of optical bistability

We start from the dressed mode formulation of optical bistability, given in a previous paper. By performing anexact adiabatic elimination of the atomic modes, we derive a closed system of time evolution equations for the field modes, that play the role of order parameters. In particular in the simplest setting of two unstable modes the problem is reduced to a set of only two differential equations in time, that fully include both nonlinearity and propagation. Thus we can describe self-pulsing in terms of a simple two-dimensional phase space, which allows for treating cw and pulsing states on the same footing. We determine thefull domain of existence of the self-pulsing state and describe how this state varies with the control parameters. In particular we find hysteresis cyclesof novel type, that involve both cw and pulsing states, thereby enriching the phenomenology of Optical Bistability. A part of the boundary of the domain of existence of the self-pulsing state is found to be a line of Hopf bifurcations, which points out the existence of ahigher order bifurcation in our system. In conclusion, our procedure exploits and develops in the best way Haken's theory of generalized Ginzburg-Landau equations for phase-transition-like phenomena in systems far from thermal equilibrium.