Do Solitonlike Self-Similar Waves Exist in Nonlinear Optical Media?

Abstract

We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks.

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

“…We have observed that the second-and thirdorder RWs transform to first-order RW-like structures when a parameter appearing in the harmonic trap (timeindependent and time-dependent traps) is varied. We have then analyzed the characteristics of triplet and sextet patterns of matter RWs for (1). We have also constructed one-breather and two breather solutions of (1).…”

“…(1). In this section we analyze how the breather structures get modified in the condensates when we vary the strength of the external trap parameter.…”

“…Past explorations of GP equation in BECs have paved the way for important developments in manipulating coherent matter waves for application, including atom interferometry [32], coherent atom transport [33] and quantum information processing or quantum computation [34]. Therefore, it is of high significance to study the dynamics of RWs and breather profiles of the GP equation (1). However only few attempts have been made to identify and analyze the RWs and breather solutions of (1) [35][36][37][38][39][40].…”

“…During the past several years considerable interest has been shown in exploring localized nonlinear waves in the variable coefficient nonlinear Schrödinger (NLS) equation and its generalizations [1][2][3]. The motivation comes from the fact that NLS equation and its variants appear in several branches/topics of physics, including nonlinear optics [4,5] and Bose-Einstein condensates (BECs) [6][7][8], etc.…”

Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation

“…The NLS equation describing light propagation in optics [11] with real external potentials or/and gain-andloss distributions has been investigated [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] since the refractive index of the optical waveguide can be complex [29,30]. It is surprising to find that if the complex refractive index satisfies the property of the paritytime (PT ) symmetry [31], that is, if the real and imaginary parts of the refractive index are the even and odd functions of spatial position, respectively, then the propagation constant of the light can still be in all-real spectrum range, hence admitting stationary beam transmission [32][33][34][35].…”