Propagation dynamics of tripole breathers in nonlocal nonlinear media
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ORIGINAL PAPER
Propagation dynamics of tripole breathers in nonlocal nonlinear media Jian-Li Guo · Zhen-Jun Yang · Li-Min Song · Zhao-Guang Pang
Received: 16 February 2020 / Accepted: 18 July 2020 © Springer Nature B.V. 2020
Abstract We demonstrate the propagation dynamics of optical breathers in nonlinear media with a spatial nonlocality, which is governed by the nonlocal nonlinear Schrödinger equation, by employing the variational approach. Taking a tripole breather as an example, the approximate analytical solution is obtained and the physical propagation properties, such as the evolution of the critical power, the spot size, the wavefront curvature, and the intensity distribution of the breather, have been discussed in detail. The physical reasons for the evolution of the tripole breathers are analyzed by borrowing the ideas from Newtonian mechanics. It is found that the analytical results obtained by the variational approach agree well with the numerical results of the nonlocal Schrödinger equation for the strong nonlocal case, especially when the incident power approaches the critical power. Keywords Nonlinear Schrödinger equation · Breather · Variational approach
1 Introduction The evolution dynamics of laser beams (solitons or breathers) in nonlocal nonlinear optical systems is J.-L. Guo · Z.-J. Yang (B)· L.-M. Song · Z.-G. Pang College of Physics, Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, Shijiazhuang 050024, China e-mail: [email protected]
dominated phenomenologically by the nonlocal nonlinear Schrödinger equation (NNLSE) [1–5]. Nonlocal nonlinearity means that the nonlinear response at a certain spatial point is determined not only by the optical beam at that point but also by the beam in its vicinity [1–3], which have been found in many physical systems, such as nematic liquid crystals [6–8], photorefractive materials [9–11], thermooptical materials [12,13], lead glass [14,15], and so on. On the basis of NNLSE, many problems on beam propagation have been made great achievements and various solitons’ or breathers’ forms [16], for example the propagation characteristics of soliton in erbium doped fiber [17], and Gaussian solitons [1, 2], Laguerre–Gaussian and Hermite–Gaussian solitons [18,19], Ince–Gaussian solitons [20], high-order revivable complex-valued hyperbolic-sine-Gaussian solitons [21], matter-wave breathers [22], discrete breathers [23], and Peregrine breathers [24] have been found and theoretically studied, and interest in interaction of some beams in nonlinear media has grown extremely [25]. In general, most common methods for studying beam evolution are perturbation theory [26,27] and linearization techniques [28], the separation variable method [29–31], and variational approach [32,33]. Moreover, the research on beam propagation characteristics is mainly based on statistical characteristics. Taking the variational approach as an example, many research results have shown that the variational approach can be used to solve the propagation evo
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