Spatiotemporal Airy Ince–Gaussian wave packets in strongly nonlocal nonlinear media

Abstract

The self-accelerating Airy Ince–Gaussian (AiIG) and Airy helical Ince–Gaussian (AihIG) wave packets in strongly nonlocal nonlinear media (SNNM) are obtained by solving the strongly nonlocal nonlinear Schrödinger equation. For the first time, the propagation properties of three dimensional localized AiIG and AihIG breathers and solitons in the SNNM are demonstrated, these spatiotemporal wave packets maintain the self-accelerating and approximately non-dispersion properties in temporal dimension, periodically oscillating (breather state) or steady (soliton state) in spatial dimension. In particular, their numerical experiments of spatial intensity distribution, numerical simulations of spatiotemporal distribution, as well as the transverse energy flow and the angular momentum in SNNM are presented. Typical examples of the obtained solutions are based on the ratio between the input power and the critical power, the ellipticity and the strong nonlocality parameter. The comparisons of analytical solutions with numerical simulations and numerical experiments of the AiIG and AihIG optical solitons show that the numerical results agree well with the analytical solutions in the case of strong nonlocality.

Spatiotemporal hollow multi-ring optical solitons in strongly nonlocal nonlinear media

“…The 1+3D model of a linearly polarized optical field with an envelope u satisfies the Maxwell equation. To the nonlinear homogeneous material, u follows the general nonlocal nonlinear Schrödinger equation as 1 , 24 , 27 , 28 i∂u∂z+μ∇⊥2u−κ2∂2u∂t2+ρN(I)u=0,where u=u(rfalse→,Z,t) is the paraxial beam. The intensity I=I(r→)=I(r→,z)=|u|2.…”

“…By its symmetry, we keep the second-order term, and letting u(r→,Z,t)=ψ(r→,z,t)exp(iρR0P0z), Eq. (1) is transformed as follows: 26 , 28 i∂ψ∂Z+12(∂2ψ∂X2+∂2ψ∂Y2+∂2ψ∂T2)−P02Pcr2ψ=0.Equation (2) is the normalized dimensionless Snyder–Mitchell model, 2 where ψ(X,Y,Z,T) is the envelope of the optical field. (X,Y,Z,T) are the dimensionless coordinates.…”

“…The 1 þ 3D model of a linearly polarized optical field with an envelope u satisfies the Maxwell equation. To the nonlinear homogeneous material, u follows the general nonlocal nonlinear Schrödinger equation as 1,24,27,28 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 4 ; 3 4 1…”

“…By its symmetry, we keep the second-order term, and letting uðr; Z; tÞ ¼ ψðr; z; tÞ expðiρR 0 P 0 zÞ, Eq. ( 1) is transformed as follows: 26,28 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 4 ; 1 7 0…”

Collapse arrest in a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam in nonlocal nonlinear media

“…In a strongly nonlocal nonlinear media, the normalized intensity distribution of an Airy beam is always periodic [37][38][39]. Propagation characteristics of a truncated Airy beam [40], an Airy-Laguerre-Gaussian light bullet [41], a chirped Airy beam [42], spatiotemporal Airy Ince-Gaussian wave packets [43], an inward-focusing ring Airy beam [44], and rotating elliptic vortex complex Airy solitons [45] have also been extensively demonstrated in nonlocal nonlinear media. Nonlocality [46,47] also has deep impacts on the coherent [38,[48][49][50] and incoherent [51] interactions of an Airy beam, leading to the formation of bound states.…”