Two-dimensional Modulation Instability and Higher-Order Soliton Clusters in Nematic Liquid Crystals with Competing Re-Orientational and Thermal Nonlocal Nonlinearities

We investigate two-dimensional modulation instability (MI) and higher-order soliton clusters in nematicliquid crystals with competing re-orientational and thermal nonlocal nonlinearities. With linear-stabilityanalysis, we show nonlocality can suppress effectively MI of two-dimensional plane wave. By employingvariational (Lagrangian) approach, bifurcated solutions of higher-order solitons, i.e., Hermite-Gaussian (HG)and Laguerre-Gaussian (LG) soliton clusters are obtained analytically. Propagation dynamics of both upperand lower branches of solitons are demonstrated numerically. Properties, such as stable propagation distanceand mode transformation between HG and LG modes are also discussed in detail.