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 nematic liquid crystals with competing re-orientational and thermal nonlocal nonlinearities. With linear-stability analysis, we show nonlocality can suppress effectively MI of two-dimensional plane wave. By employing variational (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 upper and lower branches of solitons are demonstrated numerically. Properties, such as stable propagation distance and mode transformation between HG and LG modes are also discussed in detail.