The authors demonstrate experimentally that interaction between nonlocal solitons in nematic liquid crystals (NLCs) can be controlled by the degree of nonlocality. For a given beam width, the degree of nonlocality can be modulated by changing the pretilt angle ${\theta }_0$ of NLC molecules through bias voltage $V$ . As $V$ increases (so does ${\theta }_0$ ), the degree of nonlocality decreases. When the degree of nonlocality is below a critical value, the solitons behave in the way like their local counterpart, i.e., in-phase solitons attract while out-of-phase solitons repulse each other. Such a voltage-controlled interaction between the solitons can be readily implemented in experiments.

We have introduced a novel class of higher-order spatial optical Ince–Gaussian solitons (IGSs) that constitute the third complete family of exact and orthogonal soliton solutions of the Snyder–Mitchell model. The transverse structure of the IGSs is characterized by the Ince polynomials and has an inherent elliptical symmetry. The IGSs form the exact and continuous transition modes between Hermite–Gaussian solitons and Laguerre–Gaussian solitons.

Starting from the vector angular spectrum of the electromagnetic beam, the analytical vectorial structure of the radially polarized beams (RPBs) is presented. The energy flux distributions of the RPBs are demonstrated. The physical pictures of the RPBs are well illustrated from the vectorial structure. This particular electromagnetic field is entirely transverse magnetic, and on axis it only has a longitudinal $\left(z\right)$ electric-field component (i.e., no transverse electric field and no magnetic field at all on axis).

In analogy to a perturbed harmonic oscillator, we calculate the fundamental and some other higher order soliton solutions of the nonlocal nonlinear Schödinger equation (NNLSE) in the second approximation in the generally nonlocal case. Comparing with numerical simulations we show that soliton solutions in the second approximation can describe the generally nonlocal soliton states of the NNLSE more exactly than that in the zeroth approximation. We show that for the nonlocal case of an exponential-decay type nonlocal response the Gaussian-function-like soliton solutions cannot describe the nonlocal soliton states exactly even in the strongly nonlocal case. The properties of such nonlocal solitons are investigated. In the strongly nonlocal limit, the soliton’s power and phase constant are both in inverse proportion to the fourth power of its beam width for the nonlocal case of a Gaussian function type nonlocal response, and are both in inverse proportion to the third power of its beam width for the nonlocal case of an exponential-decay type nonlocal response.

The spatial optical solitons with ellipse-shaped spots have generally been considered to be a result of either linear or nonlinear anisotropy. We investigate a class of spiraling elliptic solitons in nonlocal nonlinear media without both linear and nonlinear anisotropy. The spiraling elliptic solitons carry the orbital angular momentum (OAM), which plays a key role in the formation of such solitons, and are stable for any degree of nonlocality except the local case if the response function is Gaussian. During the propagation of such solitons, the rate of decay of the OAM is extremely low. The formation of such solitons can be attributed to effective anisotropic diffraction (linear anisotropy) resulting from the OAM. Our variational analytical result is confirmed by direct numerical simulation of the nonlocal nonlinear Schr\"odinger equation.

We have introduced a novel (to our knowledge) class of complex-variable-function (CVF)—Gaussian solitons that constitute the exact soliton solutions of the Snyder–Mitchell model. The CVF–Gaussian solitons whose transverse structure has an inherent rotation are the product of an arbitrary analytic CVF and a Gaussian function. A distribution factor that is the parameter for the description of the transverse distribution of the CVF–Gaussian solitons is discussed.