Exact and approximate solutions for optical solitary waves in nematic liquid crystals

Nematic liquid crystals: An excellent playground for nonlocal nonlinear light localization in soft matter

“…2 Nematicon solutions of the systems (3.1) and (3.2), conversely, are stable in both (1 + 1) and (2 + 1) dimensions. 33,35,36,49 This change in stability character is due to the coupling with the elliptic director Eq. (3.2).…”

“…However, the origin of nematicon stability appears more involved than this as in (2 + 1) dimensions the widths of the beam and the director response are similar for low amplitude nematicons. 49 The key to understanding stability is the effect of the elliptic nature of the director Eq. (3.2) and its relation to nonlocality.…”

“…While no general nematicon solutions are known, isolated nematicon solutions have been found in (1 + 1) and (2 + 1) dimensions. 49 In (1 + 1) dimensions an isolated nematicon solution was found by looking for a solitary wave solution of the form…”

“…49 However, the solution of Abel's equation of the second kind is extremely involved, so that the nematicon solution is too, limiting its use.…”

“…(3.1) and (3.2), which are linearized about the pre-tilt θ 0 , in both (1 + 1) and (2 + 1) dimensions. 49 However, a peculiar type of bistability has been found for the nematicon equations…”