Effective breaking of the action-reaction principle using spatial solitons

We discuss a class of interactions between self-confined optical beams breaking the action-reaction principle. The effective force intertwining the beams does not satisfy momentum conservation, paving the way to the potential existence of situations where both beams are pushed in the same direction, in turn leading to the so-called diametric drive. In our theoretical proposal the interaction between the two light beams is enabled by optical nonlinearity. The nonlinearity is assumed to change sign with the light polarization, in turn allowing the two light beams to be attracted or repelled by an inhomogeneous region according to the photon polarization. We demonstrate that this exotic type of nonlinear spin-orbit-like interaction can be achieved in nematic liquid crystals (NLCs). In fact, depending on the input polarization, in NLCs a change in temperature corresponds to a focusing or defocusing index change. For the polarization seeing a thermal defocusing response (corresponding to the extraordinary component), the self-confinement is ensured by the simultaneous action of reorientational nonlinearity.

Figure 1

(a) Behavior of $n_{\perp }$ and $n_{\parallel }$ vs temperature $T$ for the NLC E7, where the transition to the isotropic phase occurs for $T_{NI}=58{}^{\circ }\text{C}$. (b) Extraordinary refractive index $n_e$ vs angle $\theta$ for three different temperatures. The wavelength is 1064 nm.

Figure 2

First to third column: Distribution of the total intensity on the plane $xz$ for different input powers when the NLC is simultaneously excited by an ordinary and an extraordinary wave, placed in $x=-20\mu \mathrm{m}$ and $x=0\mu \mathrm{m}$, respectively. The input beamwidth of the extraordinary is $4\mu \mathrm{m}$, whereas for the ordinary it is $10\mu \mathrm{m}$. Each row (column) corresponds to fixed extraordinary (ordinary) input power. Last column: Corresponding beam trajectories on the plane $xz$ computed using the centroid of the intensity distribution. Solid and dashed lines correspond to the extraordinary and the ordinary waves, respectively. In each panel the extraordinary power is fixed: Accordingly, a largest bending for the solid curves (extraordinary waves) corresponds to a larger repulsion due to the increasing ordinary power. The three ordinary trajectories in each panel are almost overlapping given that the extraordinary power is fixed. The wavelength is 1064 nm.

Figure 3

Evolution along $z$ of the distance between the extraordinary and ordinary wave for a fixed extraordinary power $P_e=10\mathrm{mW}$ and four different values of $P_o$. From bottom to top, it is $P_o=0.01$, 10, 30, and 60 mW.

Figure 4

Coevolution of the extraordinary (blue) and ordinary (red) wave for $P_e=P_o=20\mathrm{mW}$ in a cell 3 mm long along $z$; input waists are identical to Fig. 2. The initial separation is $10\mu \mathrm{m}$. Left and central insets: The corresponding intensity distributions on the plane $xz$. Right inset: Trajectories of the respective centers of mass; symbols correspond to parabolic best-fitting.