Light-assisted spontaneous birefringence and magnetic-domain formation in a suspension of gyrotropic nanoparticles

We show that linearly polarized light in a suspension of gyrotropic nanoparticles can experience modulation instability, which leads to spatial separation of right- and left-circularly polarized waves. Such a separation preserves zero full angular momentum of the electromagnetic field; thus, the time-reversal symmetry is broken only locally. Eventually, this instability results in the formation of the lattice of spatial solitons with alternating right and left circular polarization. As magnetic moments of nanoparticles tend to reorient parallel to the wave vector in circularly polarized light, every spatial soliton captures a static magnetic field directed along or opposite to the wave vector depending on the direction of the field angular momentum; therefore, the soliton lattice altogether looks like an array of magnetic domains with antiferromagnetic ordering.

Figure 1

Reorientation of magnetic nanoparticles in electromagnetic field: Left panel: linearly polarized light; magnetic moments are chaotically directed. Right panel: circularly polarized light; magnetic moments reorient along the light angular momentum.

Figure 2

Instability growth rate $\mathrm{\Lambda }$ as a function of the transverse wave number $K_{\perp }$ for three amplitudes: $W_0=0.3,0.7$, and 0.5138. The second wave-number scale given on the top is $k_{\perp }/k_0$. The dotted lines correspond to reduced growth rate in the case of nonzero damping ($\mathrm{\Lambda }\to \mathrm{\Lambda }-\gamma$ with $\gamma =0.05$ and $W_0=0.5138,0.7$), and in the case of $W_0=0.3$ the instability vanishes.

Figure 3

Nonlinear spatial dynamics of (a) the helicity function $G(x,z)={\left|U\right|}^2-{\left|V\right|}^2$ and (b) the total field amplitude $\sqrt{{\left|U\right|}^2+{\left|V\right|}^2}(x,z)$. Initial linearly polarized plane wave with the amplitude $\sqrt{2}{W}_0=0.73A_C$ perturbed by small random noise undergoes modulation instability and eventually splits into left and right polarized filaments.

Figure 4

(a) Spatial evolution of the field spectrum, $W_k={\left|U\right|}_k^2+{\left|V\right|}_k^2$ of initial linearly polarized plane wave. The color illustrates the function ${log}_{10}{W}_k(k,z)$, and the spectrum averaged over the propagation distance, $\langle W_k\rangle (k/k_0)$ is shown in the inset. (b) Mean wave number of the field spectrum, $\langle k/k_0\rangle =\int \left|k\right|/k_0{W}_{k}dk/\int W_{k}dk$, as a function the propagation distance $z$.

Figure 5

Nonlinear spatial dynamics of (a) the helicity function $G(x,z)={\left|U\right|}^2-{\left|V\right|}^2$, (b) the total field amplitude $\sqrt{{\left|U\right|}^2+{\left|V\right|}^2}(x,z)$, and (c) the normalized helicity density $C={\left(\right|U|}^2-{\left|V\right|}^2{)/(\left|U\right|}^2+{\left|V\right|}^2)$. Initial linearly polarized bell-shaped beam with the amplitude $0.73A_C$ and the width 0.0144 cm perturbed by small random noise undergoes modulation instability and eventually splits into left and right polarized filaments. The other parameters of the simulation are given in the text.

Figure 6

(a) Spatial evolution of the field spectrum $W_k={\left|U\right|}_k^2+{\left|V\right|}_k^2$ of initial linearly polarized bell-shaped beam. The color illustrates the function ${log}_{10}{W}_k(k,z)$, and the spectrum averaged over the propagation distance ${\langle W_k\rangle }_z$ as a function of $k/k_0$ is shown in the inset. (b) Mean wave number of the field spectrum $\overline{k}/k_0=\int \left|k\right|/k_0{W}_{k}dk/\int W_{k}dk$ as a function the propagation distance $z$.

Figure 7

(a) Nonlinear spatial dynamics of the helicity function $G(x,y,z)={\left|U\right|}^2-{\left|V\right|}^2$ of initial linearly polarized 2D wave beam: the isosurface $G(x,y,z)=1.34$ (red filaments) and $G(x,y,z)=-1.34$ (blue filaments). (b) Mean wave number of the field spectrum $\langle k/k_0\rangle =\int \sqrt{k_x^2+k_y^2}/k_0{W}_{k}dk/\int W_{k}dk$ as a function of the propagation distance $z$.

Figure 8

Nonlinear spatial dynamics of initial linearly polarized 2D wave beam. The distribution of the function $F(x,y)=\left|U\right|-\left|V\right|$ is depicted at different $z$ positions. Black contour denotes points where $F=0$, and thus the field is linearly polarized.