Mie scattering of Laguerre-Gaussian beams: Photonic nanojets and near-field optical vortices

We study Mie scattering of Laguerre-Gaussian (LG) light beams remodelled using the method of far-field matching. The theoretical results are used to analyze the optical field in the near-field region for purely azimuthal LG beams characterized by a nonzero azimuthal mode number $m_{\mathrm{LG}}$. The morphology of photonic nanojets and the near-field structure of optical vortices associated with the components of the electric field are both found to be highly sensitive to the mode number $m_{\mathrm{LG}}$.

Figure 1

Near-field intensity distributions of the total wave field in (a) the $x\text{−}z$ plane and (b) the $y\text{−}z$ plane for the LG beam with $m_{\mathrm{LG}}=0$, $f=0.05$, and $|{\mathbf{R}}_d|=0$. The parameters are as follows: $R_p=\lambda$ is the scatterer radius and $n_p=1.3$ ($n_m=1.0$) is the refractive index inside (outside) the particle.

Figure 2

Near-field intensity distribution in the $x\text{−}z$ plane of (a) the incident wave beam and (b) the total wave field for the LG beam with $m_{\mathrm{LG}}=1$, $f=0.05$, and $|{\mathbf{R}}_d|=0$. Other parameters are described in the caption of Fig. 1.

Figure 3

Near-field intensity distribution in the $x\text{−}z$ plane of (a) the incident wave beam and (b) the total wave field for the LG beam with $m_{\mathrm{LG}}=2$, $f=0.25$, and $|{\mathbf{R}}_d|=0$.

Figure 4

Near-field intensity distribution in the $x\text{−}z$ plane of (a) the incident wave beam and (b) the total wave field for the LG beam with $m_{\mathrm{LG}}=2$, $f=0.25$, and ${\mathbf{R}}_d=(0,0,\lambda )$.

Figure 5

Near-field intensity distribution in the $x\text{−}z$ plane of (a) the incident wave beam and (b) the total wave field for the LG beam with $m_{\mathrm{LG}}=3$, $f=0.25$, and ${\mathbf{R}}_d=(0,0,\lambda )$.

Figure 6

Near-field phase maps of the electric-field components $E_z$ (a)–(c) and $E_x$ (d)–(f) in the planes $z=0$ (a),(b),(d),(e) and $z=R_p$ (c),(f) for the LG beam with $m_{\mathrm{LG}}=2$ and $f=0.1$. (a) [(d)] Phase map of the electric-field component $E_z^{\left(\mathrm{LG}\right)}$ [$E_x^{\left(\mathrm{LG}\right)}$] of the incident wave beam in the $x\text{−}y$ plane ($z=0$). (b),(c) [(e),(f)] Phase maps for the electric-field component $E_z$ [$E_x$] of the total light wave field in the planes $z=0$ and $z=R_p$, respectively.

Figure 7

Near-field intensity maps of the electric-field components $|E_z{|}^2$ (a)–(c) and $|E_x{|}^2$ (d)–(f) in the planes $z=0$ (a),(b),(d),(e) and $z=R_p$ (c),(f) for the LG beam with $m_{\mathrm{LG}}=2$ and $f=0.1$. (a) [(d)] Intensity distribution for the $z$ [$x$] component, $|E_z^{\left(\mathrm{LG}\right)}{|}^2$ [$|E_x^{\left(\mathrm{LG}\right)}{|}^2$], of the incident wave beam in the $x\text{−}y$ plane ($z=0$). (b),(c) [(e),(f)] Intensity distributions for the $z$ [$x$] component of electric field of the total light wave field in the planes $z=0$ and $z=R_p$, respectively.