Since Lorenz-Mie theory was put forward, the scattering and absorption of electromagnetic waves by tiny particles have been widely studied. In recent years, coated media spheres have caught extensive attention from scholars due to their wide applications in various fields, including radar cross section (RCS), nanomaterials, and spectroscopy. Owing to different values of dielectric constants and magnetic permeability in various directions of anisotropic materials, significant changes occur in the internal electromagnetic field of a uniaxial anisotropic coated (UAC) sphere when a laser is incident from different directions, which significantly influences its surface RCS. The previous literature mainly studies the electromagnetic scattering of a single planar wave and a single Gaussian beam on coated spheres. However, in the optical manipulation of small particles, it is easier to employ two or more beams to capture and manipulate the particles than adopting only one laser beam. Therefore, it is essential to investigate the electromagnetic scattering problem of a UAC sphere by dual focused Gaussian beams for achieving optical manipulation of coated spheres.

Based on the generalized Lorenz-Mie theory (GLMT), we study the scattering characteristics of a UAC sphere which is induced by two focused Gaussian beams with arbitrary directions. According to the orthogonality of spherical vector wave functions (SVWFs), the expression of dual Gaussian beam in terms of SVWFs is derived. By introducing the Fourier transform, the electromagnetic field expansion in the anisotropic coated area is obtained. The electromagnetic fields in each region of the UAC sphere are expanded in terms of the SVWFs, and by combining the boundary conditions, the scattering coefficients and the radar scattering crosssection of uniaxial anisotropic coated sphere illuminated by two Gaussian beams are obtained.

The effects of the incident angle of dual beams, particle inner diameter, the ratio of coating thickness to the inner diameter, electrical anisotropy, and magnetic anisotropy on scattering intensity are analyzed. The results indicate that when the two Gaussian beams irradiate the coated sphere along different directions, the RCS will exhibit two maxima in the incident direction. Meanwhile, when the two beams propagate in opposite directions, the RCS of the E plane always exhibits a symmetrical distribution, while the RCS of the H plane exhibits two minima at ±90°, but the angular distribution does not show any significant changes (Fig. 3). As the waist width of the dual beams increases, both the E plane and H plane RCS will continuously rise due to the larger illuminated area on the UAC sphere (Fig. 4). The RCS increases with the rising inner radius of the particle around 0° and 180°, but becomes oscillatory around ±90°. When the inner radius is larger than the wavelength, the RCS value will increase slowly and tend to be stable if the inner radius increases continuously (Fig. 5). The variation of thickness, dielectric constant, and magnetic permeability of the anisotropic coating can bring significantly changed electromagnetic field in the coated region, leading to more complex scattering phenomena. Changing the ratio of coating to internal radius shows that with different angles, different variations occur in RCS (Fig. 6). When the electrical anisotropy is equal to 1, the coating material is isotropic and the RCS reaches the maximum at 90°. However, with the anisotropy increase or decrease, the RCS will reduce. The angular distribution of the whole E plane RCS will become more oscillatory with the rising electrical anisotropy. Contrary, the electrical anisotropy changes do not affect the RCS angular distribution on the H plane (Fig. 7). By varying the magnetic anisotropy of the UAC sphere, the magnetic anisotropy changes have a much greater influence on the RCS angular distribution of H plane than that of E plane (Fig. 8).

Based on the GLMT, we provide a method to calculate the RCS of the UAC sphere irradiated by dual beams. Theoretically, this method is suitable for spherical particles with arbitrary coating thickness and inner radius, and the spherical shell particles made of different anisotropic materials can be simulated and analyzed by changing the particle parameters. By comparing the RCS angular distribution of a degenerate UAC sphere under the illumination of dual Gaussian beams with the results in literature, it is confirmed that our theory and program are accurate. The theory and numerical analysis are expected to provide a theoretical basis for the scattering and optical operations of anisotropic coated particles by multiple lasers.