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In this paper, we generalize the method of moments (MOM) based on the surface integral equation (SIE) method to investigate the scattering properties of complicated shaped biological cells illuminated by a Laguerre-Gaussian beam (LGB). We introduce the Lorentz-gauge vector potential with slowly varying envelope amplitude which satisfies the paraxial wave equation to obtain the electric and magnetic field components of the incident beam. The SIE method is applied to compute the scattering field of arbitrary shaped biological cells, the MLFMA is utilized to efficiently solve the resulting matrix equations, and a home-made FORTRAN program is written. Then we explore the influence of the beam parameters (radial parameter, azimuthal parameter, waist radius, and beam center position of a LGB) on the differential scattering cross section (DSCS) for a red blood cell at great length. Some numerical results on the DSCS for complicated shaped biological cells, such as a fusiform cell and a bacteriophage anatomy illuminated by a LGB are given, showing the powerful capability of our approach. As a rapidly advancing field, the investigation of the scattering properties on complicated shaped biological cells illuminated by a LGB will hold a wealth of potential for the study of fundamental properties of light and exciting applications in the medical field.

Scattering of an arbitrarily incident Bessel beam by fractal soot aggregates is numerically investigated. The incident beam is described by the vector expressions of the zero-order Bessel beam in combination with rotation Euler angles. The scattering problems involving fractal soot aggregates are formulated with a hybrid vector finite element-boundary integral-domain decomposition method. Some numerical results are included to show the scattering behaviors of fractal soot aggregates when they are illuminated by Bessel beams.