Qingchao Shang

Analysis of the radiation force and torque exerted on a chiral sphere by a Gaussian beam

Under the framework of generalized Lorenz-Mie theory, we calculate the radiation force and torque exerted on a chiral sphere by a Gaussian beam. The theory and codes for axial radiation force are verified when the chiral sphere degenerates into an isotropic sphere. We discuss the influence of a chirality parameter on the radiation force and torque. Linearly and circularly polarized incident Gaussian beams are considered, and the corresponding radiation forces and torques are compared and analyzed. The polarization of the incident beam considerably influences radiation force of a chiral sphere. In trapping a chiral sphere, therefore, the polarization of incident beams should be chosen in accordance with the chirality. Unlike polarization, variation of chirality slightly affects radiation torque, except when the imaginary part of the chirality parameter is considered.

Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam

Using the theory of electromagnetic scattering of a uniaxial anisotropic sphere, we derive the analytical expressions of the radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam. The beams propagation direction is parallel to the primary optical axis of the anisotropic sphere. The effects of the permittivity tensor elements ε(t) and ε(z) on the axial radiation forces are numerically analyzed in detail. The two transverse components of radiation forces exerted on a uniaxial anisotropic sphere, which is distinct from that exerted on an isotropic sphere due to the two eigen waves in the uniaxial anisotropic sphere, are numerically studied as well. The characteristics of the axial and transverse radiation forces are discussed for different radii of the sphere, beam waist width, and distances from the sphere center to the beam center of an off-axis Gaussian beam. The theoretical predictions of radiation forces exerted on a uniaxial anisotropic sphere are hoped to provide effective ways to achieve the improvement of optical tweezers as well as the capture, suspension, and high-precision delivery of anisotropic particles.

Electromagnetic scattering by a uniaxial anisotropic sphere located in an off-axis Bessel beam

Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.

Calculation of electromagnetic scattering by a large chiral sphere

Expressions of scattering coefficients for calculating scattering by large chiral spheres are derived by using logarithmic derivatives and ratios of Riccati-Bessel functions. The improved expressions can be easily applied to the case of an arbitrarily shaped beam incidence. A simplified expression of the scattered field in the far field is obtained for the case of x-polarized plane-wave incidence. To verify the correctness and accuracy of the theory and codes, our results are compared with those in literature and those calculated by Mie theory. Radar cross sections of a large chiral sphere are numerically studied. It is found that the rainbow phenomenon of a chiral sphere is very different from that of an isotropic sphere.

Calculation of radiation force and torque exerted on a uniaxial anisotropic sphere by an incident Gaussian beam with arbitrary propagation and polarization directions

On the basis of spherical vector wave functions and coordinate rotation theory, the expansion of the fields of an incident Gaussian beam with arbitrary propagation and polarization directions in terms of spherical vector wave functions is investigated, and beam shape coefficients are derived. Using the results of electromagnetic scattering by a uniaxial anisotropic sphere, the analytical expressions of the radiation force and torque exerted on a homogeneous absorbing uniaxial anisotropic sphere by the arbitrary incident Gaussian beam. We numerically analyze and discuss the following: the effects of an anisotropic absorbing dielectric on the axial and transverse radiation forces exerted by an off-axis Gaussian beam on a uniaxial anisotropic sphere; the variations in the axial, transverse, and resultant radiation forces (with incident angle β and polarization angle α) imposed by an obliquely Gaussian beam on a uniaxial anisotropic sphere; and the results on the characteristics of the three components of the radiation forces versus the center-to-center distance between the sphere and beam. Selected numerically results on the radiation torque exerted on a stationary uniaxial anisotropic transparent or absorbing sphere by a linearly polarized Gaussian beam are shown, and the results are compared with those exerted an isotropic sphere. The accuracy of the theory and code is confirmed by comparing the axial radiation forces with the results obtained from references.

Analysis of rainbow scattering by a chiral sphere

Based on the scattering theory of a chiral sphere, rainbow phenomenon of a chiral sphere is numerically analyzed in this paper. For chiral spheres illuminated by a linearly polarized wave, there are three first-order rainbows, with whose rainbow angles varying with the chirality parameter. The spectrum of each rainbow structure is presented and the ripple frequencies are found associated with the size and refractive indices of the chiral sphere. Only two rainbow structures remain when the chiral sphere is illuminated by a circularly polarized plane wave. Finally, the rainbows of chiral spheres with slight chirality parameters are found appearing alternately in E-plane and H-plane with the variation of the chirality.

Light scattering of a Laguerre–Gaussian vortex beam by a chiral sphere

Since the development of the generalized Lorenz-Mie theory, electromagnetic scattering by arbitrary beams has drawn growing interest. The Laguerre-Gaussian (LG) vortex beam is well known for its orbital angular momentum. With the aim of investigating the analytical solution to the scattering of a chiral sphere by a LG vortex beam, particular attention is paid to the expansion expression of the LG vortex beam. The expansion coefficients are derived based on the expansion of a Hermite Guassian beam as the LG vortex beam can be expressed as the superposition of Hermite Guassian modes. The numerical results of the incident beam expansion coefficients convergence and the scattered field comparison with the reference prove the validity of the theoretical analysis and computation codes. The results reveal that there exists an optimal sphere size for the maximum scattered field which is determined by the topological charge, beam waist radius, and beam center position. The investigation could provide a foundation for the optical manipulation of chiral particles by a LG vortex beam.

Radiation force on a chiral sphere by a Gaussian beam

Based on the generalized Lorenz-Mie theory (GLMT), the incident Gaussian beam and scattered fields of the chiral sphere are expressed in terms of the spherical vector wave functions. An expression of the radiation force on the chiral sphere in a Gaussian beam is derived from the theory of electromagnetic momentum. The influence of the chiral parameter, the beam waist radius and the radius of the chiral sphere on radiation force is discussed numerically.

Analysis of scattering and polarization characteristics of chiral sphere with a large-size parameter

Based on the spherical vector wave functions, we research the scattering of a homogeneous chiral sphere to a plane wave. The expansion coefficients of scattered fields and internal fields are obtained through the boundary condition at the sphere interface. The logarithmic derivatives of Ricatti-Bessel functions are introduced in order to avoid the numerical overflow of high-order terms or larger argument spherical Bessel function and the problem of the accumulative error in the matrix calculation. Thus, the scattering characteristics of a chiral sphere with larger size parameter can be studied numerically. Moreover, the influence of chiral parameter on the polarization properties is also numerically analyzed.

Reflection and transmission of Laguerre Gaussian beam from uniaxial anisotropic multilayered media

Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian (LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.