Theoretical Studies On Optical Trapping And Cylindrically Symmetric Vector Beams

Since Ashkin of Bell Lab demonstrated in 1970 that the gradient force in optical field can trap micro-particle,optical trapping or optical tweezer has emerge as a powerful tool with wide-reaching applications in the study of microscopic field covering from atoms,molecules,sub-micron to the dimension of the order of hundreds micron.Centered on the interaction between the trapping beam and the particle,this thesis completed the following work.1.An improved T-matrix method is proposed,which is capable of dealing with the scattering by non-axis-symmetrical and complicated-shape particles.The new method discretizes the surface of the particle by a set of triangles.It is therefore applicable to calculating the scattering field by particles with complicated shape.2.For T-matrix method,a technique of speeding the calculation of the scattered field is presented.In computing the scattering fields,the determination of the T-matrix involves matrix multiplication and inversion,which consumes considerable time when the size of the particle is large.Petrov et al.proposed an improved matrix inversion method.Based on this improved inversion,we present another fast technique for calculating the scattering fields.Our method obtains the scattered field by directly multiplying the matrix and the incident field coefficients,operation between which can be completed by the improved matrix inversion.Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al.3.Complex-source-point spherical wave(CSPSW) vector potential is introduced to describe radially polarized beam(R-TEM₀₁).The vector potential expression represented by the conventional Lax perturbative series method become rather complicated with increasing the accuracy.The CSPSW vector potential acquires very simple form in mathematics and exactly satisfies the Ho equation.4.The method of representing a fifth-order corrected radially polarized Laguerre-Gauss beam(R-TEM_nl) is obtained.By using the Lax perturbative series method,we derive the vector potential expression with second-order correction from which 5th-order corrected R-TEM_nl is found.Meanwhile,a scalar Laguerre-Gauss wave accurate to any order is obtained.5.The possibility of improving axial trapping efficiency by raidally polarized beams is proved theoretically.In optical trapping,radiation forces on the particle are,in general,divided into the gradient force and the scattering force,and the latter needs to be reduced as weak as possible in axial trapping and its amplitude depending on the z component S_z of Poynting vector.Radially polarized fields acquire zero radial field component near the focus,leading to a vanishing S_z near the focus.Thus the scattering force can be weakened significantly.Our calculation strongly confirms this.6.Double-ring radially polarized beam(DR R-TEM₀₁) is suggested to further reduce the scattering force in optical trapping.The fields of inner and outer rings of a DR R-TEM₀₁ are polarized in instantly opposite direction along the radius. After being focused,the beam develops two intensity rings of radial component and the inner intensity is less than that of R-TEM₀₁ in the same region.Since S_zis proportional to the radial component intensity,we predict that DR R-TEM₀₁ could give higher axial trapping efficiency provider that the particle size falls into the inner ring.