| It is well-known that the polarization distribution of vector beam can be changed by spatial variation.This characteristic makes the vector beam have potential application value in various frontier fields.Simultaneously,the focusing field evolution of vector beam can be explored by phase modulation,and the corresponding regulation ability of different parameters can be also comprehended.Therefore,these research results can be widely used in particle micromanipulation,super-resolution imaging and optical information transmission.In this paper,the tightly focusing characteristic of Bessel Gaussian,hyperbolic cosine Gaussian and Lorentz Gaussian beams with phase modulation is studied based on the Richards Wolf vector diffraction theory.The main research contents and results are demonstrated as follows:Combining the characteristics of power order phase and helical conical phase,a power exponential hybrid spiral conical phase is proposed.The analytical formula for the Bessel-Gaussian beam with power order mixing helical-conical phase wavefront when they are tightly focused on the focal plane is given.At the same time,the effects of the topological charge number L、the power order n、the eccentricity parameters K、the beam parameterβfor the tightly focusing characteristics of beam are studied and analyzed.Results show that the topological charge number L can finely adjust the opening of the spiral-like curve at the focal plane.The power order n can adjust the energy distribution in the focus area.By increasing eccentricity parameters K,the position of the maximum intensity spot will move along with y-coordinate axis.When the beam parameterβchanges,the number of intensity peaks on the focal plane changes.Besides,some optical gradient force distributions are investigated to illuminate the applications of these alterable focal patterns.A method of simultaneous polarization modulation and cosine phase modulation is proposed,the analytical formula for the cosh-Gaussian beam with polarization mixing cosine phase modulation when they are tightly focused on the focal plane is given.At the same time,the effects of the polarization parameter C、the tunable parameters D、the phase modulation parameter m and the decentered parameterβfor the beam focusing properties are studied and analyzed.The results that show adjusting the polarization parameter C,a tunable focal shift and a continuous shifting of focus on both directions of the optical axis can be achieved.When the tunable parameters D is positive,the optical chain with tunable length can be structured by increasing D.When D is negative,there will appear a special optical trap focus mode which the numbers of optical traps can be changed by tailoring D.When the phase modulation parameter m increases,the focal pattern will wholly enlarge along the longitudinal direction.By increasing the decentered parameterβ,the shape of the light intensity distribution in the focusing region can be remarkably adjusted.Besides,by combining the theories and analyzing the field patterns in the transverse plane,there is an electric field intensity dependence on the azimuthal angleφ.A well-designed of sinusoidal phase is proposed,and the analytical formula for the linearly polarized Lorentz-Gaussian vortex beam with sinusoidal phase modulation when they are tightly focused on the focal plane is given.Meanwhile,the effects of the relative Gaussian parameter w_x、the relative Lorentz parameterγ_y、the topological charge number m、the sinusoidal modulation parameter n and the propagation distance z on the beam focusing characteristics are studied and analyzed.Results show that the focus pattern in the horizontal direction at the focal region can be compressed by increasing relative Gaussian parameter w_x.As the relative Lorentz parameterγ_ychanges,the focus pattern will separate in the vertical direction of the optical field.With the variation of topological charge number m,a special tunable optical dark trap focusing mode can be obtained.Through changing the sinusoidal modulation parameter n,the regular trilateral,quadrangle,pentagon,and hexagon-shaped of focusing mode can be correspondingly constructed.Besides,on increasing propagation distance z,the focusing mode in the near focusing region always exhibits hexagon-shaped patterns,which reflects that this special focusing mode has a good stability. |
