Study On Properties Of Cylindrically Polarized Vector Beams

As a nonuniform polarization, the cylindrically polarized vector beams have drawn growing attention due to their unique adavantages in the application of modern optics. The vectoriality, polarization properties, propagation properties, nonparaxial behavior and beam quality of the cylindiraclly polarized vector beams are extensively studied in the thesis. The main contents of this thesis are included as follow:(1) The nonparaxial and paraxial propagation properties of the cylindrically polarized beams in free space are investigated. On the basis of the vectorial Rayleigh-Sommerfeld formulas, the analytical expressions for the electric field of the cylindrically polarized Laguerre-Gaussian beams (LGBs) propagating in free space are derived. The radially polarized, azimuthally polarized and paraxial cases can be viewed as the special cases of the general result. The analyses show that both the ratio of waist width to wavelength and the beam order play an important role in the nonparaxial behavior. As the ratio of waist width to wavelength decreases and the beam order increases, the nonparaxiality of the radially and azimuthally polarized beams becomes more obvious. The longitudinal component of the electric field of the radially polarized beams compared with the transverse component can be increasingly neglected with the increasing ratio of waist width to wavelength, the decreasing beam order and the increasing propagation distance.(2) The nonparaxial and paraxial propagation properties of the radially and azimuthally polarized beams diffracted at a circular aperture are studied. The analytical expressions for the electromagnetic fields of the apertured radially and azimuthally polarized LGBs are obtained based on the vectorial Rayleigh-Sommerfeld formulas. The general result can reduce to the unapertured and paraxial cases. The analyses indicate that the magnetic field of the radially polarized beams takes on azimuthal polarization, and the magnetic field of the azimuthally polarized beams takes on radial polarization. The nonparaxiality of the apertured radially and azimuthally polarized beams depends on the ratio of waist width to wavelength, the beam order and the truncation parameter. In addition, the beam diffraction effect should be considered, and it increases as the aperture radius decreases. The longitudinal component of the electric field of the apertured radially polarized beams compared with the transverse component can be increasingly neglected with the increasing ratio of waist width to wavelength, the decreasing beam order and the increasing truncation parameter.(3) The propagation properties of the radially and azimuthally polarized vector beams close to the source are described. The contribution of the propagating and evanescent waves to the radially and azimuthally polarized beams is separated by the vector angular spectrum method, and the analytical expressions for the propagating and evanescent waves of the radially and azimuthally polarized LGBs in the source region are derived without any approximation. The results show that the waist width, the beam order, and the propagation distance affect the behavior of the evanescent waves. The contribution of the evanescent waves to the radially and azimuthally polarized beams close to the source becomes more obvious with the smaller ratio of waist width to wavelength and the larger beam order. The beam order has no influence on the profiles of the evanescent waves of the transverse and longitudinal components of the electric field. The effect of the evanescent waves can be increasingly neglected with the increasing ratio of waist width to wavelength, the decreasing beam order and the increasing propagation distance. Moreover, the contribution of the evanescent waves to the radial polarization is much stronger than it to the azimuthal polarization.(4) The vectorial structure and beam quality of the cylindrically polarized beams in the far feild are investigated. In terms of the vector angular spectrum method, the electromagnetic fields of the cylindrically polarized LGBs can be expressed as a sum of the transverse electric (TE) term and the transverse magnetic (TM) term. The analytical electromagnetic expressions for the TE and TM terms of the cylindrically polarized beams in the far field are given by the method of stationary phase. The beam quality of the cylindrically polarized beams in the far feild is measured by the power in the bucket (PIB) beyond the paraxial approximation. The results indicate that the energy flux distributions of the TE term, the TM term, the whole beam, and the far-field beam quality depend on the the ratio of waist width to wavelength, the beam order and the angle between the electric field vector and the radial direction. As the ratio of waist width to wavelength increases, the beam order decreases and the electric field vector points to the azimuthal direction, the cylindrically polarized beams has the more compact energy flux distribution, the larger value of PIB, the better energy focusability and the better far-field beam quality. The azimuthal polarization compared with the radial polarization has the better energy focusability and the better beam quality in the far field beyond the paraxial approximation.(5) The far-field vectorial structure and beam quality of the cylindrically polarized beams diffracted at a circular aperture are studied. The electromagnetic fields of the apertured cylindrically polarized LGBs can be decomposed into the TE and TM terms by the vector angular spectrum method. The analytical electromagnetic expressions for the TE and TM terms of the apertured cylindrically polarized beams in the far field are obtained based on the method of stationary phase. The far-field beam quality of the apertured cylindrically polarized beams is measured by the PIB in the nonparaxial regime. The analyses show that the circular aperture does not change the vectorial structure and polarization properties of the cylindrically polarized beams. The ratio of waist width to wavelength, the beam order, the truncation parameter and the angle between the electric field vector and the radial direction have a great impact on the far-field vectorial stucture and beam quality. As the ratio of waist width to wavelength increases, the beam order decreases, the truncation parameters increases and the electric field vector points to the azimuthal direction, the apertured cylindrically polarized beams has the more compact energy flux distribution, the larger value of PIB, the better energy focusability and the better far-field beam quality. In the nonparaxial regime, the apertured azimuthally polarized beams compared with the apertured radially polarized beams have the better energy focusability and the better beam quality in the far feild.