Second Harmonic Generation From Nanosphere Of Centrosymmetric Mateiral Excited By Focused Beams

Within the electric dipole approximation, second harmonic generation (SHG) isforbidden in the bulk of a centrosymmetric media. However, the symmetry of thebulk is broken at the surface or interface of the medium and then dipole generationwould be allowed. When magnetic-dipole and electric-quadrupole interactions areconsidered, however, second-order processes can occur even in the bulk ofcentrosymmetric materials. Recently, SHG of nanoparticles comprised ofcentrosymmetric media has attracted great interest of scientific community.Subwavelength particles can be used as subwavelength emitters or optical indicatorsfor diagnostic in medicine and biology. In addition, subwavelength particles aresometimes studied by optical microscopic techniques. In those cases, subwavelengthparticles are often illuminated by focused beams. However, the plane-waveapproximation or the paraxial approximation was assumed in most of the relevanttheoretical works. Because of the tensorial nature of SHG, the effect of thelongitudinal field component on SHG can become remarkable under certaincircumstances. Therefore, this dissertation investigate the surface and bulk secondharmonic (SH) responses of centrosymmetric nanosphere excited by focused planewave, focused cylindrical vector beam and focused optical vortices, respectively. Themajor contents and results are shown as follows:1) The expressions of focused plane wave, focused cylindrical vector beam andfocused optical vortices are greatly simplified by the integral expressionI, m. Then,according to the differential recursion formula between the Bessel functions withdifferent order, the analytical expression of the field gradient of different focusedbeams is derived.2) Based on vector diffraction theory of focused beams, nonlinear Rayleigh-Gans-Debye theory and phenomenological model for SHG of centrosymmetric media, atheoretical model for SHG from centrosymmetric nanoparticles excited by focusedbeams is developed. By using this model, when centrosymmetric nanoparticles are excited by focused plane wave, focused cylindrical vector beam, and focused opticalvortices, the surface and bulk SH responses are investigated, respectively.3) We study and compare the nonlinear responses of centrosymmetric nanospheresexcited by plane wave and focused plane wave. The results show that with increasingnumerical aperture, the SH radiation patterns of the surface response hardly changes.For the case of plane-wave excitation, the bulk contribution related to the parameter vanishes. However, for the larger value of the numerical aperture (NA), therelative magnitude of the bulk response related to greatly increases and becomescomparable to the bulk response corresponding to At the same time, for the case ofa focused beam as the excitation field, the bulk response from the parameter is moresensitive to the ratio and phase difference of the two orthogonal components of theincident beam. As the size of nanoparticle increases, the total second harmonicradiation intensity have a maximum when the nanoparticle is excited by focusedplane wave while for the case of plane-wave excitation the intensity monotonicallyincreases.4) The surface and bulk nonlinear responses of centrosymmetric nanosphere excitedby focused cylindrical vector beams with different polarization rotation angles0arefurther studied. The calculated surface SH radiation angular patterns show that thereis the distinct difference between the surface responses stemming from differentsurface nonlinear susceptibility elements and significant backward propagating SHGcan be generated, which is further explained by the distributions of the fieldcomponents and the surface SH polarizations. When excited by a focused radiallypolarized beam, the bulk responses corresponding to different bulk parameters arealmost similar and the same order of magnitude, due to the fact that only the termE z E z/zis dominant. For the case of an azimuthally polarized incident beam, thebulk response relate to the parameter′vanishes because there are no the componentsE and Ez. However, different bulk polarization distributions result in the differencebetween the bulk radiation patterns corresponding to and.5) When excited by focused doughnut beams with different topological charge m,SHG from centrosymmetric nanospheres is also investigated. For m=±1, thelongitudinal field component induced by depolarized effect is dominant and then strong backward propagating SHG presents in surface response. When m=±2, thecontribution of the weakest field component Eyis obvious, because of theinhomogeneity in the distributions of the excitation field and the tensorial nature ofSHG.