| Mirrors are highlighted because of the absence of chromatic aberration and theacquirement of NA close to1which make them attractive in areas such as confocalmicroscopy technology, photolithography technology, optical storage andnanoparticle trapping technology. The secondary aspheric mirrors feature lowprocessing difficulty, unique focusing properties, and so they become the researchfocus of academic staffs. Due to the focused electric fields relate to the vector natureof the incident wave, it is necessary to focused apply vector diffraction theory, whenanalyzing optical systems with high numerical aperture.The vectorial diffraction theory of focusing property of elliptical mirror arefirstly studied. The three dimensional expressions of focusing electric field ofelliptical mirror based on the Debye-Wolf integral has been derived in the case oflinearly polization beam incidence, so the vector theory for focusing property ofelliptical mirror has been constructed. The three dimensional distribution offocusing fields in the elliptical mirror system have been described in the cases ofradially polarized illumintation based the previous focusing model. And also theimaging property of electric dipole in elliptical mirror has been studied. For thefocusing problem of parabolic mirror, the three dimensional expressions of focusingelectric field in parabolic mirror with aperture angle greater than π/2has beenderived, by means of solving the boundary value problem of parabolic mirror basedon the Stratton-Chu integral. Particularly, the experiment to confirm the assumptionof the retroreflective field in the process has been performed. The conclusions arepresented as follows.Firstly, the apodization factor for elliptical mirrors has been derived andrigorous elliptical mirror focusing formula based on spherical wave transformationhas been derived further. The simulation results show, the width of the main lobe inelliptical mirror system in y-axis direction is12.07%less than that of apalanatic lenssystem with x direction linearly polarized illumination. For radially polarizedillumination, the lateral component of focusing field in elliptical mirror is almostzero. Therefore, theory basis is giving for the application of elliptical mirror in highresolution confocal microscopy and near field optics.Secondly, the rigorous theory of dipole imaging has been studied in theelliptical mirror system and double apalanatic lens system separately. Thesimulation results show, if the dipole is at focus with parallel polarization, thefocusing spot will be like doughnut, while the focusing spot are solid circle in the case of perpendicular polarization. If the diploe is defocusing, simulation resultsshow, off-axis aberration such as coma in mirror systems are sensitive. The imagingproperty of electric dipole in elliptical mirror will make the determination of thespatial orientation of dipole easy.Finally, the three dimensional expressions of focusing electric field in parabolicmirror with aperture angle greater than π/2has been derived, by means of solvingthe boundary value problem of parabolic mirror based on the Stratton-Chu integral.Simulation results show, for linearly polarized illumination, the contribution fromsurface integral by incident beam dominates the focusing field, however, thecontributions from the surface integral of retroreflective field and the contourintegral are negligible. |
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