Focusing of stochastic electromagnetic Gaussian Schell-model beams through a high numerical aperture objective

Based on vectorial Debye diffraction theory, the focusing properties of stochastic electromagnetic Gaussian Schell-model beams in the focal region of high numerical aperture objective are investigated. Expressions for the intensity distribution and the degree of polarization are derived near the focus. Numerical calculations are performed to analyze the influences of varying corresponding parameters on the changes in the intensity distribution and in the degree of polarization in the focal region.     

Tight Focusing of Radially and Azimuthally Polarized Vortex Beams through a Dielectric Interface

Based on vectorial Debye theory, tight focusing of radially and azimuthally polarized vortex beams passing through a dielectric interface are studied. The intensity distribution in the focal region is illustrated by numerical calculations. We show the influence of numerical-aperture （NA） on the full-width at half maximum （FWHM） of the focal spot or the focal hole. It has been found that compared with the azimuthally polarized Besse~Gaussian （BG） beams, the longitudinal component in the z direction of the radially polarized BG beams has no influence on the FWHM of the focal spot and hole, but enhances the total light intensity.     

Focusing of partially coherent Bessel-Gaussian beams through a high-numerical-aperture objective

The focusing properties of partially coherent Bessel-Gaussian beams passing through a high-numerical-aperture objective are studied based on vectorial Debye theory. Expressions for the intensity distribution, degree of coherence |mu|, and degree of polarization P are derived near the focus. Numerical calculations are performed to analyze the influences of varying corresponding parameters on the intensity distribution, |mu|, and P in the focal region. It is shown that the intensity, |mu|, and P in the focal region are all influenced by varying the effective coherent length L(c) of incident beams and maximal angle alpha determined by the numerical aperture of the objective. Also, the linearly polarized incident field is found to be depolarized after it is focused by a high-numerical-aperture objective.     

Tightly focusing of spirally polarized Quadratic Bessel Gaussian beam through a dielectric interface

Based on vector diffraction theory, the tight focusing properties of spirally polarized axisymmetric Bessel-modulated Gaussian beam through a dielectric interface on high numerical aperture (NA) are investigated theoretically. The optical intensity distribution in the focal region of high NA objective lens is investigated in detail by numerical calculations. The results show that the focal shift induced in the focal region is by mismatch of refractive indices across the dielectric interface. It is also found that the optical intensity in focal region of spirally polarized Quadratic Bessel Gaussian (QBG) beam can be altered considerably by changing spiral parameter C that indicates the polarization spiral degree of the incident beam.     

实现ICF束匀滑的二元光学器件设计与制作

 采用爬山法和模拟退火法相结合的混合优化算法,设计得到了二元光学器件的良好位相结构;基于高斯分布随机信号模型,分析了二元光学器件对输入波面位相畸变的宽容度。首次针对波长λ＝1.053μm研制了φ10mm的连续位相二元光学器件,并通过多级衰减片及CCD实现了焦斑光强分布测量,结果表明得到了边缘陡峭、旁瓣小、中心主瓣具有一定均匀性、且没有中心零级锐脉冲的焦斑光强分布。     

Tightly focusing of linearly polarized vortex beams through a dielectric interface

Based on vectorial Debye theory, the tightly focusing properties of linearly polarized vortex beams through a dielectric interface are studied. Then the intensity distribution in the focal region is investigated in detail by numerical calculations. The focal shifts induced by the mismatch of the refractive indices across the interface has been found. And the dependence of focal shifts and spot size of the focused field on the probe depth and numerical aperture of the objective are presented. Furthermore, the characteristic of intensity pattern of the cross section of the focused field is illustrated, finding that the intensity pattern rotates with the propagation of beams.     

Large aperture continuous phase diffractive optical element to realize uniform focal spot

Uniform focal spot, with flat top, steep edge, low side lobe and high light efficiency, is required in many high power laser system. Using diffractive optical element (DOE) to realize such uniform illumination has many advantages, such as high light efficiency of pure phase modulation, strong flexibility of phase design and so on. A kind of hybrid algorithm based on hill-climbing and simulated annealing is utilized for phase design, owing to the strong convergence of the hill-climbing and the global optimization potential of the simulated annealing. A continuous phase DOE with diameter 100 mm has been fabricated by a rotating hollowed-out mask and ion-etching on the K9-glass substrate. The interferogram of the DOE is given to show the smoothness of the phase distribution. The intensity distribution of the focal spot are measured by a general CCD, and a series of attenuators are used to increase the dynamic range of the measurement. The results after data-processing show that the uniform focal spot with certain uniformity at the main lobe, sharp edge, low side lobe and without sharp peak at the zero order has been obtained.     

Effect of annular obstruction on tight focusing of partially coherent radially polarized Vortex beam

Based on vectorial Debye theory, the effect of annular apodization of tightly focused partially coherent radially polarized vortex beams in the focal field of high NA lens is studied. The intensity distribution in the focal region is illustrated by numerical calculations. It is found that the focal depth of the generated focal segment strongly dependent on the source coherence length for unobstructed case and the presence of annular aperture reduces the variation of focal depth with source coherence length.     

The focus of light – theoretical calculation and experimental tomographic reconstruction

We present numerical calculations on the field distribution in the focus of an optical system with high numerical aperture. The diffraction integrals which are based on the Debye approximation are derived and evaluated for a radially polarized input field with a doughnut-shaped intensity distribution. It is shown that this mode focusses down to a spot size significantly smaller as compared to the case of linear polarization. An experimental setup to measure the three-dimensional intensity distribution in the focal region is presented, which is based on the knife-edge method and on tomographic reconstruction. Received: 14 July 2000 / Published online: 30 November 2000     

实现光束变换的连续位相衍射光学器件的研制

本文利用基于模拟退火法和爬山法相结合的混合优化算法,实现光束变换的连续位相衍射光学器件的设计。通过灰阶掩膜板及离子刻蚀工艺,研制了 Φ１００ｍ ｍ 的连续位相衍射光学器件。通过多级衰减片及ＣＣＤ 实现了焦斑光强分布测量。测量结果表明：边缘陡峭、旁瓣小、中心主瓣具有一定均匀性,且没有中心零级锐脉冲的焦斑光强分布     

Intensity distribution around the focal regions of real axicons

We present a theoretical and experimental study of the intensity distribution of a laser beam, after its propagation through a real axicon. We show that, while an ideal axicon generates Bessel-like radial intensity profile and smooth on-axis intensity around the focal region, in practice, the bluntness of the tip of the axicon causes significant deviations from these profiles. In particular, strong oscillations occur on the on-axis intensity. The input beam size also plays a strong role; for small beams the axicon acts more like a conventional lens, while for the large ones, it exhibits two focal regions. We also propose scheme for apodization. In all cases, the experiments match closely with the calculations. Our results show that axicons cannot be assumed to always generate smooth on-axis intensities and the structures coming from the real profiles should be taken into account for most applications.     

The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration

We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and w_r of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.     

圆锥透镜对球面入射光的聚焦衍射特性

首次导出了圆锥透镜对球面入射波的聚焦衍射计算公式,分析了其轴上能量分布与横向场能量分布特性. 数值计算结果表明,选择合适的球面入射波可以扩展焦深,改善光强分布,同时保证横向场能量分布要求. 对于半径20 mm,锥角θ=1×10^－2的圆锥透镜,采用曲率半径为1200~1400 mm的球面入射波,可扩展焦深200 mm到120 mm,光强的均匀性有明显改善,横向场能量分布形状改变量不超过15 μm,完全达到应用要求.     

Extending the depth of focus with high NA lens axicon

Based on vectorial Debye theory, tight focusing of x-polarized beam with high NA lens axicon is studied. The high NA lens axicon utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distribution in the focal region is illustrated by numerical calculations. We show that the high NA lens axicon system can generates a sub wavelength beam (0.826λ) with depth of focus around 10λ.     

Effects of low order atmosphere-turbulence aberrations on the vortex carrying Gaussian beam

The normalized intensity distributions at the focal plane of a vortex carrying Gaussian beam propagating in weak/middle turbulent atmosphere channel with z-tilt aberration, defocus aberration, astigmatism aberration or total turbulent aberration are discussed by numerical calculation. Our results show that the effect of z-tilt aberration on the intensity distribution of optical vortex beam is main effect of total turbulent aberration. In weak turbulent region, the effects of defocus and astigmatism aberration on the intensity distribution of a vortex carrying Gaussian beam can be ignored. In middle turbulent region, the effect of z-tilt aberration is still the most significant, but the effects of defocus and astigmatism aberrations, specially the effect of astigmatism on the center dark core of the intensity distribution at focal plane, can no longer be disregarded. Our results also show that for three low order aberrations, the beam with values of the topological charge, the beam have larger beam-radius and undergo smaller effects of z-tilt turbulent aberration on the doughnut distribution. For defocus aberration, the radius of the center dull of beam intensity increases with the values of topological charges increasing. And for astigmatism aberration, the beam with odd number topological charges, the center dull speck of beam intensity becomes to the bright speck. But for even number topological charges, the center dull speck of beam intensity maintains the dull one.     

Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams

By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities.     

Optical vortices in focal regions

Optical vortices in focal regions are studied using the Debye approximation. We discuss how scalar vortices give rise to different intensity structures in the focal region for a certain class of apertures. Vortices in cylindrical symmetric polarization distributions form new complex structures in the focal region, and in some cases the intensity is no longer zero on the optical axis. In particular, we find that for an azimuthal polarization distribution the local circulation deviates from that of the vortex impinging on the lens. On the other hand, upon using a radially polarized field distribution combined with an annular aperture, only the electric-field component along the optical axis remains, and the field structure is the same as in the scalar case.     

Surface plasmon polariton-based optical beam profiler

We describe a surface plasmon polariton- (SPP-) based device for measuring the intensity distribution of strongly focused light beams. A gold thin film configured as a sharp step is positioned in the focal region of a light beam, converting light into SPPs. The SPPs emit directional leakage radiation into the glass substrate beneath the thin film. The intensity of the leakage radiation is proportional to the intensity of the incident local light at the position of the step, allowing us to reconstruct the optical field profile by scanning the thin film's edge through the focal region.     

Focal switching of partially coherent modified Bessel–Gaussian beams passing through an astigmatic lens with circular aperture

The axial intensity distribution of partially coherent modified Bessel–Gaussian (PCMBG) beams passing through an astigmatic lens with circular aperture is derived on the basis of Collins formula. The influences of truncation parameter δ and astigmatic coefficient α on the axial intensity distribution are presented. The research shows that the axial intensity changes with the variation of α, and twice focal switches have been found. Furthermore, the physical interpretation of the twice focal switches is given and is also illustrated by numerical calculations. It has been revealed that the existence of astigmatism and the effect of the truncation parameter are the two main reasons for the twice focal switches of PCMBG beams passing through an astigmatic lens with circular aperture.     

High-frequency field intensity along focal point of a long metallic parabolic reflector coated by a magnetized plasma layer using oblique incidence

Theoretical analysis of the electromagnetic field distribution in the focal region of a long metallic parabolic reflector that has its surface covered with a magnetized plasma layer is derived. The incident wave is considered to be with a general oblique incidence for both parallel and perpendicular polarizations. The electromagnetic field intensity expressions along the focal region are obtained accurately using Maslov's method. The effects of plasma thickness on the reflected and transmitted field distributions are investigated. The effects of other physical parameters such as the angle of incidence and the plasma and cyclotron frequencies on the transmitted fieldintensity distribution along the focal region are also studied. The results obtained by Maslov's method and Kirchhoff's approximation are found to be in a good agreement.