Spectral switches of partially coherent light focused by a filter-lens system with chromatic aberration

It is shown that when partially coherent polychromatic light is focused by a filter-lens system with chromatic aberration, a spectral shift exists in the focused field, and a spectral switch that is defined as a sharp transition of the spectral shift also takes place at some positions of the focused field. The influence of the chromatic aberration of the lens, the coherence of the partially coherent light in the filter (a circular aperture), the radius of the aperture, and the spectral width of the partially coherent light in the aperture on the spectral shift and the spectral switch are investigated in detail. The numerical results show that these parameters affect the spectral shift and the spectral switch significantly. Potential applications of the spectral shift and the spectral switch of the partially coherent light are discussed.     

Spatial correlation properties of focused partially coherent light

We investigate the spatial coherence properties in the focal region of a converging, spatially partially coherent wave field. In particular, we find that, depending on the effective coherence length of the field in the aperture, the longitudinal and transverse coherence lengths in the focal region can be either larger or smaller than the corresponding width of the intensity distribution. Also, the correlation function is shown to exhibit phase singularities.     

Spectral changes and spectral switches of partially coherent beams focused by an aperture lens

Starting from the propagation law of partially coherent polychromatic light in the space-frequency domain, detailed numerical results and physical analysis are given to elucidate spectral changes and spectral switches at the geometrical focal plane of Gaussian Schell-model beams focused by an aperture lens. It is found that, in contrast to the aperture-induced spectral anomalies of spatially fully coherent polychromatic light, for partially coherent polychromatic light aperture diffraction plays an important role in spectral switching, but the truncation parameter, spectral correlation, and bandwidth all affect its spectral behavior.     

Changes of intensity distribution of a tightly focused plane-wave pulse induced by lens dispersion

The tightly focusing properties of a linearly polarized plane-wave pulse through a high numerical aperture (NA) lens with dispersion are formulated. The effects of lens dispersion on the tightly focused intensity distribution in the focal region are studied in detail. It is found that, because of the lens dispersion, the intensity of the side lobe of the focused light spot strengthens in the transverse direction and the size of the main lobe of the focused light spot increases in the longitudinal direction as the pulse duration decreases. In addition, we compare the effects of dispersion of lens made by different types of glass on tightly focusing properties of a pulse beam. The results will be helpful to choose suitable high NA objective lens in experiment.     

Spherical gradient-index polymer lens with low spherical aberration

A sphere lens with a spherical gradient index (GRIN) was prepared by the modified suspension polymerization technique. GRIN spheres with quadratic- and linear-index distributions were obtained by two different methods to confirm the effect of the GRIN profile on the focusing property of the sphere lens. It was confirmed in both theory and experiment that the spherical aberration of such GRIN spheres was remarkably decreased compared with that of a homogeneous sphere.     

Generalized Gouy phase for focused partially coherent light and its implications for interferometry

The Gouy phase, sometimes called the phase anomaly, is the remarkable effect that in the region of focus a converging wave field undergoes a rapid phase change by an amount of π, compared to the phase of a plane wave of the same frequency. This phenomenon plays a crucial role in any application where fields are focused, such as optical coherence tomography, mode selection in laser resonators, and interference microscopy. However, when the field is spatially partially coherent, as is often the case, its phase is a random quantity. When such a field is focused, the Gouy phase is therefore undefined. The correlation properties of partially coherent fields are described by their so-called spectral degree of coherence. We demonstrate that this coherence function does exhibit a generalized Gouy phase. Its precise behavior in the focal region depends on the transverse coherence length. We show that this effect influences the fringe spacing in interference experiments in a nontrivial manner.     

平顶多高斯光束通过球差透镜的聚焦特性

利用广义惠更斯-菲涅耳衍射积分公式,研究了平顶多高斯光束通过球差透镜的聚焦特性。推导出轴上光强分布的表达式,并对轴上光强进行大量的数值计算及分析。研究结果表明,当平顶多高斯光束的阶数N一定时,透镜的球差将在很大程度上影响光束的聚焦特性;当透镜的球差一定时,N值的改变将影响轴上最佳聚焦点的位置;当无球差时,轴上最佳聚焦点并不在几何焦点处,轴上最佳聚焦点位置随着N值增加向几何焦点靠近,例如当阶数N由0增大为1时,则归一化最佳聚焦点由0.91增大到0.98。     

多束部分相干光通过强湍流对光强闪烁的影响

在Rytov方差的基础上,利用Andrews的唯像闪烁模型,推导出部分相干光通过强大气湍流后其对数光强起伏方差的公式,并用此公式对部分相干光通过强湍流后给光强闪烁造成的影响进行了仿真。其结果表明,当光源的相干性变差,即变为部分相干光后,对数光强起伏方差变小;当采用多束部分相干光时,接收面上光强起伏方差得到明显改善,而且光束越多,改善越明显。     

Shannon entropy of partially polarized and partially coherent light with Gaussian fluctuations

We propose to analyze Shannon entropy properties of partially coherent and partially polarized light with Gaussian probability distributions. It is shown that the Shannon entropy is a sum of simple functions of the intensity, of the degrees of polarization, and of the intrinsic degrees of coherence that have been recently introduced. This analysis clearly demonstrates the contribution of partial polarization and of partial coherence to the characterization of disorder of the light provided by the Shannon entropy, which is a standard measure of randomness. We illustrate these results on two simple examples.     

Optical superresolution of focused partially spatially coherent laser beams

We report design theories of a diffractive superresolution element (DSE) to implement optical superresolution of focused partially spatially coherent laser beams. The design problem of the DSE can be transformed into a problem of linear programming to obtain a globally optimal solution. By using the design theories, some fundamental limits of optical superresolution of focused partially spatially coherent laser beams are proposed, and several design examples are provided. As expected, both the fundamental limits and the design examples show that worse spatial coherence will cause worse superresolution performance. The design theories provide a design approach with partially coherent beams and may be useful for other design problems under partially coherent illumination.     

Spatial correlation properties of focused partially coherent vortex beams

The spatial correlation properties in the geometrical focal region of a converging, partially coherent vortex wave field are analyzed. Expressions are derived for a pair of points on the axis of symmetry and for a pair of points in the focal plane. It is found that the longitudinal and transverse coherence lengths in the focal region change with the variation of the topological charge and the normalized coherence length of the vortex field. In addition, the degree of coherence is shown to possess phase singularities.     

Three-dimensional imaging by partially coherent light under nonparaxial condition

In this paper, we present the theory of three-dimensional (3D) imaging using partially coherent light under the nonparaxial condition. Using the linear system approach, we derive the image intensity in terms of the 3D nonparaxial transmission cross coefficient (TCC) and the transmission function defined in this paper. We present that the 3D TCC can be calculated by multiple applications of the 3D fast Fourier transform instead of the six-dimensional integral in the original formula. Using the simplified formula, we simulate phase contrast and Nomarski differential interference contrast (DIC) imaging of a transparent 3D object. Within our knowledge, the 3D model for the DIC based on the 3D nonparaxial TCC is the most rigorous approach that has been suggested. It demonstrates clearly the optical sectioning effect of DIC.     

Focal shift of a focused partially coherent Laguerre-Gaussian beam of all orders

Abstract

We explore the focusing properties of a partially coherent Laguerre–Gaussian (LG) beam of all orders, particularly the focal shift (i.e. the shift of the actual focal plane away from the geometrical focal plane). We derive the analytical expressions for the average intensity and the effective beam width of a focused partially coherent LG beam, and we adopt the minimum effective beam width instead of the conventional maximum on-axis intensity to determine the actual focal plane. It is found that the focused beam shape, minimum effective beam width and the focal shift of a focused partially coherent LG beam are determined by its initial coherence width, radial mode order and azimuthal mode order (i.e. topological charge) together. Our results may be useful for optical trapping and micro-fabrication, where precise focal position and prescribed beam shape are required.     

Correlated imaging with partially coherent light for remote sensing

Based on the extended Huygens–Fresnel integral and the theory of coherence of light field, we have investigated the correlated imaging by using the transverse normalized second-order intensity fluctuation correlation function with partially coherent light radiation. The imaging for a reflected object with relative long distance is determined by the feature of speckle-to-speckle correlation. By using the correlation function, we study the effects of imaging distance, the sizes of object lens and reference lens, the source’s transverse coherent width and its transverse size on the quality of correlated imaging. Numerical results show that the parameters of imaging system and the properties of partially coherent light source have significant influences on the imaging resolution and visibility. For an object lens with large enough diameter, the resolution is determined by the transverse coherent width of light source. On the contrary, it depends on the aperture of object lens. The magnification of the system depends only on the propagation distance. This speckle-to-speckle correlated imaging with unbalanced arms have potential applications in remote sensing due to its unique features.     

Optical trapping Rayleigh dielectric particles with focused partially coherent dark hollow beams

The focusing properties of coherent and partially coherent dark hollow beams (DHBs) through a paraxial ABCD optical system are theoretically investigated. It is found that the evolution behavior of the intensity distribution of focused partially coherent DHBs is closely related to their spatial coherence. The radiation forces (RFs) of focused coherent and partially coherent DHBs acting on a Rayleigh dielectric particle are also theoretically investigated. Numerical results show that the coherent and partially coherent DHBs can be focused into a tight focal spot, which can be used to stably trap a Rayleigh dielectric particle with high refractive index at the focus point. The influences of different beam parameters, including the spatial coherence, beam waist width, beam order, and hollow parameter of partially coherent DHBs, on the RFs and the trap stiffness are analyzed in detail. Finally, the stability conditions for effective trapping particles are also discussed.