Vector Hermite-Gaussian correlated Schell-model beam

Hollow rectangular multi-Gaussian Schell-model source

We introduced a new class of a partially coherent source that can generate a field with a hollow rectangular profile, named the hollow rectangular multi-Gaussian Schell-mode source. The dependence of distribution of far-zone spectral density on the properties of the proposed source was analyzed. The results show that one can control the distribution properties of the far-zone intensity profile, including the thickness of the hollow edge, the shape of the hollow, the size of the hollow, and the orientation of the hollow, by adjusting the corresponding structural parameters of the source.

Statistical properties of an electromagnetic Gaussian Schell-model beam propagating in uniaxial crystals along the optical axis

Within the angular-spectrum representation, we study the partially coherent beam propagating in uniaxial crystals along the optical axis. By a method of vortex expansion, we derive the analytical solution for the cross-spectral density (CSD) function of an electromagnetic Gaussian Schell-model (EGSM) beam. We demonstrate that the analytical expression of CSD function can be written into a quasi-coherent-mode representation, whose basis vectors are constructed by the elegant Laguerre-Gaussian (eLG) functions. Several limits of the analytical solution are examined and good agreements with previous theories are obtained. Moreover, we calculate the energy density and degree of polarization (DOP) of the EGSM beam, from which the effects of coherent degree on the propagating properties are revealed. It is found that the energy conversion between circularly polarized components becomes rapid when the degree of coherence is decreasing. For all degree of coherence, the energy density and DOP exhibit a similar saturated behavior in the far field.

Vector partially coherent beams with prescribed non-uniform correlation structure

We introduce a general strategy for the synthesis of vector partially coherent beams (PCBs) with a prescribed non-uniform correlation structure. With it, we characterize a specific family of such beams, termed radially polarized Hermite non-uniformly correlated (RPHNUC) beams. These beams possess unusual propagation properties compared to vector PCBs with uniform correlation structure; for example, they maintain their dark hollow core and evolve multi-ring structures. These beams may prove useful in free-space optical communications, optical trapping, and polarization-sensitive imaging.

Partially Coherent Flat-Topped Beam Generated by an Axicon

The intensity distribution of a partially coherent beam with a nonconventional correlation function, named the multi-Gaussian Schell-model (MGSM) beam, focused by an axicon was investigated in detail. Our numerical results showed that an optical needle with a flat-topped spatial profile and long focal depth was formed and that we can modulate the focal shift and focal depth of the optical needle by varying the width of the degree of coherence (DOC) and the parameters of the correlation function. The adjustable optical needle can be applied for electron acceleration, particle trapping, fiber coupling and percussion drilling.

Polychromatic wave-optics models for image-plane speckle. 1. Well-resolved objects

Polychromatic laser light can reduce speckle noise in wavefront-sensing and imaging applications that use direct-detection schemes. To help quantify the achievable reduction in speckle, this paper investigates the accuracy and numerical efficiency of three separate wave-optics methods. Each method simulates the active illumination of extended objects with polychromatic laser light. In turn, this paper uses the Monte Carlo method, the depth-slicing method, and the spectral-slicing method, respectively, to simulate the laser-object interaction. The limitations and sampling requirements of all three methods are discussed. Further, the numerical efficiencies of the methods are compared over a range of conditions. The Monte Carlo method is found to be the most efficient, while spectral slicing is more efficient than depth slicing for well-resolved objects. Finally, Hu's theory is used to quantify method accuracy when possible (i.e., for well-resolved objects). In general, the theory compares favorably to the simulation methods.

Polychromatic wave-optics models for image-plane speckle. 2. Unresolved objects

Polychromatic laser light can reduce speckle noise in many wavefront-sensing and imaging applications. To help quantify the achievable reduction in speckle noise, this study investigates the accuracy of three polychromatic wave-optics models under the specific conditions of an unresolved object. Because existing theory assumes a well-resolved object, laboratory experiments are used to evaluate model accuracy. The three models use Monte-Carlo averaging, depth slicing, and spectral slicing, respectively, to simulate the laser-object interaction. The experiments involve spoiling the temporal coherence of laser light via a fiber-based, electro-optic modulator. After the light scatters off of the rough object, speckle statistics are measured. The Monte-Carlo method is found to be highly inaccurate, while depth-slicing error peaks at 7.8% but is generally much lower in comparison. The spectral-slicing method is the most accurate, always producing results within the error bounds of the experiment.

Complex Gaussian representations of partially coherent beams with nonconventional degrees of coherence

We adopt the recently introduced complex Gaussian function to expand the partially coherent beams with nonconventional degrees of coherence, and derive detailed representations of Hermite-Gaussian correlated Schell-model beam, elliptical Laguerre-Gaussian correlated Schell-model beam, and multi-Gaussian correlated Schell-model beam. Complex Gaussian representation of a partially coherent beam provides a convenient way for treating its propagation. As an application example, we explore the self-splitting properties of a Hermite-Gaussian correlated Schell-model beam propagating in a uniaxial crystal with the help of the complex Gaussian representation, and it is found that the uniaxial crystal can be used to control the splitting properties.

Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements

Perfect vortex beams are the orbital angular momentum (OAM)-carrying beams with fixed annular intensities, which provide a better source of OAM than traditional Laguerre-Gaussian beams. However, ordinary schemes to obtain the perfect vortex beams are usually bulky and unstable. We demonstrate here a novel generation scheme by designing planar Pancharatnam-Berry (PB) phase elements to replace all the elements required. Different from the conventional approaches based on reflective or refractive elements, PB phase elements can dramatically reduce the occupying volume of system. Moreover, the PB phase element scheme is easily developed to produce the perfect vector beams. Therefore, our scheme may provide prominent vortex and vector sources for integrated optical communication and micromanipulation systems.