3D Optical Field Research Articles

The invariance and distortion of vectorial light across a real-world free space link

Vectorial structured light, where the polarization is inhomogeneously distributed in space, has found a myriad of applications in both 2D and 3D optical fields. Here, we present an experimental study of the invariance and distortion of vectorial light through a real-world medium of atmospheric turbulence. We show that the amplitude and polarization structure are both severely distorted by the turbulent medium, yet the non-separability of these two degrees of freedom remains invariant. We monitor this invariance under a range of beam types and atmospheric conditions, over extended time periods, revealing the unitary nature of atmospheric turbulence in our experiment. Our results provide conclusive evidence that invariance and distortion are not mutually exclusive and that the degree of classical entanglement remains unaltered through such channels, and will be of interest to the large community interested in classical and quantum communication in free space.

Influence of Off-Axis Noncanonical Vortex on the Dynamics of Energy Flux

In this article, we analyze the impact of the off-axis noncanonical vortex on the dynamics of 3D energy flux. The results reveal that the properties of energy flux are significantly influenced by the anisotropy parameter σc of the off-axis noncanonical vortex. It is demonstrated that by adjusting the anisotropy parameter, we can control the transverse energy flux, from the position of the transverse energy tornado and the distribution of the transverse energy strength to the rotation direction of the transverse energy flux as the beam propagates. The interesting phenomenon, the reversed energy flux, is also closely related to the anisotropy parameter. The position and size of the reversed energy flux region, as well as the production of two energy tornadoes with opposite rotating directions, resembling a Chinese “Taiji” pattern, can be controlled by varying the anisotropy parameter. This result will potentially provide a new freedom for tailoring the 3D optical field and be useful in optical manipulation and processing.

X-type vortex and its effect on beam shaping

In this article we propose a new type of optical vortex, the X-type vortex. This vortex inherits and develops the conventional noncanonical vortex, i.e. it no longer has a constant phase gradient around the center, while the intensity keeps invariant azimuthally. The strongly focusing properties of the X-type vortex and its effect on the beam shaping in three-dimensional (3D) fields are analyzed. The interesting phenomena, which cannot be seen in canonical vortices, are observed, for instance the ‘switch effect’ which shows that the intensity pattern can switch from one transverse axis to another in the focal plane by controlling the phase gradient parameter. It is shown that by adjusting the phase gradient of this vortex, the focal field can have marvelous patterns, from the doughnut shape to the shapes with different lobes, and the beam along propagation direction will form a twisting shape in 3D space with controllable rotation direction and location. The physical mechanisms underlying the rule of the beam shaping are also discussed, which generally say that the phase gradient of the X-type vortex, the orbital angular momentum, the polarization and the ‘nongeneric’ characteristic contribute differently in shaping fields. This new type of vortex may supply a new freedom for tailoring 3D optical fields, and our work will pave a way for exploration of new vortices and their applications.

Matrix algorithm for 3D nonparaxial optical field modeling under arbitrary spatial coherence.

Nonparaxial modeling of optical field propagation at distances comparable to the wavelength and under arbitrary spatial coherence is crucial for micro- and nano-optics. Fourier and Fresnel transform-based algorithms are unable to simulate it accurately because of their paraxial approach. A nonparaxial matrix algorithm, supported by the theoretical model that characterizes the optical field and the setup configuration in terms of sets of real and virtual point emitters, is capable of simulating the 3D optical field distribution in the volume delimited by the input and the output planes placed at a very short distance from each other by using experimental data as entries. The algorithm outcomes are accurate predictions of the power spectrum of interference and diffraction experiments. Simulations of specific experimental situations, including speckle phenomena, illustrate the algorithm's capabilities.

Generation of Spiral Spin Density Vectors With A Circularly Polarized, Vortex Beam

Spiral spin density vectors refer to the spiral trajectory of the spin density vectors in three dimensional (3D) space, and similar to the polarization Mobius strip, polarization knots and photonic wheel, are also special polarization structures in 3D optical field and only exist in three dimensions. In this article, we propose a new way to generate the spiral spin density vectors with a long spiral range. This is realized by strongly focusing a circularly polarized beam with one off-axis vortex. In this field, the spiral interval of spin density vectors theoretically always exists on the propagation axis, and its position can be controlled by the beam size parameter $f/w_0$ . The polarization variation and the spiral spin density vectors are discussed analytically along the propagation direction. It is found that the spiral shape and spiral ‘speed’ can be adjusted by the off-axis distance of the vortex and the semi-aperture angle of the focusing system respectively. A special spiral behavior of the spin density vector at the geometrical focus is also observed in this focused field. The spiral spin density vectors supply a new rotational degree of freedom in 3D optical field and our finding may have applications in optical micro-manipulations.

Controlling three-dimensional optical fields via inverse Mie scattering.

Controlling the propagation of optical fields in three dimensions using arrays of discrete dielectric scatterers is an active area of research. These arrays can create optical elements with functionalities unrealizable in conventional optics. Here, we present an inverse design method based on the inverse Mie scattering problem for producing three-dimensional optical field patterns. Using this method, we demonstrate a device that focuses 1.55-μm light into a depth-variant discrete helical pattern. The reported device is fabricated using two-photon lithography and has a footprint of 144 μm by 144 μm, the largest of any inverse-designed photonic structure to date. This inverse design method constitutes an important step toward designer free-space optics, where unique optical elements are produced for user-specified functionalities.

Intensity and spin anisotropy of three-dimensional polarization states.

Anisotropy is a natural feature of polarization states, and only fully random three-dimensional (3D) states exhibit complete isotropy. In general, differences between the strengths of the electric field components along the three orthogonal directions give rise to intensity anisotropy. Moreover, polarization states involve an average spin whose inherent vectorial nature constitutes a source of spin anisotropy. In this work, appropriate descriptors are identified to characterize quantitatively the levels of intensity anisotropy and spin anisotropy of a general 3D polarization state, leading to a novel interpretation for the degree of polarimetric purity as a measure describing the overall polarimetric anisotropy of a 3D optical field. The mathematical representation, as well as the physical features of completely intensity-isotropic 3D polarization states with a maximum spin anisotropy, are also examined. The results provide new insights into the polarimetric field structure of random 3D electromagnetic light states.

Geometric representation of polarization for a general three-dimensional optical field

On the basis of previous work in this area, we propose a new geometric representation of polarization for a general three-dimensional (3D) optical field. This representation is based on the characteristic and eigenvalue decompositions of the 3 × 3 coherency matrix, which is appropriate for all 3D polarized optical fields, including totally polarized, partially polarized and totally un-polarized optical fields. Based on this representation method, the degree of polarization for an arbitrary 3D optical field can be characterized by a unique point located on a spatial equilateral triangle. Correspondingly, the 3D state of polarization can be illustrated by the 3D distribution maps of polarization ellipse quantitatively.

Degree of polarization in 3D optical fields generated from a partially polarized plane wave

We show that, for 3D random electromagnetic fields that are created by optical systems from a partially polarized plane wave, two different definitions of the 3D degree of polarization proposed in literature have a monotonic one-to-one correspondence, thus providing the same information about the field's polarization state. Examples of 3D fields obeying this result are the evanescent wave generated in total internal reflection, the tightly focused beam, and the far field scattered from an electric point dipole.

Fabrication of three-dimensional photonic crystals with the Talbot self-imaging effect

The authors experimentally demonstrate an approach to fabricating three-dimensional (3D) photonic crystals (PCs) by using the Talbot self-imaging effect. A two-dimensional (2D) chess-board grating is employed to generate a 3D optical field pattern based on the Talbot effect in polymer-dispersed liquid crystal (PDLC) materials for the PCs. Square and hexagonal shaped PCs with sub-micron scale are obtained and confirmed experimentally by optical microscopy, atomic force microscopy and optical diffraction patterns. It is shown that the method is feasible and convenient for 3D PCs fabrication.