Vector Diffraction Research Articles

Sub-60-nm isotropic 3D super-resolution microscopy through self-interference field excitation

Due to its unique optical sectioning capability, confocal laser scanning microscopy (CLSM) can provide highly sensitive, highly specific imaging of specimens in three dimensions and has been recognized as an indispensable tool for biological and medical studies. Nonetheless, the spatial resolution of CLSM is constrained by the diffraction nature, with λ/2 resolution laterally (xy) and 1.5λ resolution axially (z). To improve the imaging resolution beyond the diffraction limit as well as to achieve its isotropy, we present a strategy of mirror-assisted self-interference field excitation (SIEx) highly nonlinear microscopy. The imaging principle has been theoretically modeled and investigated in accordance with the Wolf vector diffraction theory. The experimental demonstration of isotropic three-dimensional SIEx nanoscopy, assisted with the ultrahigh-order optical nonlinearity of photon avalanching nanoparticles, was achieved utilizing a common laser-scanning microscope configuration, resulting in a lateral resolution of 54 nm (λ/15) and an axial resolution of 57 nm (λ/15) with one single beam from a low-power, continuous-wave, near-infrared laser (19kW⋅cm−2). We further extended the applicability of the SIEx scheme to biological imaging and demonstrated super-resolution imaging for immunolabeled actin filaments of BSC-1 cells with an isotropic full width at half maximum of ∼67nm (λ/13). Our facile SIEx methodology can, in principle, be seamlessly integrated with the existing and widely available laser-scanning fluorescence microscopes without adding any complexity, thereby enabling their capability of 3D isotropic super-resolution imaging.

An Efficient Hybrid Method for Calculating the Focal Field of a Cassegrain Antenna

The evaluation of the focal field of Cassegrain antennas is crucial for the design and optimization of the complex feeds in quasi-optical systems. However, employing traditional physical optics methods generates high computational complexity and is inefficient. An accurate and efficient calculation method of Cassegrain antennas’ focal fields that involves a range of incidence angles is proposed, which integrates ray tracing and vector diffraction integration (RT-VDI) theories. It can calculate the focal field in any given or predefined incident direction, not limited to the case of axial incidence. In addition, the use of the equivalent parabolic theory greatly simplifies the process of integral calculation. Moreover, ray tracing and integration operations are executed upon the calculation of the reflector to further improve efficiency. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

Generation of variable light fields by radially polarized chirped circular Airy vortex beams

Based on Richards-Wolf vector diffraction theory, the tight focusing properties of radially polarized chirped circular Airy vortex beams (RP-CCAVBs) are theoretically investigated using a high numerical aperture objective lens in the paper. The results shown that super-resolution scalable optical needles, dark channels, elliptical optical cages, and optical oscillations can be obtained by adjusting the scale factor, exponential attenuation coefficient, main ring radius, and topological charge of optical vortex in the incident RP-CCAVBs. The DOF of optical needle and dark channels is exponent dependent on scaling factor ω of RP-CCAVBs. And the position optical needle and dark channels can be moved by changing chirped parameter of RP-CCAVBs. The size of obtained optical cages can be adjusted by changing the radius of main rings in RP-CCAVBs. The intensity distribution of the obtained optical oscillations is intensely affected by parameter a and chirp parameter of RP-CCAVBs.

Generation of extremely strong accelerating electric field by focusing radially polarized THz pulses with a paraboloid ring

Efficient acceleration of electrically charged particles by focused electromagnetic pulses requires a strong accelerating electric field as well as a sufficiently large interaction region. Single-cycle terahertz pulses are promising candidates for such applications due to their advantageous wavelength and available peak electric field at the MV/cm level. We propose and characterize a focusing optics for a possible electron vacuum accelerator. This consists of a reflaxicon for beam shaping and a ring-like segment of an on-axis parabolic mirror for tight focusing of the radially polarized THz pulse in order to reach a strong accelerating electric field. The electric field distribution in the focal region was determined by the Stratton–Chu vector diffraction method. Semi-analytical and purely analytical formulae were also derived, simplifying the computation procedure. By focusing radially polarized single-cycle terahertz pulses with 3mJ pulse energy, calculations predict accelerating electric field component in the order of 100MV/cm, well suitable for particle acceleration.

Numerical Simulation and Experimental Investigation of Single-Point Picosecond Laser Ablation inside K9 Glass

K9 glass is a classical transparent material widely used in high-power optical systems due to its high-temperature resistance. However, the precision machining of K9 glass is difficult. The laser processing method, characterized by being non-contact, having a small heat-affected zone, and having high processing precision, is commonly employed for processing intricate structures. In this study, the vector diffraction model is employed to simulate the internal electric field inside the material when focused by objective lenses with varying numerical apertures. Furthermore, the temperature field is simulated. The simulation considered the nonlinear absorption of the material, the stretching of the focal dot due to spherical aberration, and the energy loss of the laser during the focusing process. The experiment indicated that the ablated area consists of numerous small, ablated dots and that multiple ablated areas emerged under an NA of 0.6. This study can provide valuable references for the research of the interaction between lasers and glass materials.

Unlocking ultra-high holographic information capacity through nonorthogonal polarization multiplexing

Contemporary studies in polarization multiplexing are hindered by the intrinsic orthogonality constraints of polarization states, which restrict the scope of multiplexing channels and their practical applications. This research transcends these barriers by introducing an innovative nonorthogonal polarization-basis multiplexing approach. Utilizing spatially varied eigen-polarization states within metaatoms, we successfully reconstruct globally nonorthogonal channels that exhibit minimal crosstalk. This method not only facilitates the generation of free-vector holograms, achieving complete degrees-of-freedom in three nonorthogonal channels with ultra-low energy leakage, but it also significantly enhances the dimensions of the Jones matrix, expanding it to a groundbreaking 10 × 10 scale. The fusion of a controllable eigen-polarization engineering mechanism with a vectorial diffraction neural network culminates in the experimental creation of 55 intricate holographic patterns across these expanded channels. This advancement represents a profound shift in the field of polarization multiplexing, unlocking opportunities in advanced holography and quantum encryption, among other applications.

Modeling the focusing of a radially polarized laser beam with an initially flat-top intensity profile

Radially polarized light beams present very interesting and useful behavior for creating small intensity spots when tightly focused, and manipulating nanostructures or charged particles via their longitudinal field. The modeling of the propagation of such vector beams, however, is almost always done using the lowest-order fundamental radially polarized beam or a single higher-order mode due to the complexity of vector diffraction theory. We show how a flat-top radially polarized beam, relevant for high-power lasers, can be modeled analytically using a sum of higher-order beams, describe a number of interesting qualities of such beams, and compare to numerically solved integral descriptions.

Angular dispersion and diffraction imaging analysis in a light wave oblique incident two-dimensional crossed grating

Based on the vector diffraction theory, the angular dispersion and diffraction imaging are analyzed in parallel light oblique incident two-dimensional crossed gratings. The results show that the angular dispersion presents a kind of increase-decrease-increase oscillatory change, and the maximum value of diffractive polar angle dispersion and total dispersion present an abrupt point. The angular dispersion is limited by the light wave incidence angle and two-dimensional gratings crossed angle. In addition, some obvious pincushion distortion has been formed in some cases. The angular dispersion increases with the increase of grating crossed angle in the permissible range, leading to enhancement of the diffraction imaging distortion. The results imply that there is an inherent relationship between the angular dispersion and the diffraction imaging in parallel light oblique incident crossed gratings.

Vortex Circular Dichroism: An experimental technique to assess the scalar/vectorial regime of diffraction.

In classical electrodynamics, light-matter interactions are modelled using Maxwell equations. The solution of Maxwell equations, which is typically given by means of the electric and magnetic field, is vectorial in nature. Yet it is well known that light-matter interactions can be approximately described in a scalar (polarization independent) way for many optical applications. While the accuracy of the scalar approximation can be theoretically computed, to the best of our knowledge, it has never been determined experimentally. Here, we introduce Vortex Circular Dichroism ( VCD), an optical measurement that has the required features to assess the vectoriality of diffraction. VCD is measured as the differential transmission (or absorption) of left and right circularly polarized vortex beams. We test the VCD measurement with two different systems: i) an experimental set of single circular nano-apertures drilled in a gold film with diameters ranging from 150 to 1950 nm; and ii) a theoretical set of golden spheres with the same diameters as the nano-apertures. We observe that in both systems, VCD > 0 for smaller diameters, VCD ≲ 0 for intermediate values and VCD ≈ 0 for larger values of the diameter. Furthermore, the simulations show that a diffraction process characterized by a VCD ≈ 0 ( VCD ≠ 0) is polarization-independent (polarization-dependent). As a result, we relate VCD ≠ 0 to a vectorial diffraction, and VCD ≈ 0 to a scalar one. Overall, our results show compelling evidence that it is possible to experimentally assess the scalar/vectorial regime of a diffraction process, and that the VCD technique possesses the required features to measure the vectoriality of diffraction processes involving plasmonic cylindrically symmetric structures.

The numerical analysis of low diffraction efficiency phenomenon at the blaze wavelength for echelle gratings

In this paper, we explain and unify the low diffraction efficiency behavior of echelle gratings at blaze wavelengths under Littrow mount in terms of the metal refractive index (RI). The similarity in the diffraction efficiency (DE) behavior (e.g., efficiency decline and valley-like diffraction curves for low-efficiency orders) of echelle gratings with different metals at TM polarization points the research line of sight to the RIs. Further, the numerical calculations based on the rigorous vector diffraction theory show that the efficiency behavior of the echelle grating at TM polarization is extremely sensitive to the imaginary part of the RI. This is because there is a series of low light-collecting ability (LCA) regions as the imaginary part of the RI changes in the echelle grating, resulting in several disturbed DE zones. In addition, the increase in groove depth improves the LCA at both polarizations, which moves away from the low LCA region at the TM polarization. This leads to low polarization sensitivity and higher DE for echelle gratings, further revealing the essence of the efficiency improvement by increasing the groove depth. From the RI to the LCA, these results will give new concepts to designing and fabricating broadband high-efficiency echelle gratings.

Optical Force Effects of Rayleigh Particles by Cylindrical Vector Beams.

High-order cylindrical vector beams possess flexible spatial polarization and exhibit new effects and phenomena that can expand the functionality and enhance the capability of optical systems. However, building a general analytical model for highly focused beams with different polarization orders remains a challenge. Here, we elaborately develop the vector theory of high-order cylindrical vector beams in a high numerical aperture focusing system and achieve the vectorial diffraction integrals for describing the tight focusing field with the space-variant distribution of polarization orders within the framework of Richards-Wolf diffraction theory. The analytical formulae include the exact three Cartesian components of electric and magnetic distributions in the tightly focused region. Additionally, utilizing the analytical formulae, we can achieve the gradient force, scattering force, and curl-spin force exerted on Rayleigh particles trapped by high-order cylindrical vector beams. These results are crucial for improving the design and engineering of the tightly focused field by modulating the polarization orders of high-order cylindrical vector beams, particularly for applications such as optical tweezers and optical manipulation. This theoretical analysis also extends to the calculation of complicated optical vortex vector fields and the design of diffractive optical elements with high diffraction efficiency and resolution.

Propagation of focused scalar and vector vortex beams in anisotropic media: A semianalytical approach

In the field of structured light, the study of optical vortices and their vectorial extension—vectorial vortex beams—has garnered substantial interest due to their unique phase and polarization properties, which make them appealing for many potential applications. Combining the advantages of vortex beams and anisotropic materials, unique possibilities for electromagnetic field tailoring and manipulation can be achieved in nonlinear optics, quantum and topological photonics. These applications call for a comprehensive modeling framework that accounts for properties of both anisotropic materials and vector vortex beams. In this paper, we describe a semianalytical model that extends the vectorial diffraction theory to the case of focused vortex beams propagating through a uniaxial slab, considering both the cases of scalar and vectorial vortices in the common framework of a Laguerre-Gaussian mode basis. The model aims to provide a comprehensive description of the methodology, enabling the implementation of complex beam transmission through, reflection from, and propagation in uniaxial anisotropic materials for specific applications. As a demonstration of its versatility, we apply the developed approach to describe propagation of high-order vortex beams in uniaxial materials with various dispersion characteristics, exploring the elliptic, hyperbolic and epsilon-near-zero regimes. We show how variations of the medium anisotropy modify the beam structure due to the vectorial nature of their interaction, which results from the different permittivities of the medium for transverse and longitudinal field components. The applicability of the approach can be extended to artificially structured media if they can be described by effective medium parameters. The developed formalism will be useful for modeling interaction of complex beams with uniaxial materials, allowing a common framework for a large variety of situations, which can also be extended beyond the electromagnetic waves. Published by the American Physical Society 2024

Deep‐subwavelength characteristics of focused vector double‐petal linear edge dislocation beams

AbstractRecently, vector beams with special intensity and phase distribution have received much attention due to their unique properties. In this paper, we construct the double‐petal linear edge dislocation (DPLED) beams based on Gaussian vortex beams. The distribution of intensity, polarization, and spin angular momentum (SAM) of the DPLED beams is analyzed in tightly focused based on the Richards‐Wolf vector diffraction theory. The significant difference is occurred in light field, polarization SAM, and polarization distributions before and after focusing of DPLED beams. It's of certain importance for expanding the application of vector beams in optical control, optical imaging, and other fields.

Generation of a super-oscillation magnetization hotspot by reversing the electric dipole array radiation

We propose an all-optical approach to realize a super-oscillatory longitudinal magnetization hotspot with about 0.1λ in a 4π focusing system using time-reversed dipole radiation and vector diffraction theory calculations. Such a magnetization behavior is induced by focal fields of opposite polarities in the central and peripheral regions based on the inverse Faraday effect. By regulating the destructive interference in the central and peripheral regions of the focal field, a super-oscillating magnetization field is generated. Moreover, two important parameters affect the size of the magnetization field are also explored. Superoscillating magnetization hotspots in the focal region can be achieved by either increasing δ (the intensity of electric field) or reducing dn (the distance of electric field). The achieved ultrasmall magnetization spot shows great prospects in high-density magnetic recording, magnetic resonance imaging, and magnetic sensors.

S-polarized light-sheets improve resolution and light-efficiency in oblique plane microscopy

Oblique plane microscopy (OPM) offers 3D optically sectioned imaging with high spatial- and temporal-resolution while enabling conventional sample mounting. The technique uses a concatenation of three microscopes, two for remote focusing and a tilted tertiary microscope, often including an immersion objective, to image an oblique sample plane. This design induces Fresnel reflections and a reduced effective aperture, thus impacting the resolution and light efficiency of the system. Using vectorial diffraction simulations, the system performance was characterized based on illumination angle and polarization, signal to noise ratio, and refractive index of the tertiary objective immersion. We show that for samples with high fluorescent anisotropy, s-polarized light-sheets yield higher average resolution for all system configurations, as well as higher light-efficiency. We also provide a tool for performance characterization of arbitrary light-sheet imaging systems.

Vector diffraction based on 3D Huygens-Fresnel principle and vector decomposition in Cartesian coordinate

We proposed vector diffraction equations based on 3D Huygens-Fresnel principle and vector decomposition in Cartesian coordinate. Our expression should more accurate than classical Richards-Wolf diffraction, because the deduction of Richards-Wolf diffraction used a number of approximation, while our expression is based on two fundamental physical principles: vector decomposition and Huygens-Fresnel principle. Our expressions mathematical strictly satisfy conservation of energy, while Richards-Wolf’s method is based on the geometrical law of conservation of energy and RCWA(Rigorous Coupled Wave Analysis) is also an approximation. The simulated results of our vector diffraction equations with different NA (numerical aperture) are almost the same as Richards-Wolf diffraction results. Traditional Richards-Wolf vector diffraction equations, which are based on angular spectrum of plane wave, have no clear geometrical meaning, while our vector diffraction equations here have clear geometrical meaning. Our approach of vector diffraction to scalar diffraction is much simpler than Richards-Wolf’s approach. The generation of x/y/z components and their properties in the image plane can be investigated clearly by vector decomposition and synthesis. Their intensity ratios can be explained using paraxial approximation very well. The integral region of exit pupil could be reduced because of the symmetric property of the light vector decomposition and synthesis, thus our expressions have advantages on numerical simulation. Our analysis also indicate that light must ‘polarize’ in other extra dimensions and photon spin is a ‘polarize/resonate’ state in extra dimensions. Also, there is a potential convenient ability to study vector optical transfer function (OTF) analytically in Cartesian coordinate.

Tightly focused optical skyrmions and merons formed by electric-field vectors with prescribed characteristics

Abstract Optical skyrmions, which are topological quasi-particles with nontrivial electromagnetic textures, have garnered escalating research interest recently for their potential in diverse applications. In this paper, we present a method for generating tightly focused optical skyrmion and meron topologies formed by electric-field vectors under 4π-focusing system, where both the topology types (including Néel-, Bloch-, intermediate- and anti-skyrmion/meron) and the normal direction of the two-dimensional topology projection plane can be tailored at will. By utilizing time-reversal techniques, we analytically derive the radiation pattern of a multiple concentric-ring array of dipoles (MCAD) to obtain the required illumination fields on the pupil planes of the two high numerical aperture lenses. The Deby vector diffraction integral theory is employed to calculate the corresponding tightly focused field, and their topology characteristics are quantitatively evaluated by the electric-field vector distribution. The results demonstrate that arbitrary electric-field based skyrmion and meron can be conveniently generated by adjusting the oscillation direction of each dipole in the MCAD and the normal direction of the dipole array. The generated optical topologies with fully controllable degrees of freedom provide potential applications in optical information processing, transmission, and storage.

Displacement measurement error of grating interferometer based on vector diffraction theory

Displacement measurement error of grating interferometer based on vector diffraction theory

Research on focusing of a triangle-exponential function modulation spiral polarization cosh-Gaussian vortex beam

The focus pattern of a triangle-exponential function modulation spiral polarized hyperbolic-cosine-Gaussian (cosh-Gaussian) vortex beam is examined according to the vector diffraction theory and the focus intensity with different parameters is disputed. By adjusting the polarization parameter C, the number of the focusing peaks can be changed: Specifically, as the absolute value of the polarization parameter C augments, so does the number of the focus peaks. When the beam parameter β is modified, the focus pattern is compressed and stretched in both the axial and radial directions, respectively, which helps to precisely adjust the shape of the focus pattern in the focus region. Meanwhile, the trigonometric modulation parameter l can change the axial component of the focus region. With a change in the trigonometric modulation parameter l, the focus pattern finally evolves into the light-like chain structure and the position of the focus peak in the axial direction also can be controlled. This shows that the correlation properties enrich our understanding of the cosh-Gaussian vortex beam. Therefore, cutting-edge optical applications including optical transmission, optical shaping, and multiple optical sensing could benefit from these results.

Design of an optical linear-discriminant filter: optimization for enhancement of filter transmittance and discrimination accuracy.

To discriminate fine concave and convex defects on a dielectric substrate, an optical machine learning system is proposed. This system comprises an optical linear-discriminant filter (OLDF) that performs linear discriminant analysis (LDA) of the scattered-wave distribution from target samples. However, the filter output from the OLDF is considerably weak and cannot be measured experimentally. Therefore, an algorithm is also proposed to improve the discrimination accuracy and filter transmittance. The designed filter is validated using a rigorous optical simulator based on vector diffraction theory. We also analyze and discuss a mechanism that provides high transmittance with high discrimination accuracy.