Roadmap on computational methods in optical imaging and holography [invited].

Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging. In addition to registering the perspectives of the modern-day architects of the above research areas, the roadmap also reports some of the latest studies on the topic. Computational codes and pseudocodes are presented for computational methods in a plug-and-play fashion for readers to not only read and understand but also practice the latest algorithms with their data. We believe that this roadmap will be a valuable tool for analyzing the current trends in computational methods to predict and prepare the future of computational methods in optical imaging and holography. Supplementary Information: The online version contains supplementary material available at 10.1007/s00340-024-08280-3.

Stacked Polarizing Elements for Controlling Parameters of Surface Relief Gratings Written in Photosensitive Materials.

Photosensitive materials are widely used for the direct fabrication of surface relief gratings (SRGs) without the selective etching of the material. It is known that the interferometric approach makes it possible to fabricate SRGs with submicron and even subwavelength periods. However, to change the period of the written SRGs, it is necessary to change the convergence angle, shift a sample, and readjust the interferometric setup. Recently, it was shown that structured laser beams with predetermined, periodically modulated polarization distributions can also be used to fabricate SRGs. A structured laser beam with the desired polarization distribution can be formed with just one polarizing optical element-for example, the so-called depolarizer, a patterned micro-retarder array. The use of such stacked elements makes it possible to directly control the modulation period of the polarization of the generated laser beam. We show that this approach allows one to fabricate SRGs with submicron periods. Moreover, the addition of q-plates, elements effectively used to generate cylindrical vector beams with polarization singularities, allows the efficient formation of fork polarization gratings (FPGs) and the fabrication of higher-order fork-shaped SRGs. Full control of the parameters of the generated FPGs is possible. We demonstrate the formation of FPGs of higher orders (up to 12) by only adding first- and second-order q-plates and half-wave plates to the depolarizers. In this work, we numerically and experimentally study the parameters of various types of SRGs formed using these stacked polarizing elements and show the significant potential of this method for the laser processing of photosensitive materials, which often also serve as polarization sensors.

Vectorial spin Hall effect of light upon tight focusing.

The spin Hall effect of light is a manifestation of angular momentum conservation in the process of spin-orbit interaction of light. This optical Hall effect is exhibited in tight focusing of a circularly polarized asymmetric input beam as a shift of the center of gravity of the focal spot in the transverse plane, perpendicular to the direction/axis of symmetry breaking. It is commonly established that the direction of this shift depends on the sign of the spin. Here we show, for the first time, to the best of our knowledge, both analytically and by numerical simulation, that different Cartesian components of an asymmetric circularly polarized focused beam shift in opposite directions by different amounts. Moreover, these shifts depend on the type and degree of the asymmetry and thus can be tuned/controlled. We show how these field components' shifts are related to spin and orbital angular momentum shifts. These findings shed new light on the spin optical Hall effect, facilitate new/simpler ways to measure it, and may broaden the gamut of its applications in manipulation and trapping of particles by light and precision metrology.

Simplifying the Experimental Detection of the Vortex Topological Charge Based on the Simultaneous Astigmatic Transformation of Several Types and Levels in the Same Focal Plane.

It is known that the astigmatic transformation can be used to analyze the topological charge of a vortex beam, which can be implemented by using various optical methods. In this case, in order to form an astigmatic beam pattern suitable for the clear detection of a topological charge, an optical adjustment is often required (changing the lens tilt and/or the detection distance). In this article, we propose to use multi-channel diffractive optical elements (DOEs) for the simultaneous implementation of the astigmatic transformations of various types and levels. Such multi-channel DOEs make it possible to insert several types of astigmatic aberrations of different levels into the analyzed vortex beam simultaneously, and to form a set of aberration-transformed beam patterns in different diffraction orders in one detection plane. The proposed approach greatly simplifies the analysis of the characteristics of a vortex beam based on measurements in the single plane without additional adjustments. In this article, a detailed study of the effect of various types of astigmatic aberrations based on a numerical simulation and experiments was carried out, which confirmed the effectiveness of the proposed approach.

Free-Space Transmission and Detection of Variously Polarized Near-IR Beams Using Standard Communication Systems with Embedded Singular Phase Structures.

We propose to achieve multichannel information transmission in free space by means of variously polarized beams. The interaction of vortex beams of various orders with the main polarization states is theoretically analyzed. The passage of beams with different polarization states through multi-order diffractive optical elements (DOEs) is simulated numerically. Using the simulation results, tables of code correspondence of diffraction order numbers to the presence of phase vortices in the analyzed beams are constructed, which allow one to determine diffraction orders that carry information about various polarization states. The performed experiment made it possible to study the recognition of the first order cylindrical polarization state formed by a Q-plate converter using a phase DOE. In the experiment, these elements were built into a commercial fiber-optic communication system operating at the near-IR frequencies. After detecting the beam polarization state, beams of the required diffraction orders are efficiently coupled into optical fiber using an additional phase element. The developed optical detection system also provides channel suppression of homogeneously polarized components, which are supposed to be used for transmission of other channels.

Plasmonic Refractive Index and Temperature Sensor Based on Graphene and LiNbO3.

A high-efficiency dual-purpose plasmonic perfect absorber sensor based on LiNbO3 and graphene layers was investigated in this paper for the refractive index and thermal sensing. The sensor design was kept simple for easy fabrication, comprising a LiNbO3 substrate with a quartz layer, thin layer of graphene, four gold nanorods, and a nanocavity in each unit cell. The nanocavity is located in the middle of the cell to facilitate the penetration of EM energy to the subsurface layers. The proposed sensor design achieved an output response of 99.9% reflection, which was easy to detect without having any specialized conditions for operability. The performance of the device was numerically investigated for the biomedical refractive index range of 1.33 to 1.40, yielding a sensitivity value of 981 nm/RIU with a figure-of-merit of 61.31 RIU-1. By including an additional polydimethylsiloxane polymer functional layer on the top, the device was also tested as a thermal sensor, which yielded a sensitivity level of -0.23 nm/°C.

Polarization-Sensitive Patterning of Azopolymer Thin Films Using Multiple Structured Laser Beams.

The polarization sensitivity of azopolymers is well known. Therefore, these materials are actively used in many applications of photonics. Recently, the unique possibilities of processing such materials using a structured laser beam were demonstrated, which revealed the key role of the distribution of polarization and the longitudinal component of light in determining the shape of the nano- and microstructures formed on the surfaces of thin azopolymer films. Here, we present numerical and experimental results demonstrating the high polarization sensitivity of thin azopolymer films to the local polarization state of an illuminating structured laser beam consisting of a set of light spots. To form such arrays of spots with a controlled distribution of polarization, different polarization states of laser beams, both homogeneous and locally inhomogeneous, were used. The results obtained show the possibility of implementing a parallel non-uniform patterning of thin azopolymer films depending on the polarization distribution of the illuminating laser beam. We believe that the demonstrated results will not only make it possible to implement the simultaneous detection of local polarization states of complex-shaped light fields but will also be used for the high-performance fabrication of diffractive optical elements and metasurfaces.

Wavelength-Tunable Vortex Beam Emitter Based on Silicon Micro-Ring with PN Depletion Diode.

Herein we propose a design of a wavelength-tunable integrated vortex beam emitter based on the silicon-on-insulator platform. The emitter is implemented using a PN-depletion diode inside a microring resonator with the emitting hole grating that was used to produce a vortex beam. The resonance wavelengths can be shifted due to the refractive index change associated with the free plasma dispersion effect. Obtained numerical modeling results confirm the efficiency of the proposed approach, providing a resonance wavelength shift while maintaining the required topological charge of the emitted vortex beam. It is known that optical vortices got a lot of attention due to extensive telecommunication and biochemical applications, but also, they have revealed some beneficial use cases in sensors. Flexibility in spectral tuning demonstrated by the proposed device can significantly improve the accuracy of sensors based on fiber Bragg gratings. Moreover, we demonstrate that the proposed device can provide a displacement of the resonance by the value of the free spectral range of the ring resonator, which means the possibility to implement an ultra-fast orbital angular momentum (de)multiplexing or modulation.

Metalenses for the generation of vector Lissajous beams with a complex Poynting vector density.

We propose a method for the design of metalenses generating and focusing so-called vector Lissajous beams (VLBs), a generalization of cylindrical vector beams (CVBs) in the form of vector beams whose polarization vector is defined by two orders (p, q). The designed metalenses consist of subwavelength gratings performing the polarization transformation of the incident linearly polarized laser beams and a sublinearly chirped lens term for the realization of the beam focusing. The possibility of using VLBs for the realization of laser beams with a complex Poynting vector is theoretically shown. The certain choice of orders (p, q) of the generated VLBs makes it possible to control the type of various electromagnetic field components as well as the components of the complex Poynting vector. For example, in contrast to VLBs, the classical types of CVBs cannot provide an imaginary part in the longitudinal component of the Poynting vector. Such light fields are promising for exciting non-standard forces acting on the trapped nano- and microparticles.

Breaking the symmetry to structure light.

We show that by breaking the symmetry of a beam subjected to tight focusing, namely by obscuring half of it or, equivalently, shifting the beam away from the lens axis, it is possible to obtain novel light properties in the focal spot which, to the best of our knowledge, have not been observed before. For example, a linearly polarized beam half-obstructed or shifted from the axis generates longitudinal and transverse electrical field components, both of which peak on-axis. The ratio of the intensities of these two components can be tuned by changing the shift distance, the size, and the azimuthal location of the displaced incoming beam. Moreover, such symmetry breaking of a linearly polarized beam acts as a catalyst for producing distributions of circular polarization/longitudinal spin angular momentum, as well as orbital angular momentum, in the focal plane. The simple method for generating co-incident longitudinal and transverse components with a controllable ratio may find applications in laser machining, particle manipulation, etc.

Enlightening Arago-Poisson spot using structured light.

We show that structured light can amplify the intensity of an Arago-Poisson bright spot, the cornerstone proof of the wave nature of light, by several orders of magnitude. Specifically, we use a thin annular beam produced by either an axicon-lens combination or two axicons to illuminate an opaque circular obstacle. Experimental results confirm the numerical calculations. By judiciously choosing our scheme's parameters, the bright spot intensity can be higher than that of the original beam, meaning that structured light facilitates "focusing" of light behind an obstacle. This amplification, in addition to didactic elucidation of this classical effect, can find use in optical alignment/metrology, lithography, aberration measurements, as well as in basic science studies of the Arago-Poisson spot in matter waves.

Modern Types of Axicons: New Functions and Applications.

Axicon is a versatile optical element for forming a zero-order Bessel beam, including high-power laser radiation schemes. Nevertheless, it has drawbacks such as the produced beam's parameters being dependent on a particular element, the output beam's intensity distribution being dependent on the quality of element manufacturing, and uneven axial intensity distribution. To address these issues, extensive research has been undertaken to develop nondiffracting beams using a variety of advanced techniques. We looked at four different and special approaches for creating nondiffracting beams in this article. Diffractive axicons, meta-axicons-flat optics, spatial light modulators, and photonic integrated circuit-based axicons are among these approaches. Lately, there has been noteworthy curiosity in reducing the thickness and weight of axicons by exploiting diffraction. Meta-axicons, which are ultrathin flat optical elements made up of metasurfaces built up of arrays of subwavelength optical antennas, are one way to address such needs. In addition, when compared to their traditional refractive and diffractive equivalents, meta-axicons have a number of distinguishing advantages, including aberration correction, active tunability, and semi-transparency. This paper is not intended to be a critique of any method. We have outlined the most recent advancements in this field and let readers determine which approach best meets their needs based on the ease of fabrication and utilization. Moreover, one section is devoted to applications of axicons utilized as sensors of optical properties of devices and elements as well as singular beams states and wavefront features.

Spatial-Light-Modulator-Based Multichannel Data Transmission by Vortex Beams of Various Orders.

We report an atmospheric multichannel data transmission system with channel separation by vortex beams of various orders, including half-integer values. For the demultiplexing of the communication channels, a multichannel diffractive optical element (DOE) is proposed, being matched with the used vortex beams. The considered approach may be realized without digital processing of the output images, but only based on the numbers of informative diffraction orders, similar to sorting. The system is implemented based on two spatial light modulators (SLMs), one of which forms a multiplexed signal on the transmitting side, and the other implements a multichannel DOE for separating the vortex beams on the receiving side. The stability of the communication channel to atmospheric interference and the crosstalk between the channels are investigated.

Recent Advances in Generation and Detection of Orbital Angular Momentum Optical Beams-A Review.

Herein, we have discussed three major methods which have been generally employed for the generation of optical beams with orbital angular momentum (OAM). These methods include the practice of diffractive optics elements (DOEs), metasurfaces (MSs), and photonic integrated circuits (PICs) for the production of in-plane and out-of-plane OAM. This topic has been significantly evolved as a result; these three methods have been further implemented efficiently by different novel approaches which are discussed as well. Furthermore, development in the OAM detection techniques has also been presented. We have tried our best to bring novel and up-to-date information to the readers on this interesting and widely investigated topic.

Sector sandwich structure: an easy-to-manufacture way towards complex vector beam generation.

Complex polarization-phase transformations that are realized using easy-to-manufacture optical elements are considered. The manufacturing technology of such elements is based on the angular discretization of the required polarization and phase distributions, which allows one to make optical elements in the form of sector sandwich structures consisting of polarized and phase plates stacked together. We analyze analytically and study numerically the main types of such sector sandwich structures for the formation of cylindrical polarizations of various orders. New effects are observed, which result in the appearance of complex polarized beams with vortices of various orders, arising after the passage through polarizing plates and their combinations with differently rotated phase plates. The results of the experimental study of the formed beams using a multichannel diffraction filter are consistent with theory.

Spectral control of the orbital angular momentum of a laser beam based on 3D properties of spiral phase plates fabricated for an infrared wavelength.

This paper examines the spectral properties of a spiral phase plate (SPP) generating orbital angular momentum (OAM) beams. A simple method is proposed for calculating the resulting OAM by measuring only two maximum expansion coefficients. A comparative numerical simulation of the proposed and traditional methods is performed. An SPP is fabricated for generation of an OAM with integer values at infrared and visible wavelengths. Qualitative experimental studies of the changes in a generated OAM with a change in the operating wavelength are performed using the spatial filtering method. The experimental results are found to agree with the results of numerical simulation. Beams with integer and fractional OAM values are obtained experimentally by changing the wavelength.

Vector Lissajous laser beams.

We consider a new type of vector beam, the vector Lissajous beams (VLB), which is of double order (p,q) and a generalization of cylindrical vector beams characterized by single-order p. The transverse components of VLBs have an angular relationship corresponding to Lissajous curves. A theoretical and numerical analysis of VLBs was performed, showing that the ratio and parity of orders (p,q) affect the properties of different components of the electromagnetic field (EF) (whether they be real, imaginary, or complex). In addition, this allows one to engineer the imaginary part of the longitudinal component of the electromagnetic field and control the local spin angular momentum density, which is useful for optical tweezers and future spintronics applications.

Caustics of the vortex beams generated by vortex lenses and vortex axicons.

In this work, the propagation of vortex beams is treated using a catastrophe theory approach. Analytic expressions are deduced to describe caustic surfaces produced by vortex lenses and vortex axicons. The obtained analytics allow us to explain the formation of the shadow region along the optical axis for vortex beams using geometric optics (previously, the zero axial intensity was explained just by diffraction effects). Thus, the presence of a vortex eikonal leads to a fundamental change in the type of axial caustic. Another important distinction of the caustics produced by vortex beams from those produced by nonvortex radial beams has been shown to consist in wavelength-dependence. The results of numerical simulation show that the propagation operator defined using a geometrical optics approximation agrees well with the numerical simulation results obtained using a nonparaxial diffraction operator based on the conical wave expansion.

Influence of optical forces induced by paraxial vortex Gaussian beams on the formation of a microrelief on carbazole-containing azopolymer films.

The paper discusses photoinduced microrelief formation in a film of an azopolymer. A theoretical study of the effect of laser beam polarization on the balance of optical forces acting under the direct action of paraxial Gaussian beams on the irradiated substance was made. We show that taking into account the gradient and scattering components of the force does not allow us to correctly describe the shape of the microasperities obtained on a carbazole-containing azopolymer. An approximation function is presented that describes the dependence of the microasperities' shapes on the non-gradient component of the optical force of laser radiation in the absence and presence of a vortex phase. A comparative analysis of the approximation results and experimentally obtained microreliefs was carried out.

Wavefront Aberration Sensor Based on a Multichannel Diffractive Optical Element.

We propose a new type of a wavefront aberration sensor, that is, a Zernike matched multichannel diffractive optical filter, which performs consistent filtering of phase distributions corresponding to Zernike polynomials. The sensitivity of the new sensor is theoretically estimated. Based on the theory, we develop recommendations for its application. Test wavefronts formed using a spatial light modulator are experimentally investigated. The applicability of the new sensor for the fine-tuning of a laser collimator is assessed.