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.

Composite Diffraction-Free Beam Formation Based on Iteratively Calculated Primitives.

To form a diffraction-free beam with a complex structure, we propose to use a set of primitives calculated iteratively for the ring spatial spectrum. We also optimized the complex transmission function of the diffractive optical elements (DOEs), which form some primitive diffraction-free distributions (for example, a square or/and a triangle). The superposition of such DOEs supplemented with deflecting phases (a multi-order optical element) provides to generate a diffraction-free beam with a more complex transverse intensity distribution corresponding to the composition of these primitives. The proposed approach has two advantages. The first is the rapid (for the first few iterations) achievements of an acceptable error in the calculation of an optical element that forms a primitive distribution compared to a complex one. The second advantage is the convenience of reconfiguration. Since a complex distribution is assembled from primitive parts, it can be reconfigured quickly or dynamically by using a spatial light modulator (SLM) by moving and rotating these components. Numerical results were confirmed experimentally.

Multi-Spiral Laser Patterning of Azopolymer Thin Films for Generation of Orbital Angular Momentum Light.

Recently, the realization of the spiral mass transfer of matter has attracted the attention of many researchers. Nano- and microstructures fabricated with such mass transfer can be used for the generation of light with non-zero orbital angular momentum (OAM) or the sensing of chiral molecules. In the case of metals and semiconductors, the chirality of formed spiral-shaped microstructures depends on the topological charge (TC) of the illuminating optical vortex (OV) beam. The situation is quite different with polarization-sensitive materials such as azopolymers, azobenzene-containing polymers. Azopolymers show polarization-sensitive mass transfer both at the meso and macro levels and have huge potential in diffractive optics and photonics. Previously, only one-spiral patterns formed in thin azopolymer films using circularly polarized OV beams and double-spiral patterns formed using linearly polarized OV beams have been demonstrated. In these cases, the TC of the used OV beams did not affect the number of formed spirals. In this study, we propose to use two-beam (an OV and a Gaussian beam with a spherical wavefront) interference lithography for realization spiral mass transfer with the desired number of formed spirals. The TC of the OV beam allows for controlling the number of formed spirals. We show the microstructures fabricated by the laser processing of thin azopolymer films can be used for the generation of OAM light at the microscale with the desired TC. The experimentally obtained results are in good agreement with the numerically obtained results and demonstrate the potential of the use of such techniques for the laser material processing of polarization-sensitive materials.

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.

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.

Hybrid design of diffractive optical elements for optical beam shaping.

Hybrid methods combining the geometrical-optics and diffraction-theory methods enable designing diffractive optical elements (DOEs) with high performance due to the suppression of stray light and speckles and, at the same time, with a regular and fabrication-friendly microrelief. Here, we propose a geometrical-optics method for calculating the eikonal function of the light field providing the generation of a required irradiance distribution. In the method, the problem of calculating the eikonal function is formulated in a semi-discrete form as a problem of maximizing a concave function. For solving the maximization problem, a gradient method is used, with analytical expressions obtained for the gradient. In contrast to geometrical-optics approaches based on solving the Monge-Ampére equation using finite difference methods, the proposed method enables generating irradiance distributions defined on disconnected regions with non-smooth boundaries. As an example, we calculate an eikonal function, which provides the generation of a "discontinuous" irradiance distribution in the form of a hexagram. It is shown that the utilization of the hybrid approach, in which the obtained geometrical-optics solution is used as a starting point in iterative Fourier transform algorithms, enables designing DOEs with a quasi-regular or piecewise-smooth microrelief structure. The calculation results are confirmed by the results of experimental investigations of a DOE generating a hexagram-shaped irradiance distribution.

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.

Generation of Complex Transverse Energy Flow Distributions with Autofocusing Optical Vortex Beams.

Optical vortex (OV) beams are widely used for the generation of light fields with transverse energy flow inducing orbital motion of the nano- and microparticles in the transverse plane. Here, we present some new modifications of OV beams with autofocusing properties for shaping complex transverse energy flow distributions varying in space. The angular component of the complex amplitude of these beams is defined by the superpositions of OV beams with different topological charges. The proposed approach provides a convenient method to control the three-dimensional structure of the generated autofocusing OV beams. The control of the transverse distribution of an autofocusing beam provides a wide variety of generated fields with both rotating and periodic properties, which can be used in the field of laser manipulation and laser material processing. Thus, the obtained numerical results predict different types of motion of the trapped particles for the designed OV autofocusing beams. The experimental results agree with modeling results and demonstrate the principal possibility to shape such laser beams using spatial light modulators.

Laser manipulation of airborne microparticles behind non-transparent obstacles with the help of circular Airy beams.

An approach for the realization of three-dimensional laser manipulation of agglomerations of carbon nanoparticles behind non-transparent obstacles in the air is proposed and investigated. The approach is based on the use of circular Airy beams (CABs), which are structured laser beams with self-healing and autofocusing properties. The possibility to trap and guide both single and multiple microparticles in the case of a non-distorted CAB and a CAB distorted by an on-axis metal rod is demonstrated. We believe that these results open new possibilities for the control of trapped particles that are out of sight and hidden by different obstacles.

Orbital angular momentum and topological charge of a multi-vortex Gaussian beam.

We report on a theoretical and numerical study of a Gaussian beam modulated by several optical vortices (OV) that carry same-sign unity topological charge (TC) and are unevenly arranged on a circle. The TC of such a multi-vortex beam equals the sum of the TCs of all OVs. If the OVs are located evenly along an arbitrary-radius circle, a simple relationship for the normalized orbital angular momentum (OAM) is derived for such a beam. It is shown that in a multi-vortex beam, OAM normalized to power cannot exceed the number of constituent vortices and decreases with increasing distance from the optical axis to the vortex centers. We show that for the OVs to appear at the infinity of such a combined beam, an infinite-energy Gaussian beam is needed. On the contrary, the total TC is independent of said distance, remaining equal to the number of constituent vortices. We show that if TC is evaluated not along the whole circle encompassing the singularity centers, but along any part of this circle, such a quantity is also invariant and conserves on propagation. Besides, a multi-spiral phase plate is studied for the first time to our knowledge, and we obtained the TC and OAM of multi-vortices generated by this plate. When propagated through a random phase screen (diffuser) the TC is unchanged, while the OAM changes by less than 10% if the random phase delay on the diffuser does not exceed half wavelength. Such multi-vortices can be used for data transmission in the turbulent atmosphere.

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.

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.

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.

Demonstration of a simple technique for controllable revolution of light-absorbing particles in air.

The rotation of optically trapped particles is used in many applications for the realization of different micromechanical devices, such as micropumps, microrotors, and microgyroscopes, as well as for the investigation of particle interactions. Although for transparent micro-objects in both liquid media and vacuum, the rotation can easily be realized by transfer of the spin angular or orbital angular momentum from the light to the object. In the case of light-absorbing micro-objects in gaseous media, such transfers are insignificant in comparison with the thermal effects arising from the photo- and thermo-phoresis phenomena initiating the movement of trapped particles in a laser beam. Currently, proposed methods using a single focused laser beam, tapered-ring optical traps, or single and multiple bottle beams (BBs) have various limitations-for example, the inability to control the direction of the revolution of trapped particles or the low revolution frequency and small revolution angles. Here we propose a simple method for the realization of the revolution of airborne light-absorbing particles. The method is based on a combination of a circular diaphragm and a rotating cylindrical lens, enabling the generation of linear optical BBs. Our results show the flexibility and reliability of the proposed technique, allowing such laser traps to be used in various optical systems for the manipulation of micro-objects with different dimensions and shapes.

Variable transformation of singular cylindrical vector beams using anisotropic crystals.

We demonstrated and investigated, both theoretically and experimentally, the transformation of cylindrical vector beams with an embedded phase singularity under the condition of focusing perpendicularly to the axis of the anisotropic calcite crystal. Theoretical and numerical analysis, performed on the basis of decomposing the light field into a set of plane waves for an anisotropic medium, allowed us to study the dependence of the structural transformation of the initial laser beam on the polarisation and phase state in detail. The proposed approach allows one to perform the visual recognition of cylindrically-polarised vector beams of various orders and can be used for the demultiplexing of information channels in the case of polarisation-division multiplexing. The experimentally-obtained results agree with the theoretical findings and demonstrate the reliability of the approach.

Dynamic focal shift and extending depth of focus based on the masking of the illuminating beam and using an adjustable axicon.

We investigate several methods of focus shift and focus extension in detail. These methods are divided into two groups: (1) changing the radius of the illuminating beam and/or limiting diaphragm; and (2) adding an optical system with an adjustable element (lens or axicon). In the cases of a planar and Gaussian illuminating beam, values of the focus position and depth of focus (DOF) are calculated theoretically and numerically, depending on the beam radius. In addition, theoretical and numerical evaluations of displacement and DOF increase for the focusing system with the adjustable lens or axicon obtained. We show that these methods for changing the parameters of the focal area provide flexibility and efficiency in the control of its characteristics. Recommendations about possible applications in which such control is important are formulated on the basis of the results obtained.

Calculation of fractional orbital angular momentum of superpositions of optical vortices by intensity moments.

Two simple and high-efficiency techniques for measuring the orbital angular momentum (OAM) of paraxial laser beams are proposed and studied numerically and experimentally. One technique relies on measuring the intensity in the Fresnel zone, followed by calculating the intensity that is numerically averaged over angle at discrete radii and deriving squared modules of the light field expansion coefficients via solving a linear set of equations. With the other technique, two intensity distributions are measured in the Fourier plane of a pair of cylindrical lenses positioned perpendicularly, before calculating the first-order moments of the measured intensities. The experimental error grows almost linearly from ~1% for small fractional OAM (up to 4) to ~10% for large fractional OAM (up to 34).

Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates.

Nowadays, the well-known cylindrical vector beams (CVBs) - the axially symmetric beam solution to the full-vector electromagnetic wave equation - are widely used for advanced laser material processing, optical manipulation and communication and have a great interest for data storage. Higher-order CVBs with polarisation order greater than one and superpositions of CVBs of various orders (hybrid CVBs) are especially of interest because of their great potential in contemporary optics. We performed a theoretical analysis of the transformation of first-order CVBs (radially and azimuthally polarised beams) into hybrid higher-order ones using phase elements with complex transmission functions in the form of the cosine or sine functions of the azimuthal angle. Binary multi-sector phase plates approximating such transmission functions were fabricated and experimentally investigated. The influence of the number of sectors and a height difference between neighbouring sectors, as well as the energy contribution of the different components in the generated hybrid higher-order CVBs were discussed in the context of polarisation transformation and vector optical field transformation in the focal region. The possibility of polarisation transformation, even in the case of weak focusing, is also demonstrated. The simple structure of the profile of such plates, their high diffraction efficiency and high damage threshold, as well as the easy-to-implement polarisation transformation principle provide advanced opportunities for high-efficient, quickly-switchable dynamic control of the generation of structured laser beams.

Aberration laser beams with autofocusing properties.

We investigate theoretically, numerically, and experimentally a novel type of laser beam-an aberration laser beam (ALB). To generate the ALB, a diffractive optical element with a phase transmission function having an arbitrary radial dependence of power q and a periodic angular dependence of sin(mϕ) or cos(mϕ) form can be used. Such a light distribution is more general than classic aberrations including Zernike polynomials. We demonstrate that such radial nonuniformity results in autofocusing properties of ALBs. The autofocusing feature of ALBs is analogous to that of circular Airy beams, but the ALBs' autofocusing feature has more flexibility. The presence of the periodic angular dependence in the phase results in a diffraction pattern with mth-order symmetry. Transformation of ALBs during propagation in free space is analogous to transformation of the three-Airy beams; however, the generated light distributions have an arbitrary integer order of symmetry. The presence of an additional focusing lens leads to formation of an optical field in its focal plane with symmetry that depends on the parity of m: for even m, the generated light distribution has 2mth-order symmetry, and, for odd m, it has mth-order symmetry.

Astigmatic laser beams with a large orbital angular momentum.

We show that an elliptic Gaussian beam, focused by a cylindrical lens, can be represented as a linear combination of a countable number of only even angular harmonics with both positive and negative topological charge. For the orbital angular momentum (OAM) of the astigmatic Gaussian beam, an exact expression is obtained in a form of a converging series of the Legendre functions of the second kind. It is shown that at some conditions only the terms with the positive or negative topological charge are remained in this series. Using a hybrid numeric-experimental approach, we obtained the normalized OAM of the astigmatic beam, equal to 109, which is just 6% different from the exact OAM of 116, calculated by the equation. To generate such laser beams, there is no need in special optical elements such as spiral phase plates. The OAM of such beams can be adjusted by varying the waist radius of the Gaussian beam and the focal length of the cylindrical lens. The OAM of such beams can reach large values.