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The results of experimental and theoretical studies of the evolution of the small-scale transverse structure of high-power femtosecond laser radiation propagating in air in the multiple filamentation mode are presented. It has been found that the presence of intensity inhomogeneities in the initial transverse profile of the laser beam leads to the formation of spatially isolated light channels due to the Kerr self-focusing effect. When the power in these channels exceeds a certain threshold value (the critical power), radiation filamentation occurs in them. The parameters of these light channels are theoretically estimated on the basis of the diffraction-ray model of single filamentation. It is shown that for a laser beam with a centimeter radius and subterawatt power, the initial radius of intensity inhomogeneities in the transverse profile has a characteristic value of several millimeters.

Results of theoretical study of the femtosecond Ti:Sa laser pulse propagation in air under the influence of the normal group velocity dispersion are presented. The use of the diffraction-ray tube method for an analysis of numerical solutions of the nonlinear Schrodinger equation in chromatic dispersion medium with the Kerr and plasma nonlinearity makes it possible to determine the main regularities of the femtosecond laser pulse selffocusing and filamentation in air for various pulse durations, initial beam radii, and peak powers. It is shown that under the influence of the group velocity dispersion, the filamentation terminates with an increase in the initial radius of the laser beam even at high values of supercritical powers. With an increase in the dispersion distortions of the pulse, the radius of the energetically replenishing diffraction-ray tube, the angular divergence of the post-filamentation light channel, and the nonlinear focus coordinate normalized to the Rayleigh length increase in the central time slices of the laser pulse and its integral pattern.

Spatial resolution of conventional optics, which is necessary for nondestructive trapping of microobjects, is limited by diffraction to a value equal to half of the radiation wavelength. Despite this limitation, use of optical methods is one of the main directions in biological and biomedical researches because only these methods have a minimal impact on living organisms. The rapid advance in this area is largely owing to the development of new optical technologies and the considerable advance in mesoscale photonics, which has allowed researchers to develop techniques for controlling structured beams for optical traps. In this work, we consider some recent trends in the field of optical manipulation based on mesoscale dielectric particles.

We report the results of theoretical modelling of photonic nanojets (PNJs) formed by laser radiation scattering on a single-layer ordered assembly of dielectric microtoroids placed on the surface of a transparent matrix (silicone film). Using the method of computational electrodynamics (FDTD), the main PNJ parameters (length, width, peak intensity) are analysed under the conditions of mutual influence of the light fields of neighbouring microparticles. It is shown that the main factor affecting the PNJ characteristics under study is the spatial configuration of the radiation-scattering particle, namely, the internal diameter of its cross section. It is found that for certain configurations of toroid placement in a cluster, a PNJ ensemble is implemented with parameters significantly better than those for a single toroid.

An experimental setup and experiments on measurements and calculation of light pressure on constructional materials at different light angles are presented. This calculation is necessary to determine the lighting properties of a material and the total solar pressure moment. Industrial metal-knitted textile was used as a constructional material. Metal-knitted textile is a material for large-diameter spacecraft antennas. More than 4000 experimental measurements of the transmittance and reflection coefficients of the metal-knitted textile were carried out for the calculation.

Characteristics of the domain of multiple filamentation in air are estimated based on the numerical solution of a nonlinear Schrodinger equation in the single filamentation statement. The method of diffraction-ray tubes was used to describe the single filamentation of laser pulses. The efficiency of this method for interpreting experimental results and predicting effects is shown, which is important when planning experiments. The characteristic size of small-scale intensity inhomogeneities in the laser centimeter-radius beam profile, which induce a multiple filamentation of femtosecond pulses, is shown to be several millimeters. An increase in the initial laser beam radius during telescoping increases the sizes of the initial small-scale intensity inhomogeneities, and reduces their power. This leads to an increase in the distance to the start of filamentation. An increase in the initial beam power promotes the elongation of the filaments and increases their number.

A new concept of an all-optical wavelength-selective two-channel switch based on the photonic hook effect without the use of micromechanical devices or nonlinear materials is proposed. A prototype of such a device based on an off-axis Fresnel zone plate is considered and its main parameters are discussed. Due to the unique property of the photonic hook to change its curvature with respect to the irradiation wavelength λ, this switch is a promising candidate for the implementation of optical switching in modern optoelectronics and miniature ‘on-a-chip’ devices. Numerical simulation shows that the optical isolation of switched channels for a switch with linear dimensions of about (6λ)3 based on an off-axis zone plate can reach 18 – 20 dB during operation in the wavelength range of 1.5 – 1.9 μm.

We compare transverse structure evolution and energy deposition into the medium within focused multifilament arrays created using two different types of diffraction optical elements (DOEs): TEM11 phase plate and a Dammann grating. We show that the employment of the Dammann grating provides a robust way to create regular multifilament arrays, which is far less dependent on laser beam quality than one using the phase plate.

The results are presented of experiments on controlling the characteristics of the multiple filamentation domain of femtosecond laser pulses along atmospheric paths via variations in the initial spatial focusing, beam radius, and pulse energy, as well as the optical field structure at the initial beam aperture.

Based on numerical simulation and qualitative analysis, the effect of the group velocity dispersion on the formation of light structures during self-focusing and filamentation of femtosecond Ti:sapphire laser pulses in air is studied. The main features of the filamentation have been determined at various pulse duration, initial beam radii, and peak radiation powers based on the results of numerical solutions of the nonlinear Schrodinger equation in a Kerr-plasma dissipative dispersion medium and using the diffraction-beam tube approach. Dispersion is detected in the cases where the dispersion length is not a minimum at the scale of the process. It is shown that the relative (normalized to Rayleigh length) coordinate of the beginning of filamentation increases as the dispersion distortions of the pulse increase, and the filamentation channel length is reduced. For shorter laser pulses (tens of femtoseconds), the filamentation ceases as the laser beam radius increases. The size of the energy-replenishing diffraction-beam tube and the angular divergence of postfilamentation light channels increase for this class of pulses.

Results of the theoretical study of the propagation of femtosecond pulses of a Ti:Sapphire laser in air under self-focusing and filamentation are presented. The self-focusing of laser pulses is analyzed on the basis of the method of diffraction-beam tubes. The analysis established that specific light structures were formed in a laser beam during self-focusing. One of such structures is an energy-replenishing diffraction-beam tube, which provides the necessary energy for filamentation and has the form of a high-intensity light channel during postfilamentation pulse propagation. The dependences of the radius and power of the energy-replenishing tube on the initial beam radius and peak power at a fixed pulse length are derived. It is revealed that the energy consumption of radiation for the filamentation decreases with an increase in the beam radius. The peak power contained in the energy-replenishing light tube during the postfilamentation laser pulse propagation does not exceed the critical self-focusing power of a Gaussian beam and weakly depends on the initial pulse parameters.

The results of theoretical studies of spatially localized near-field light structures (photonic nanojets) formed when laser radiation is scattered on a meta-surface having the form of an ordered single-layer assembly of dielectric microparticles (spheres, cones) embedded in a transparent matrix (silicone film) are presented. The behavior of the main parameters of the localized light structures (length, width, and peak intensity) under the effects of light fields of neighboring microparticles is thoroughly analyzed by using computational electrodynamics to solve Maxwell’s equations with the finite-difference time-domain method (FDTD). It is ascertained that the main factors which affect the parameters of photonic nanojets under study are the spatial orientation of the microcones and the depth of their immersion in the silicone matrix. It is shown that several spatial configurations of the microassembly of the cones allow the creation of an ensemble of photonic nanojets with specific parameters, which are unattainable for isolated microcones. Ordered clusters of spherical particles have an advantage in terms of a comprehensive assessment of the parameters of photonic nanojets.

The results of experimental and theoretical studies of femtosecond laser pulse filamentation with use of a bimorph deformable mirror are presented. The mirror allows controlling the position of the filamentation domain throughout a model path due to phase distortions of different parts of a laser beam, determining localization of filaments and high-intensity channels in a beam cross section, and forming long (>100 m) high-intensity (1011–1012 W/cm2) weakly diverging plasma-free channels.

Propagation of a tightly focused high-power ultrashort laser pulse in an optical medium is usually substantially influenced by the medium optical nonlinearity that can noticeably affect the laser pulse parameters around the nonlinear focus and lead to unavoidable and often undesirable spatial distortions of the focal waist. We present the results of our experimental study and numerical simulations on a femtosecond Ti:Sapphire laser pulse propagation in air under different spatial focusing. We concentrated our study on spectral-angular and spatial pulse transformations under different focusing regimes - from linear to nonlinear one, when pulse filamentation occurs. For the first time to the best of our knowledge, we found the laser pulse numerical apertures range – namely, from NA = 2·10-3 to 5 10-3(for the laser pulse energy of 1 mJ), where the laser pulse distortions both in frequency-angular spectrum and pulse spatial shape are minimal. By means of the numerical simulations, we found the threshold pulse energy and peak power in a wide range of focusing conditions, within which a transition between the linear and strongly nonlinear laser pulse focusing in air takes place. This energy limit is shown to decrease with pulse numerical aperture enhancement. Our findings identify the laser pulse numerical apertures and energes adequate for getting a maximum laser intensity with a good beam quality around the focal point suitable for various laser micropatterning and micromachining technologies.

The possibility of overcoming the critical condition for localized photonic nanojet upon plane optical wave diffraction at mesoscale dielectric particle, which is commonly known as "the refractive index contrast is less than two", was recently reported in our works. To this end, the novel geometrical scheme of photonic nanojet generation in "reflection mode" was proposed based on a super-contrast microparticle (n~2) placed near a flat mirror. In this paper, through the numerical FDTD calculations of optical near-field structure of 2D and 3D dielectric microparticles (cylinder, sphere) we extend our considerations to the case of oblique particle-at-mirror illumination and present new physical phenomena arising in the considered photonic geometry. Those are the generation of a quasi-retrograde photonic nanojet following the inclined particle illumination and the formation of a curvilinear spatial region of optical field localization in the form of a "specular reflection photonic hook" (s-Hook). Two different regimes of s-Hook formation are analyzed by changing the direction of light incidence and by flat mirror rotation., 10 pages, 4 figures

Based on the diffraction-ray representation of nonlinear propagation of laser pulses, some examples of visualization of the filamentation of high-power femtosecond laser pulses in air are considered in the form of evolutionary paths of diffraction beams and light tubes. It is ascertained that a filament is supported by the light energy of the part of the beam which is inside a beam tube with the initial peak power higher than the critical power of self-focusing. This light tube is an energy reservoir for the filament. The light beam periphery holds the diffraction-beam tube which includes the filament by means of formation of a “diffractive” waveguide.

The concept of nonstationary diffraction-beam optics of high-power femtosecond laser pulses is presented. According to the concept, the power of a beam propagates along specific light structures—diffraction- beam tubes. These tubes do not intersect and do not exchange energy, but changes in their shape and cross sections during propagation show the effect of physical processes that occur with radiation in the medium. The nonstationary theory is supplemented with evolutionary equations for time-averaged diffraction rays and effective squared radii of diffraction tubes.

Results of numerical simulation of light absorption by the dimer of bilayer spherical particles consisting of a water core and a polymer shell absorbing radiation are presented. The spatial distribution and the amplitude characteristics of the volume density of the absorbed power are investigated. It is shown that for a certain spatial dimer configuration, the maximal achievable density of the absorbed power is realized. It is also established that for closely spaced microcapsules with high shell absorption indices, the total power absorbed in the dimer volume can increase in comparison with the radiation absorption by two insulated microparticles.

Results of numerical simulation of self-action in air of a sequence of ultrashort laser pulses with a carrier in the near and mid-IR regions are presented. We show that the use of a 10.6-μm pulse train allows significant elongation of the plasma channel generated during pulse filamentation and enhancement of its spatial connectivity. The filamentation of a submicron pulse train does not visibly change filamentation region parameters.

We present the results of our experimental study of the propagation dynamics of high-power femtosecond laser radiation in air with initially imposed amplitude and/or phase modulations. Depending on the modulation type and magnitude, the laser pulse upon nonlinear propagation breaks up into several high-intensity spatially localized light channels, which may or may not contain air plasma and thus are referred to as laser filaments, post-filaments, or plasmaless channels. The pulse modulations are implemented by means of control of the phase or amplitude front using a bimorph deformable mirror or amplitude masks, respectively. We show that the distance of formation and spatial length of high-intensity light channels along a propagation path strongly depend on the shapes and spatial positions of the inhomogeneities created in the transverse phase/amplitude pulse profile, but weakly depend on their sizes.

Features of laser radiation scattering and absorption by an ensemble of two identical microcapsules are theoretically studied. Each capsule is modeled by a two-layer spherical micron-size particle consisting of water core and light absorbing polymer shell. By the numerical electrodynamics techniques, it is shown that the internal structure and mutual arrangement of particles affect the spatial distribution and amplitude characteristics of the power absorbed. The highest values of the absorbed power density in model microcapsules could be attained if the particles are shifted relative to each other by a distance of about their diameter (strongly absorbing particles) or if the particles are in the geometric shadow of each other (weak absorption).

The self-action of high-power femtosecond laser beams with a radiation wavelength of 800 nm (formed by superposition of Gaussian and annular beams) in air is theoretically modelled. A detailed analysis of self-focusing and filamentation of this radiation is performed based on the numerical solution of the spectral equation of the unidirectional propagation of a wave packet with allowance for the nonlinearity of the medium, and by tracing averaged diffraction-optical rays. It is shown that, in terms of the diffraction-beam optics, the outer annulus forms a waveguide, which facilitates self-trapping of the central part of the combined beam, supplying the light energy to the filament. The spatial stability of this waveguide depends on the energy stored in the annulus and on the distance from the latter to the beam axis.

The spatial distribution and amplitude characteristics of the power absorbed inside multilayer particle-microcapsules, which consist of a liquid core and one or more polymer shells, is studied during changing the thickness and refractive index of the external shell; the position of the field localization is determined. This problem is important for the solution of practical tasks associated with opening the microcapsule shells in the appropriate spatial areas.

Results of laboratory and numerical experiments on the multiple filamentation of high-power pulse Ti:Sapphire laser radiation (740 nm) in air are presented. The postfilamentation stage of pulse propagation in the form of intensive spatially localized light structures is investigated. The angular divergence of postfilamentation channels is studied under variation in the initial laser beam focusing. The threshold distance for the refilamentation of postfilamentation channels in a glass plate is measured.

Binary Fresnel zone plates (FZP) are among the most commonly used focusing elements of 2D-planar optical circuits in micro- and nano-photonics. When the diameter and focal distance of a FZP are reduced to the wavelength dimensions, the parameters of the focal area experience strong influence by FZP constructive design (material, thickness, depth of zone relief). By means of the numerical simulations, the near-field diffraction of monochromatic optical wave on a wavelength-scale binary phase plate is investigated. We found a range of optimal depths of zone plate grooves etching as well as substrate thicknesses providing the best focusing of the incident circularly polarized optical wave in terms of maximum field intensity and minimum size of the focal spot. A certain improvement of these focus parameters can be achieved by filling the zone grooves with a dielectric having a specific refractive index contrast against the FZP substrate. Additionally, the concept of a super-focus binary phase plate with a solid immersion layer (SIL) in the form of a truncated cone made of the ZP substrate material is proposed. Similar to conventional SIL device, this flat SIL-FZP can focus a circularly polarized optical radiation into a subdiffraction spot with a full-width of the order λ/2n (n is FZP refraction index).

Specific features of optical field distribution in composite spherical particles consisting of a liquid core and nanocomposite absorbing shell are theoretically studied at different wavelengths of incident radiation. Using the numerical simulation it is shown that the thickness of the shell of the spherical microcapsule particle and its intrinsic absorption coefficient determine the character of the spatial distribution and the absorbed power. The variation of these parameters allows one to change the spatial position of efficient volume absorption regions and peak absorption values. This provides favourable conditions for opening the shells in appropriate spatial zones to release the contents of the microcapsules.

Particular properties of formation of optical fields in composite spherical microcapsules of different size consisting of a polymer absorbing shell and a nonabsorbing liquid core are considered. The numerical simulation shows that changes in the thickness of the shell grown on the fixed-radius core and in the coefficient of proper radiation of the shell determine the nature of spatial distribution and amplitude characteristics of the absorbed power. Variations in these parameters allow changing the position and peak values of the regions of the effective spatial absorption of the particles and, consequently, create conditions favorable for opening the shells in the appropriate spatial zones. This is important for the solution of practical tasks associated with the problem of release of the encapsulated material.

A model of single filamentation of a high-power ultrashort light pulse has been developed on the basis of evolutionary dependencies of phase and amplitude parameters of the light field found from the numerical solution of a nonlinear Schrodinger equation for air. A key role of aberration and diffraction effects during the formation of localized stable dynamic light structures near the propagation axis is shown. It is found that the angular divergence of the postfilamentation light channel decreases with an increase in the laser beam radius at a fixed peak pulse power and is saturated when the radius is greater than 1 mm.

We report the investigation results for spatially-localised light structures (photonic nanojets) under near-field optical radiation scattering on phase diffraction gratings. Main parameters of photonic nanojets from gratings with sawtooth, rectangular and hemispherical groove profiles are obtained by numerical electrodynamic simulation. It is found that by varying a period, degree of filling, groove shape and parameters of optically contrast coating of the diffraction grating one can control the characteristics of the produced photonic jets in a wide range.

Spatially localised light structures (photonic nanojets) formed in the near field of light scattering from an ordered ensemble of single-layer clusters of transparent glass microspheres have been theoretically studied. The main parameters of photonic nanojets (length, width, focal distance and intensity) are calculated based on numerical solution of Maxwell equations, and their behaviour under conditions of interference between neighbouring microparticles is analysed. The degree of manifestation of collective effects during the formation of a nanojet array is found to depend on the spatial structure of the ensemble of microspheres, their size and repetition period. It is found that in some cases, having chosen an appropriate configuration of a microsphere ensemble, one can improve significantly the characteristics of the photonic nanojets formed by this ensemble.

Properties of multiple filamentation of gigawatt femtosecond laser pulses in optical glass are considered. The fine structure of the plasma region that is produced upon photoionization of quartz and accompanies light filaments are analyzed experimentally and in numerical simulation. The dependence of the number, position, and length of individual generations of plasma channels on the laser energy is studied for the first time. The role of pulse refocusing events in the plasma region formation is discussed.

A specular-reflection photonic nanojet (s-PNJ) is a specific type of optical near-field subwavelength spatial localization originated from the constructive interference of direct and backward propagated optical waves focused by a transparent dielectric microparticle located near a flat reflecting mirror. The unique property of s-PNJ is reported for maintaining its spatial localization and high intensity when using microparticles with high refractive index contrast when a regular photonic nanojet is not formed. The physical principles of obtaining subwavelength optical focus in the specular-reflection mode of a PNJ are numerically studied and a comparative analysis of jet parameters obtained by the traditional schemes without and with reflection is carried out. Based on the s-PNJ, the physical concept of an optical tweezer integrated into the microfluidic device is proposed provided by the calculations of optical trapping forces of the trial gold nanosphere. Importantly, such an optical trap shows twice as high stability to Brownian motion of the captured nano-bead as compared to the conventional nanojet-based traps and can be relatively easy implemented.

The effect of "photonic nanojet" (PNJ) arising in the near-field scattering region at the surface of dielectric axisymmetric microparticles (hemisphere, axicon, combined particles) under optical illumination is considered theoretically. Numerical calculations of PNJ key parameters (length, width, peak intensity) were performed using the method of discrete-dipole approximation; the dependence of jet’s key parameters on the geometric shape of the microparticles is analyzed. We show that using a special type of combined transparent particles consisting of an axicon and two attached hemispheres, ultra-localized light fluxes with a peak intensity considerably exceeding the corresponding values for particles of simple shapes (hemisphere, axicon) can be realized.

The results of experiments and theoretical modeling of the multiple filamentation of terawatt-power femtosecond laser pulses on a 137 m long air path are presented. We use a multielement optical setup consisting of a Galilean telescope and a deformable bimorph mirror, which allows construction for the desired pulse wavefront at the optical path entrance. By introducing controlled aberrations of the pulse phase profile, we demonstrate the wide-ranging manipulations on the position and spatial structure of the filamentation region. For the first time, to the best of our knowledge, the stable wide-aperture (5 cm in diameter) ring-shaped spatial lattice of high-intense light channels is experimentally realized, which can persist over hundreds of meters in air.

We present a qualitative description of the laser-pulse filamentation phenomenon based on light field representation as a self-consistent ensemble of specific localized wave structures known as the diffraction-ray (light) tubes. These light tubes are energetically independent from each other and, at the same time, they are in close field interaction through the phase front of the light wave. The trajectories of light tube centroids represent the evolutionary line of the Poynting vector transverse component. Light tubes do not intersect in space although they can be nested, and the tubes do not exchange light energy with each other. Spatial shape and area of light tubes can vary during pulse propagation, reflecting the influence of different physical processes manifesting themselves upon radiation propagation in a medium. This diffraction-ray approach applies the attributes of the amplitude and phase analysis to the problem of laser radiation self-action and sheds light on the onset and termination conditions of laser-pulse filamentation.

The regularities of multiple filamentation of gigawatt femtosecond laser pulses in a solid dielectric (optical glass) have been considered. The fine spatial structure of the plasma region that is formed under glass photoionisation and accompanies the formation of light filaments is analysed experimentally and by means of numerical simulation. The dependence of the number, position, and extension of individual 'generations' of plasma channels on the laser pulse energy has been investigated for the first time. It is found that the distribution of the number of plasma channels over the length of a dielectric sample has a maximum, the position of which correlates well with the position of the nonlinear focus of the light beam as a whole; at the same time, the average channel length decreases with increasing pulse power, whereas the number of successive channel 'generations', on the contrary, increases.

The near field of light wave scattering by dielectric conical particles of micron dimensions (microcones) is numerically simulated. The main attention is paid to studying dimensional and amplitude parameters of a specifically spatially localized “photonic jet” region. It is shown for the first time that using a microaxicon with a definite shape yields a record-breaking increase in the extension of the appearing photonic jet to magnitudes of about two tens wavelengths of the incident radiation (by the fixed intensity level) with the preservation of the subwave transverse size of the localized light flux.

The results of numerical modeling of the near field of light wave scattering (“photonic (nano)jet”—PNJ region) by radially symmetric nonabsorbing dielectric microparticles are presented. It is shown that the homogeneous silica microparticles of different spatial shape and orientation form PNJ of different sizes and amplitudes. Photonic nanojets from hemispheres are of high extent but moderate intensity. Use of microaxicons provides for a record increase in the PNJ length of the order of twenty wavelengths of the incident radiation.

We consider a specific spatially localised light structure, namely, a 'photonic jet' formed in the near field upon scattering of an optical wave in a dielectric micron particle. Dimensional parameters and intensity of a photonic jet from microaxicons of different spatial orientation are studied theoretically. It is found for the first time that an axicon-generated photonic jet has in this case a substantially larger length compared with the case of a jet formed on a spherical particle.