Plane Wave Research Articles

Interception force assisted optical pulling of a dipole nanoparticle in a single plane wave

The optical pulling force is generally believed to originate from the recoil force due to the simultaneous excitation of multipoles in the particle, which overcomes the interception force contributing to the optical pushing force. However, we show that the interception force can induce optical pulling force on a small isotropic spherical particle with gain in a uniform electromagnetic plane wave, in which multipole excitation is negligible within the dipole regime. Based on the multipole expansion theory, a rigorous analytical expression is derived for optical force acting on a spherical particle of arbitrary size and composition illuminated by a single plane wave, regardless of its polarization. The analytical results show that the interception force, which is typically positive in a conventional dielectric particle under illumination of a single plane wave, undergoes a crossover from positive to negative by introducing appropriate gain into the dipolar dielectric nanoparticle, thereby giving rise to the optical pulling. It’s deserved to be noted that the optical pulling force assisted by the interception force does not weaken in magnitude, in fact, it exhibits a stronger magnitude compared to the optical pushing force experienced by a corresponding conventional dielectric particle.

PW-SMD: A Plane-Wave Implicit Solvation Model Based on Electron Density for Surface Chemistry and Crystalline Systems in Aqueous Solution.

Electron density-based implicit solvation models are a class of techniques for quantifying solvation effects and calculating free energies of solvation without an explicit representation of solvent molecules. Integral to the accuracy of solvation modeling is the proper definition of the solvation shell separating the solute molecule from the solvent environment, allowing for a physical partitioning of the free energies of solvation. Unlike state-of-the-art implicit solvation models for molecular quantum chemistry calculations, e.g., the solvation model based on solute electron density (SMD), solvation models for systems under periodic boundary conditions with plane-wave (PW) basis sets have been limited in their accuracy. Furthermore, a unified implicit solvation model with both homogeneous solution-phase and heterogeneous interfacial structures treated on equal footing is needed. In order to address this challenge, we developed a high-accuracy solvation model for periodic PW calculations that is applicable to molecular, ionic, interfacial, and bulk-phase chemistry. Our model, PW-SMD, is an extension of the SMD molecular solvation model to periodic systems in water. The free energy of solvation is partitioned into the electrostatic and cavity-dispersion-solvent structure (CDS) contributions. The electrostatic contributions of the solvation shell surrounding solute structures are parametrized based on their geometric and physical properties. In addition, the nonelectrostatic contribution to the solvation energy is accounted for by extending the CDS formalism of SMD to incorporate periodic boundary conditions. We validate the accuracy and robustness of our solvation model by comparing predicted solvation free energies against experimental data for molecular and ionic systems, carved-cluster composite energetic models of solvated reaction energies and barriers on surface systems, and deep-learning-accelerated ab initio molecular dynamics (AIMD). Our developed periodic implicit solvation model shows significantly improved accuracy compared to previous work (namely, solvation models in aqueous solution) and can be applied to simulate solvent effects in a wide range of surface and crystalline materials.

Non-Bloch theory for spatiotemporal photonic crystals assisted by continuum effective medium

As one indispensable type of nonreciprocal mechanism, a system with temporal modulations is intrinsically open in the physical sense and inevitably non-Hermitian, but the space and time degrees of freedom are nonseparable in a large variety of circumstances, which restrains the application of the non-Bloch band theory. Here, we investigate the spatially photonic crystals (PhCs) composed of spatiotemporal modulation materials (STMs) and homogeneous media, dubbed as the STMPhC, wherein the spatial and temporal modulations are deliberately designed to be correlated. To bypass the difficulty of the spatiotemporal correlation, we first employ the effective medium theory to account for the dispersion of fundamental bands under the influence of Floquet sidebands. Based on the continuum generalized Brillouin zone condition, we then analytically give the criteria for the existence of the non-Hermitian skin effect in the STM. Assisted by developing a numerical method that embeds the plane wave expansion in the transfer matrix, we establish the non-Bloch band theory for the low-frequency Floquet bands in the STMPhCs, in which the identification of the generalized Brillouin zone is central. We finally delve into the topological properties, including non-Bloch Zak phases and non-Bloch bulk-boundary correspondence. Our work validates the idea that the effective medium assists the non-Bloch band theory applied to the STMPhCs, which delivers a prescription to broaden the horizons of non-Bloch theory. Published by the American Physical Society 2024

Negative radiation pressure in the abelian Higgs model

Interactions of small-amplitude monochromatic plane waves with domain walls in (1+1) dimensional abelian Higgs model with a sextic potential were studied. The effective force exerted on a domain wall was derived from a linearized equation and compared with numerical simulations of the original model. It was shown that the domain walls always accelerate in one direction, regardless of the direction of the incoming wave. This implies that in some cases an effect called negative radiation pressure is observed, i.e. instead of pushing, the wave pulls the soliton.

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nose tip, and the mechanisms underlying the low Mack’s second-mode N-factor values at the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy-layer experience appreciable energy amplification for moderate to large nose-tip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the harmonic Navier–Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton–Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the generalized minimal residual method (GMRES) iterative method with a preconditioner corresponding to a simplified Jacobian without the cross-derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over a blunt cone configuration with reduced transition N factor as measured in wind-tunnel experiments. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher-frequency Mack’s second-mode instabilities farther downstream and hence can lead to a reduction in the transition N factor.

Holographic phenomenology via overlapping degrees of freedom

Abstract The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ``overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory.\ \ The numerical tools used in this work are publicly available within the \verb|GPUniverse| package, \url{https://github.com/OliverFHD/GPUniverse}~.

Signatures of top versus bottom illuminations and their predicted implications for infrared transmission microspectroscopy.

Since both top and bottom illuminations are widely used in infrared transmission measurements, in this paper, we study the effects of different illuminations on the signatures in infrared microspectroscopy. By simulating a series of dielectric samples, we show that their extinction efficiency, , remains unchanged when the direction of the incident plane wave is reversed, even though the field distributions both inside and outside of the sample may be dramatically different. We find features in that are correlated with whispering gallery modes for one beam direction and correspond to completely different field distributions for the opposite beam direction. In addition, by linking the optical theorem and the reciprocity relation of far-field scattered field, we rigorously prove the invariance of for arbitrary dielectric targets under opposite plane-wave illuminations. Furthermore, we show the difference in the apparent absorbance spectrum for opposite beam directions when considering numerical apertures.

Reflection and transmission phenomenon of plane waves at the interface of diffusive viscoelastic porous rotating isotropic medium under hall current and nonlocal thermoelastic porous solid

The response of elastic waves upon encountering the boundary between two elastic media is investigated in the present work. Whereas the top medium is thermoelastic isotropic porous, the below medium is thermoelastic rotating porous diffusive. There is an uncoupled transmitted SV-wave propagating through the medium, and the lower medium is rotating with some fixed angular frequency. When the incident wave hits the boundary, it produces four transmitted waves and five coupled quasi-reflected waves. The system is divided into longitudinal and transverse components using the Helmholtz decomposition theorem. Analytical computations of speed and reflection coefficients for transmitted and reflected waves are performed using LS theory. The outcomes are graphically represented for a particular material subject to nonlocal and fractional-order influences. Wave characteristics, such as speed and reflection coefficients for transmitted and reflected waves, are plotted versus angular frequency and angle of incidence using MATLAB programing. The conservation of energy has also been verified. In the absence of rotation, hall current, voids, viscoelasticity, and diffusion in the medium, the previous results in the literature are obtained.

Robustness of highly complex radial carpet beams in turbulent atmospheres

In this study, we report observations of propagating radial carpet beams (RCBs) through a turbulent atmosphere at ground level with a 120 m path length. RCBs are a class of nondiffracting, accelerating, self-healing, and self-amplifying beams, and generated in the diffraction of a plane wave from amplitude/phase radial gratings having different spoke numbers. Observations were made at different times of the day. The intensity profile of an RCB becomes complicated when the number of grating spokes used to generate the beam is large, and includes high intensity spots, called main intensity spots (MISs), which are symmetrically placed at the central area around the beam axis and whose number is equal to (twice) the number of spokes of the amplitude (phase) grating used to generate the beam. With the aid of a telescope and a CCD camera, successive frames of the intensity pattern of the RCBs having different levels of structural complexity are recorded at the end of the path. For the data recorded at different times of the day, we calculate the variance of displacements of MISs along the radial direction. We observe that displacements of the MISs increase with increasing mean temperature of the air; on the other hand, as the complexity of the beam intensity pattern increases, the displacements of the MISs decrease. In order to compare the resilience of different RCBs and a well-known structured beam against atmospheric turbulence, we investigate deformation of the intensity profiles of a Laguerre–Gaussian (LG) beam having a topological charge 20 and different RCBs at the end of the path. It is shown that under the same turbulence condition, highly complex RCBs are more resilient to the destructive effects of the atmospheric turbulence. In particular, for the RCBs generated with gratings having 30 spokes and more, the number of MISs of the received intensity patterns is changed by less than 1% even when the turbulence strength is high. But for the LG beam, its intensity ring is clearly broken in different places, which makes it impossible to follow its maximum intensity in the radial direction

Tunable Photonic Hook Design Based on Anisotropic Cutting Liquid Crystal Microcylinder

The selective control and manipulation of nanoparticles require developing and researching new methods for designing optical tweeters, mainly based on a photonic hooks (PHs) effect. This paper first proposes a tunable PH in which a structured beam illuminates an anisotropic cutting liquid crystal microcylinder based on the Finite-DifferenceTime-Domain (FDTD) method. The PHs generated by plane wave, Gaussian, and Bessel beam are analyzed and compared. The impact of beams and LC particle parameters on the PHs are discussed. Where the influence of the extraordinary refractive index (ne) on PHs is emphasized. Our results reveal that introducing birefringence can change the bending direction of PH. Besides, the maximum intensity of the PHs increases as ne increases regardless of the beam type. The PH generated by a plane wave has a higher maximum intensity and smaller FWHM than that generated by the Gaussian and Bessel beams. The smallest FWHM and maximum intensity of the PHs generated by the Gaussian falls between that generated by the plane wave and the Bessel beam. The PH generated by a Bessel beam has the minor maximum intensity and the largest FWHM. Still, it exceeds the diffraction limit and exhibits bending twice due to its self-recovery property. This paper provides a new way to modulate PH. This work offers novel theoretical models and the degree of freedom for the design of PHs, which is beneficial for the selective manipulation of nanoparticles. It has promising applications in Mesotronics and biomedicine.

Complex Residual Attention U-Net for Fast Ultrasound Imaging from a Single Plane-Wave Equivalent to Diverging Wave Imaging.

Plane wave imaging persists as a focal point of research due to its high frame rate and low complexity. However, in spite of these advantages, its performance can be compromised by several factors such as noise, speckle, and artifacts that affect the image quality and resolution. In this paper, we propose an attention-based complex convolutional residual U-Net to reconstruct improved in-phase/quadrature complex data from a single insonification acquisition that matches diverging wave imaging. Our approach introduces an attention mechanism to the complex domain in conjunction with complex convolution to incorporate phase information and improve the image quality matching images obtained using coherent compounding imaging. To validate the effectiveness of this method, we trained our network on a simulated phased array dataset and evaluated it using in vitro and in vivo data. The experimental results show that our approach improved the ultrasound image quality by focusing the network's attention on critical aspects of the complex data to identify and separate different regions of interest from background noise.

Transmission Loss Characteristics of Dual Cavity Impedance Composite Mufflers for Non-Planar Wave Cavity Resonance

In conventional gasoline automobiles, the engine powers the air conditioning system and engine noise can somewhat mask the noise and vibration of the air conditioning system. In pure electric vehicles, however, the absence of an engine makes the air conditioning system’s noise more noticeable, concentrated in a limited frequency range at constant speeds. As a result, aerodynamic noise from the air conditioning system is a primary noise source in electric vehicles. Pipeline silencers are the main method for reducing this noise. The current silencer design uses plane wave acoustic theory but when cavity modal resonance occurs, the transmission loss error is relatively high. This article addresses the issue of non-planar wave cavity resonance, studying the cavity modal of a muffler using the finite element method to reveal the transmission loss under cavity mode resonance. A dual cavity expansion structure of an impedance composite muffler is proposed, with sound-absorbing materials placed in the cavity to enhance acoustic performance. The analysis of the transmission loss characteristics of the impedance composite muffler provides a theoretical basis for noise control in pure electric vehicle air conditioning systems.

Achiral Plasmonic Antennas Enhance Differential Absorption To Increase Preferential Detection of Chiral Single Molecules.

Plasmonic antennas increase the photon flux in their vicinity, which can lead to plasmon-enhanced fluorescence for molecules near these nanostructures. Here, we combine plasmon-coupled fluorescence and fluorescence-detected circular dichroism to build a specific and sensitive detection strategy for chiral single molecules. Electromagnetic simulations indicate that a two-dimensional gold nanoparticle dimer antenna enhances the electric field and optical chirality of a plane wave in its near field. Furthermore, this optical chirality enhancement can be tuned based on the polarization of the incident electric field, such that enhancing the optical chirality via these antennas will increase the differential absorption of parity-inverted fields. We measured the fluorescence from single molecules of chiral absorbers-Cy5 J-dimers assembled in double-stranded DNA backbones-and achieved increased detectability of these right-handed molecules near achiral gold nanoparticle dimer antennas under right circularly polarized illumination. This strategy offers a new approach to distinguishing weakly fluorescent enantiomers.

A Pseudo-Spectral Method for Wall Shear Stress Estimation from Doppler Ultrasound Imaging in Coronary Arteries.

The Wall Shear Stress (WSS) is the component tangential to the boundary of the normal stress tensor in an incompressible fluid, and it has been recognized as a quantity of primary importance in predicting possible adverse events in cardiovascular diseases, in general, and in coronary diseases, in particular. The quantification of the WSS in patient-specific settings can be achieved by performing a Computational Fluid Dynamics (CFD) analysis based on patient geometry, or it can be retrieved by a numerical approximation based on blood flow velocity data, e.g., ultrasound (US) Doppler measurements. This paper presents a novel method for WSS quantification from 2D vector Doppler measurements. Images were obtained through unfocused plane waves and transverse oscillation to acquire both in-plane velocity components. These velocity components were processed using pseudo-spectral differentiation techniques based on Fourier approximations of the derivatives to compute the WSS. Our Pseudo-Spectral Method (PSM) is tested in two vessel phantoms, straight and stenotic, where a steady flow of 15mL/min is applied. The method is successfully validated against CFD simulations and compared against current techniques based on the assumption of a parabolic velocity profile. The PSM accurately detected Wall Shear Stress (WSS) variations in geometries differing from straight cylinders, and is less sensitive to measurement noise. In particular, when using synthetic data (noise free, e.g., generated by CFD) on cylindrical geometries, the Poiseuille-based methods and PSM have comparable accuracy; on the contrary, when using the data retrieved from US measures, the average error of the WSS obtained with the PSM turned out to be 3 to 9 times smaller than that obtained by state-of-the-art methods. The pseudo-spectral approach allows controlling the approximation errors in the presence of noisy data. This gives a more accurate alternative to the present standard and a less computationally expensive choice compared to CFD, which also requires high-quality data to reconstruct the vessel geometry.

On the phase difference of ECH waves obtained from the interferometry observation by the Arase satellite

We analyzed electrostatic electron cyclotron harmonic waves observed by the interferometry observation mode of the Arase satellite. It is found that the magnitude of the phase difference varies with the satellite spin. The spin dependence of this phase difference was investigated by examining the trend of the spin dependence for the 84 events of interferometry observation of ECH waves. We found that they are divided into two categories. One is that the phase difference tends to show sinusoidal variations as a function of the angle γB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _B$$\\end{document} between the ambient magnetic field projected on the spin plane and the electric field sensor. The other is that the phase difference is close to zero and does not depend on γB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _B$$\\end{document}. A numerical model of interferometry observation of single plane wave is constructed to explain the observed phase differences. We performed the numerical calculations when the background magnetic field was oriented in the direction often observed in the Arase satellite. The result of the calculations shows the wave vector direction relates to the spin angle with the maximum phase difference. Using this relation, we show that it may be possible to estimate the wave vector direction of ECH waves from one-dimensional interferometry data. This is expected to enable more accurate estimates of phase velocity.Graphical

Vibrational lifetimes and viscoelastic properties of ultrastable glasses.

Amorphous solids are viscoelastic. They dissipate energy when deformed at finite rate and finite temperature. We here use analytic theory and molecular simulations to demonstrate that linear viscoelastic dissipation can be directly related to the static and dynamic properties of the fundamental vibrational excitations of an amorphous system. We study ultrastable glasses that do not age, i.e., that remain in stable minima of the potential energy surface at finite temperature. Our simulations show four types of vibrational modes, which differ in spatial localization, similarity to plane waves and vibrational lifetimes. At frequencies below the Boson peak, the viscoelastic response can be split into contributions from plane-wave and quasilocalized modes. We derive a parameter-free expression for the viscoelastic storage and loss moduli for both of these modes. Our results show that the dynamics of microscopic dissipation, in particular the lifetimes of the modes, determine the viscoelastic response only at high frequency. Quasilocalized modes dominate the linear viscoelastic response at intermediate frequencies below the Boson peak.

Dispersion Analysis of Plane Wave Propagation in Lattice-Based Mechanical Metamaterial for Vibration Suppression

Phononic crystals based on lattice structures provide important wave dispersion characteristics as band structures, showing excellent compatibility with additive manufacturing. Although the lattice structures have shown the potential for vibration suppression, a design guideline to control the frequency range of the bandgap has not been well established. This paper studies the dispersion characteristics of plane wave propagation in lattice-based mechanical metamaterials to realize effective vibration suppression for potential aerospace applications. Triangular and hexagonal periodic lattice structures are mainly studied in this paper. The influence of different geometric parameters on the bandgap characteristics is investigated. A finite element approach with Floquet–Bloch’s principles is implemented to effectively evaluate the dispersion characteristics of waves in lattice structures, which is validated numerically and experimentally with a 3D-printed lattice plate. Based on numerical studies with the developed analysis framework, the influences of the geometric parameters of lattice plate structures on dispersion characteristics can mainly be categorized into three patterns: change in specific branches related to in-plane or out-of-plane vibrations, upward/downward shift in frequency range, and drastic change in dispersion characteristics. The results obtained from the study provide insight into the design of band structures to realize vibration suppression at specific frequencies for engineering applications.

Refinement of the Asymptotics of Three Charged Quantum Particles Scattering Problem Solution of the Six-Dimensional Distorted Plane Wave Type

Refinement of the Asymptotics of Three Charged Quantum Particles Scattering Problem Solution of the Six-Dimensional Distorted Plane Wave Type

Enhancing the thermoelectric performance of BiGa2X4 (X=S, Se) P-type semiconductors by optimizing charge carrier concentration or chemical potentials

We present an extensive analysis of the structural, electronic, optical, elastic, and thermoelectric properties of BiGa2X4 compounds, where X represents either sulfur (S) or selenium (Se). Our approach employed the all-electron full potential linearized augmented plane wave (FP-LAPW) technique, offering a comprehensive understanding of these materials' characteristics. The calculated lattice constants (a), the unit cell height (c), and the c/a ratio closely match experimental data, affirming the accuracy of our calculations. A pivotal focus of our study was on the electronic properties, including the indirect bandgaps (A→M−Γ) and (M→A). We found that BiGa2S4 exhibited an indirect bandgap (Eg) of 2.504 eV, while BiGa2Se4 possessed a slightly lower value of 1.878 eV. This variation was primarily attributed to the intricate interactions among bismuth, sulfur, and selenium atoms, particularly involving p−p orbital interactions. Additionally, we explored the optical characteristics of these compounds, determining their maximum absorption wavelengths. BiGa2S4 exhibited an absorption peak at 4.476 eV, whereas BiGa2Se4 displayed a slightly lower maximum absorption at 3.741 eV. Moreover, BiGa2Se4 showcases a higher dielectric constant, which augments its potential for optoelectronic applications. A critical aspect of our research is the assessment of the elastic properties, elucidating that both compounds exhibited fragility and anisotropy. We observed that at 300 K, the lattice thermal conductivity (kL) for BiGa2S4 and BiGa2Se4 was measured at 1.57W/mK and 1.14W/mK, respectively, indicating low thermal conductivity. At 1000 K, both BiGa2S4, and BiGa2Se4 exhibit significant ZT values of 0.8389 and 0.8722, respectively. The ZT values of the p-type semiconductors are notably higher than those of the n-type. At T = 900 K, the optimized ZT values for BiGa2S4, and BiGa2Se4 are found to be 0.82909 and 0.90548, respectively. Achieving these values requires either increasing the concentration of charge carriers to n = 0.11715 x 1022 cm−3 for BiGa2S4 and n = 0.0812 x 1022 cm−3 for BiGa2Se4, or reducing the chemical potentials by 0.40151 Ryd and 0.38001 Ryd, respectively.

Photophoresis of a moderately large high-viscosity droplet in slip mode

Purpose of research. To obtain analytical expressions that allow calculating the strength and velocity of a moderately large, highly viscous droplet, taking into account the direct contribution of the evaporation coefficient, linear corrections by the Knudsen number and the reactive effect of a plane wave moving in the field of mono-chromatic radiationMethods. Methods of perturbation theory, gas kinetic methods, mathematical methods for solving linear partial differential equations with variable coefficients (the system of Stokes equations, Laplace and Poisson equations) were used.Results. In a quasi-stationary approximation, a theoretical description of the photophoretic motion of a moderately large evaporating highly viscous spherical droplet (there is no circulation of matter inside the droplet and interfacial surface tension forces) in a viscous binary gas mixture is carried out. A velocity-linearized system of Navi-Stokes equations and heat and mass transfer was solved. Expressions are obtained for the fields of mass velocity, pressure, temperature and the relative numerical concentration of the first component. The strength and speed of photophoresis of a highly viscous droplet was determined by integrating a stress tensor over the surface of the particle. Under boundary conditions on the surface of a highly viscous droplet, linear corrections in terms of the Knudsen number (isothermal, thermal and diffusion slips, temperature and concentration jumps, as well as sliding due to temperature inhomogeneity along the curved surface of the particle), the reactive effect and the contribution of the direct influence of the evaporation coefficient were taken into account. The contributions to the obtained formulas for the photophoresis of a moderately large highly viscous droplet are analyzed and the preliminary transitions to the results known in the literature (moderately large and large solid particles of spherical shape) are considered Conclusion. The obtained formulas based on the hydrodynamic method allow us to evaluate the effect of the direct contribution of the evaporation coefficient and linear corrections by the Knudsen number on the strength and speed of photophoresis of a moderately large evaporating highly viscous droplet in a binary gas mixture.