Chiral Components Research Articles

Three-Component Betti Condensation for Synthesis of Aminomethylnaphthols Incorporating Deoxy-isoequilenine Scaffold-Absolute Configuration and Application

Chiral aminomethylnaphthols have been prepared highly diastereoselective by means of three-component “Betti condensation”, using steroidal 2-naphthol analogue, synthesized from estrone. The use of 2-methoxybenzaldehyde or 2-pyridinecarboxaldehyde as aldehyde component and (S)-(–)-1-phenylethan-1-amine or (S)-(–)-1-(naphthalen-2-yl)ethan-1-amine, as chiral non-racemic amine component providing the diastereoselectivity, allowed the synthesis of structurally diverse aminomethylnaphthols. The latter easily form 1,3-dihydronaphthoxazines through reaction with formaldehyde. The absolute configurations of the new aminomethylnaphthols synthesized have been determined through advanced nuclear magnetic resonance (NMR) experiments and confirmed by X-ray crystallography. The chiral steroidal aminomethylnaphthols obtained as pure diastereoisomers have been evaluated as pre-catalysts in the enantioselective addition of diethylzinc to aldehydes with enantioselectivities of up to 97% ee.

A chiral pentanidium and pyridinyl-sulphonamide ion pair as an enantioselective organocatalyst for Steglich rearrangement.

Enantioselective ion pair catalysis has gained significant attention due to its ability to exert selectivity control in various reactions. Achiral counterions have been found to play crucial roles in modulating reactivity and selectivity. The modular nature of an ion pair catalyst allows rapid alterations of the achiral counterion to achieve optimal outcomes, without the need to modify the more onerous chiral component. In this study, we report the successful development of a stable chiral pentanidium pyridinyl-sulphonamide ion pair as a nucleophilic organocatalyst for asymmetric Steglich rearrangement. The ion pair catalyst demonstrated excellent performance, leading to enantioenriched products with up to 99% ee through simple alterations of the achiral anions. We conducted extensive ROESY experiments and concluded that the reactivity and enantioselectivity were correlated to the formation of a tight ion pair in solution. Further computational analyses provided greater clarity to the structure of the ion pair catalyst in solution. Our findings reveal the critical roles of NMR experiments and computational analyses in the design and optimisation of ion pair catalysts.

Templating Polymer/Chromophore Crystallization in a Gyroid Matrix

Blending the small molecule nonlinear optical chromophore, 2-chloro-4-nitroanaline (CNA), with a semicrystalline block copolymer, polystyrene-poly(ethylene oxide) (PS-PEO), drives the formation of a bicontinuous cubic microstructure, known as gyroid (GYR), demonstrating Ia3̅d cubic space group symmetry. The morphology transition is due to the selective partitioning of CNA into the PEO domains, which happens to be the majority phase while PS forms the GYR network. Furthermore, PEO and CNA cocrystallize together, forming a single crystalline phase that exhibits a different crystal structure from the starting PEO and CNA materials. At room temperature, PEO crystals and PEO/CNA cocrystals coexist and display different melting temperatures, Tm,PEO = 45 °C and Tm,PEO/CNA = 78 °C, respectively. Interestingly, although the PEO domain is the matrix, the GYR network templates the crystallization of the PEO/CNA cocrystal by precisely controlling the cocrystal long period. Furthermore, circular dichroism (CD) measurements indicate that the crystallized sample contains a chiral component when the PEO/CNA cocrystal is present, and upon melting of the PEO/CNA cocrystal (Tm,PEO/CNA = 78 °C), the CD signal vanishes. The results shown here indicate that adding a small molecule to semicrystalline block copolymer in which one block will form a cocrystal with the small molecule opens the possibility of controlling hierarchical structure and material functionality.

Technical Advances in the Chiral Separation of Anti-diabetic Drugs Using Analytical and Bio-analytical Methods: A Comprehensive Review

Abstract:Chirality seems to be a pivotal technique in the field of science. Research teams are quite well versed in empirical separation, however, at the same time, they are clueless about the evolution of chiral separation. As per the guidelines of the United States Food and Drug Administration (US FDA), chiral drugs must be untangled before they are sold to the public. Stereogenic separation has gained prominence during the last 10 decades due to the disparate biological function of enantiomers in the stereogenic environment. Chiral drugs exhibit a wide range of bioavailability, distribution, and pharmacodynamic properties concomitantly they exert divergent pharmacological and toxicological properties. Enantiomeric chiral products could be considered safe and potent in combating various diseases including metabolic diseases like diabetes. Several studies have delineated the development of a novel analytical and bioanalytical method to detect/segregate/quantify chiral chemical components in medicinal chemistry. The same physicochemical characteristics of enantiomers have been proven to be beneficial to the estrangement of stereogenic compounds. Furthermore, the advancement of bioanalytical methods is also critical to shedding light on the destiny of distinct enantiomers in the biological environment. HPLC (High-Performance Liquid Chromatography) and CE (Capillary Electrophoresis) have been the most commonly employed separation techniques. But the technical advances are required to enhance the efficiency of detection and quantification of chiral molecules on a large scale. The current review delineates the need for the chiral separation of stereogenic antidiabetic drug compounds with technical advances. Furthermore, this research is focused on the enantioseparation of chiral antidiabetic drugs and a brief overview of the analytical and bioanalytical methods conducted on distant chiral antidiabetic drugs to improve the efficiency of chiral separation.

Discrimination of Chiral and Helical Contributions to Raman Scattering of Liquid Crystals Using Vortex Beams.

We use vortex photon fields with orbital and spin angular momentum to probe chiral fluctuations within liquid crystals. In the regime of iridescence with a well-defined pitch length of chirality, we find low energy Raman scattering that can be decomposed into helical and chiral components depending on the scattering vector and the topological charge of the incident photon field. Based on the observation of an anomalous dispersion we attribute quasielastic scattering to a transfer of angular momenta to rotonlike quasiparticles. The latter are due to a competition of short-range repulsive and long-range dipolar interactions. Our approach using a transfer of orbital angular momentum opens up an avenue for the advanced characterization of chiral and optically active devices and materials.

Essential Oil and Non-Volatile Metabolites from Kaunia longipetiolata (Sch.Bip. ex Rusby) R. M. King and H. Rob., an Andean Plant Native to Southern Ecuador.

Kaunia longipetiolata (Sch.Bip. ex Rusby) R. M. King and H. Rob. (Asteraceae) is a plant native to southern Ecuador. The dry leaves afforded, by steam distillation, an essential oil that was qualitatively and quantitatively analyzed by GC-MS and GC-FID, respectively, on two orthogonal columns of different polarity. Sesquiterpenes predominated in the volatile fraction, among which α-zingiberene (19.7-19.1%), ar-curcumene (17.3-18.1%), caryophyllene oxide (5.1-5.3%), (Z)-β-caryophyllene (3.0-3.1%), (2Z,6Z)-farnesal (2.6-3.6%), and spathulenol (2.0-2.1%) were the major components. In addition to the identified compounds, two main unidentified constituents (possibly oxygenated sesquiterpenes) with probable molecular masses of 292 and 230, respectively, were detected. They constituted about 5% and 8% (w/w), respectively, of the whole essential oil. The oil chemical composition was complemented with the enantioselective analysis of ten chiral components. Four scalemic mixtures and six enantiomerically pure terpenes were identified. An enantiomeric excess (ee) was determined for (1R,5R)-(+)-β-pinene (65.0%), (R)-(-)-α-phellandrene (94.6%), (S)-(+)-linalool (15.0%), and (R)-(-)-terpinen-4-ol (33.8%). On the other hand, (1R,5R)-(+)-α-pinene, (1R,5R)-(+)-sabinene, (S)-(-)-limonene, (S)-(+)-β-phellandrene, (1R,2S,6S,7S,8S)-(-)-α-copaene, and (R)-(+)-germacrene D were enantiomerically pure. Finally, the non-volatile fraction obtained by extraction of the leaves with MeOH was investigated. Eight known compounds were isolated by liquid column chromatographic separations. Their structures were determined by NMR spectroscopy as dehydroleucodine, kauniolide, (3S,3aR,4aR,6aS,9aS,9bR)-3-hydroxy-1,4a-dimethyl-7-methylene-5,6,6a,7,9a,9b-hexahydro-3H-oxireno[2',3':8,8a]azuleno[4,5-b]furan-8(4aH)-one, novanin, bisabola-1,10-diene-3,4-trans-diol, (R)-2-(2-(acetoxymethyl)oxiran-2-yl)-5-methylphenyl isobutyrate, eupalitin-3-O-glucoside, and 3,5-di-O-caffeoylquinic acid. Literature data about the identified metabolites indicate that K. longipetiolata is a rich source of biologically active natural products.

Enantioselective Synthesis of Pharmaceutically Relevant Bulky Arylbutylamines Using Engineered Transaminases

AbstractATAs engineered for having an enlarged small binding pocket were applied for the synthesis of enantiomerically pure (R)‐benzo[1,3]dioxol‐5‐yl‐butylamine, a chiral component of human leukocyte elastase inhibitor DMP 777 (L‐694,458). Kinetic resolution of the racemic amine was performed by using the L59A variant of the (S)‐selective ATA from Chromobacterium violaceum (Cv‐ATA), providing the residual (R)‐enantiomer in excellent yield and >99% ee. At moderate enzyme loading and absence of co‐solvent, high volumetric productivity of 0.22 mol L−1 h−1 (42.5 g L−1 h−1) was achieved. Complementarily, the (S)‐enantiomer was generated via kinetic resolution using the (R)‐selective ATA‐117‐Rd11 from Arthrobacter sp. with acetone as the amino acceptor. In an alternative approach, we employed ATA‐117‐Rd11 for the asymmetric amination of the prochiral ketone precursor, which at 86% conversion gave the (R)‐benzo[1,3]dioxol‐5‐yl‐butylamine with excellent >99% ee. We further evaluated the utility of Cv‐ATA L59A for the asymmetric synthesis of pharmaceutically relevant (S)‐1‐phenylbutan‐1‐amine, a chiral component of the deubiquitinase inhibitor degrasyn (WP1130). The enzyme showed good tolerance to high concentrations of isopropylamine, producing (S)‐1‐phenylbutan‐1‐amine in enantiomerically pure form (>99% ee).magnified image

Mixed chiral and achiral character in substituted ethane: A next generation QTAIM perspective

We use the newly introduced spanning stress tensor trajectory Uσ-space construction within next generation quantum theory of atoms in molecules (NG-QTAIM) for a chirality investigation of singly and doubly substituted ethane with halogen substituents: F, Cl, Br. Singly substituted ethane was overall achiral comprising cancelling chiral components in Uσ-space. The resultant axial bond critical point (BCP) sliding responded more strongly to the increase in atomic number of the substituted halogen than the chirality. The presence of the very light F atom was found responsible for a very high degree of achiral character of the doubly substituted ethane.

ϕ meson properties in nuclear matter from QCD sum rules with chirally separated four-quark condensates

The modification of the $\ensuremath{\phi}$ meson spectrum in nuclear matter is studied in an updated QCD sum rule analysis, taking into account recent improvements in properly treating the chiral invariant and breaking components of four-quark condensates. Allowing both mass and decay width to change at finite density, the QCD sum rule analysis determines certain combinations of changes for these parameters that satisfy the sum rules equally well. A comprehensive error analysis, including uncertainties related to the behavior of various condensates at linear order in density, the employed renormalization scale and perturbative corrections of the Wilson coefficients, is used to compute the allowed ranges of these parameter combinations. We find that the $\ensuremath{\phi}$ meson mass shift in nuclear matter is especially sensitive to the strange sigma term ${\ensuremath{\sigma}}_{sN}$, which determines the decrease of the strange quark condensate in nuclear matter. Specifically, we obtain a linear relation between the width ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}$ and mass shift $\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}$ given as ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}=a\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}+b{\ensuremath{\sigma}}_{sN}+c$ with $a=({3.947}_{\ensuremath{-}0.130}^{+0.139})$, $b=({0.936}_{\ensuremath{-}0.177}^{+0.180})$ and $c=\ensuremath{-}({7.707}_{\ensuremath{-}5.679}^{+4.791})\text{ }\text{ }\mathrm{MeV}$.

Non-Abelian bosonization in a (3+1) -d Kondo semimetal via quantum anomalies

Kondo lattice models have established themselves as an ideal platform for studying the interplay between topology and strong correlations such as in topological Kondo insulators or Weyl-Kondo semimetals. The nature of these systems requires the use of nonperturbative techniques, which are few in number, especially in high dimensions. Motivated by this we study a model of Dirac fermions in $(3+1)$ dimensions coupled to an arbitrary array of spins via a generalization of functional non-Abelian bosonization. We show that there exists an exact transformation of the fermions, which allows us to write the system as decoupled free fermions and interacting spins. This decoupling transformation consists of a local chiral, Weyl, and Lorentz transformation parameterized by solutions to a set of nonlinear differential equations, which order by order takes the form of Maxwell's equations with the spins acting as sources. Owing to its chiral and Weyl components this transformation is anomalous and generates a contribution to the action. From this we obtain the effective action for the spins and expressions for the anomalous transport in the system. In the former we find that the coupling to the fermions generates kinetic terms for the spins, a long-ranged interaction, and a Wess-Zumino-like term. In the latter we find generalizations of the chiral magnetic and Hall effects.

Helix-Sense-Selective Polymerization of Achiral Monomers for the Preparation of Chiral Helical Polyacetylenes Showing Intense CPL in Solid Film State.

Polymer-based circularly polarized luminescent (CPL) materials have attracted ever-increasing interest. However, to construct CPL materials from achiral monomers is still a big challenge. Here, a series of chiral helical substituted polyacetylenes are prepared by helix-sense-selective polymerization (HSSP) of achiral acetylenic monomers (achiral monomer + fluorescent monomer). HSSPs are accomplished in a bi-solvent mixture consisting of chloroform and chiral α-pinene (chiral component). Chirality transfers from the chiral component to the helical copolymers during polymerization, thereby endowing the copolymers with helical chirality. The resulting copolymers are then fabricated into blend films which exhibit intense optical activity and CPL. The monomer ratio and the physical state of the copolymers have significant impacts on their chiroptical and CPL properties. The maximum luminescence dissymmetry factor of the blend films can be up to 1.3 × 10-2 . The universality of the established strategy for exploring polymer-based CPL materials is demonstrated by using different achiral fluorescent monomers. The present work opens a novel alternative for developing CPL-active polymeric materials starting from achiral monomers.

Anomalous acoustoelectric effect induced by clapping modes in chiral superconductors

Clapping modes, which are relative amplitude and phase modes between two chiral components of Cooper pairs, are bosonic collective modes inherent to chiral superconductors. These modes behave as long-lived bosons with masses smaller than the threshold energy, $2|\Delta|$, for decay into unbound fermion pairs. Here, we clarify that the real/imaginary clapping modes in chiral superconductors directly couple to acoustic wave propagation when the weak particle-hole asymmetry of the normal state quasiparticle dispersion is taken into account. The clapping modes driven by an acoustic wave generate an alternating electric current, that is, the acoustoelectric effect in superconductors. Significantly, the clapping modes give rise to a transverse electric current. When the sound velocity is comparable to the Fermi velocity, as in heavy fermion compounds, the transverse current is resonantly enhanced at energy below the threshold for continuum excitations. This resonance provides a smoking-gun evidence of chiral superconductivity.

P-Terphenyl-containing symmetric tetraesters for nano-scale pitch ferroelectric liquid crystal materials

Design and studying of derivatives of fluorinated and non-fluorinated p-terphenyl-containing symmetric tetraesters as chiral components (CCs) of ferroelectric liquid crystal (FLC) materials working in deformed helix FLC (DHFLC) mode are described. The tetraesters combine a lactate and alcoholic residues in chiral tails. The new CCs induce short helix pitch (as short as 78 nm) and large spontaneous polarization (PS > 100 nC/cm2) at moderate concentrations (as low as 12 mol. %) in a non-chiral biphenylpyrimidine host. We have studied the effects of the (S)-lactate linker, terminal alkyl chains and fluorine atoms on helix pitch and other useful properties of the chiral tilted smectic (SmC*) phase induced by these CCs in the biphenylpyrimidine host. Depending on positions of the fluorine atoms, the fluorination of the p-terphenyl core shows little effect or even reduces the helical twisting power (HTP) of the CCs. At the same time, modifications in the chiral tails can essentially enhance the HTP and other CC performance characteristics. Thus, the combination of the (S)-lactate linker with a (S)-alkan-2-olic residue results in high HTP (up to 85 μm−1) even without fluorine atoms in the chiral tails. Substitution of the (S)-alkan-2-olic residue with a fluorinated analogue, viz. (R)-1,1,1-trifluoroalkan-2-ol derivative, provides further increase of the HTP in the induced SmC* phase up to the highest known to date value of 101 μm−1.

Second Harmonic Generation Properties in Chiral Sarcomeres of Drosophila Larval Muscles

Polarimetric second harmonic generation (SHG) microscopy is a label-free ultrastructural imaging technique that is applied to study molecular organization in striated muscle structure. Wild type OreR and UNC45 knockdown Drosophila melanogaster somatic larva body wall muscles are used to elucidate the influence of myosin organization on SHG imaging response. Structural changes due to varying myosin content are studied with linear polarization-in polarization-out (PIPO) SHG microscopy. PIPO SHG microscopy revealed changes in the striated pattern of somatic muscles and a reduced signal intensity correlated with reduced order of myosin filaments. The achiral and chiral susceptibility component ratios R- and C-ratios, respectively, were deduced. R-ratio values were higher in the UNC45 knockdown larva mutant compared to control, suggesting that in addition to myosin, another protein structure provide basis for a second harmonic response. The SHG active protein structure is located in the region of isotropic bands of the striated muscles. The measured C-ratio from the muscle fibers appeared to be small. Nonetheless, the wide distribution of C-ratio values of myosin filaments could be observed in the wild-type OreR muscles. Overall, this technique provides insight on how second harmonic properties change with myosin filament structure.

Asymmetric magnetic domain wall motion under lateral and normal space inversion asymmetry with interfacial Dzyaloshinskii–Moriya interaction

The magnetic anisotropy of a typical magnetic sample with an easy axis perpendicular to the surface has many advantages over an in-plane easy axis due to advantages like better thermal stability, higher data storage density, lower energy consumption, etc. The perpendicular magnetic anisotropy arises due to the spatial inversion asymmetry (SIA) at the interfaces between a ferromagnet (FM) and a heavy metal (HM). In such systems, one can achieve a current-induced magnetization reversal (CIMR) via spin–orbit torque with the assistance of an in-plane (IP) magnetic field. This IP field requirement for the CIMR process is an obstacle for the practical application. Recent studies on CIMR at magnetic fields free condition are achieved by breaking the lateral structural symmetry by achieving thickness-gradient in a particular layer. In previous reports, the SIA normal to the surface in a heterostructure leads to an asymmetric contribution as chiral damping. In this work, a system Ta/Pt/CoFeB/Pt with normal and lateral SIA has been prepared by introducing a thickness-gradient in the FM CoFeB layer, which leads to create a tilted perpendicular magnetic anisotropy. The presence of the lateral SIA gives rise to another asymmetric component besides the chiral damping component. In this study, the total asymmetric component of the Ta/Pt/CoFeB/Pt heterostructure has been calculated into two contributions Ht and Hch, to extract the distinct information of the tilt asymmetry due to the lateral SIA and the chiral damping due to the normal SIA, respectively. In this study, by varying the bottom Pt thickness of the Ta/Pt/CoFeB/Pt heterostructures we have observed that the two asymmetry contributions Ht and Hch both decreased with increasing bottom Pt thickness.

A New Essential Oil from the Leaves of the Endemic Andean Species Gynoxys miniphylla Cuatrec. (Asteraceae): Chemical and Enantioselective Analyses

A previously uninvestigated essential oil (EO) was distilled from Gynoxys miniphylla Cuatrec. (Asteraceae) and submitted to chemical and enantioselective analyses. The qualitative and quantitative analyses were conducted by GC-MS and GC-FID, over two orthogonal columns (5%-phenyl-methylpolysiloxane and polyethylene glycol stationary phases). Major constituents (≥2%) were, on both columns, respectively, as follows: α-phellandrene (16.1–17.2%), α-pinene (14.0–15.0%), germacrene D (13.3–14.8%), trans-myrtanol acetate (8.80%), δ-cadinene (4.2–4.6%), β-phellandrene (3.3–2.8%), (E)-β-caryophyllene (3.1–2.0%), o-cymene (2.4%), α-cadinol (2.3–2.6%), and α-humulene (1.7–2.0%). All the quantified compounds corresponded to 93.5–97.3% by weight of the whole essential oil, with monoterpenes counting for 53.8–55.6% of the total, and sesquiterpenes for 38.5–41.4%. For what concerns the enantioselective analyses, the chiral components were investigated through a β-cyclodextrin-based enantioselective column (2,3-diethyl-6-tert-butyldimethylsilyl-β-cyclodextrin). A total of six chiral metabolites were analysed and the respective enantiomeric excess calculated as follows: (1S,5S)-(−)-α-pinene (98.2%), (1S,5S)-(−)-β-pinene (11.9%), (1R,5R)-(+)-sabinene (14.0%), (R)-(−)-α-phellandrene (100.0%), (R)-(−)-β-phellandrene (100.0%), and (S)-(−)-germacrene D (95.5%). According to the chemical composition and enantiomeric distribution of major compounds, this EO can be considered promising as a cholinergic, antiviral and, probably, analgesic product.

SOMSpec as a General Purpose Validated Self-Organising Map Tool for Rapid Protein Secondary Structure Prediction From Infrared Absorbance Data.

A protein’s structure is the key to its function. As protein structure can vary with environment, it is important to be able to determine it over a wide range of concentrations, temperatures, formulation vehicles, and states. Robust reproducible validated methods are required for applications including batch-batch comparisons of biopharmaceutical products. Circular dichroism is widely used for this purpose, but an alternative is required for concentrations above 10 mg/mL or for solutions with chiral buffer components that absorb far UV light. Infrared (IR) protein absorbance spectra of the Amide I region (1,600–1700 cm−1) contain information about secondary structure and require higher concentrations than circular dichroism often with complementary spectral windows. In this paper, we consider a number of approaches to extract structural information from a protein infrared spectrum and determine their reliability for regulatory and research purpose. In particular, we compare direct and second derivative band-fitting with a self-organising map (SOM) approach applied to a number of different reference sets. The self-organising map (SOM) approach proved significantly more accurate than the band-fitting approaches for solution spectra. As there is no validated benchmark method available for infrared structure fitting, SOMSpec was implemented in a leave-one-out validation (LOOV) approach for solid-state transmission and thin-film attenuated total reflectance (ATR) reference sets. We then tested SOMSpec and the thin-film ATR reference set against 68 solution spectra and found the average prediction error for helix (α + 310) and β-sheet was less than 6% for proteins with less than 40% helix. This is quantitatively better than other available approaches. The visual output format of SOMSpec aids identification of poor predictions. We also demonstrated how to convert aqueous ATR spectra to and from transmission spectra for structure fitting. Fourier self-deconvolution did not improve the average structure predictions.

Third-harmonic Mie scattering from semiconductor nanohelices

Chiroptical spectroscopies provide structural analyses of molecules and nanoparticles but they require sample volumes that are incompatible with generating large chemical libraries. New optical tools are needed to characterize chirality for the ultrasmall (<1 µl) volumes required in the high-throughput synthetic and analytical stations for chiral compounds. Here we show experimentally a novel photonic effect that enables such capabilities—third-harmonic Mie scattering optical activity—observed from suspensions of CdTe nanostructured helices in volumes <<1 µl. Third-harmonic Mie scattering was recorded on illuminating CdTe helices with 1,065, 1,095 and 1,125 nm laser beams and the intensity was around ten-times higher in the forward direction than sideways. The third-harmonic ellipticity was as high as 3° and we attribute this effect to the interference of chiral and achiral effective nonlinear susceptibility tensor components. Third-harmonic Mie scattering on semiconductor helices opens a path for rapid high-throughput chiroptical characterization of sample volumes as small as 10−5 µl.

Second-harmonic generation in the surface layer of a dielectric spheroidal particle: I. Analytical solution

The problem of second-harmonic generation by a plane elliptically polarized electromagnetic wave in a thin optically nonlinear surface layer of a dielectric particle shaped as an ellipsoid of revolution is solved. The generalized Rayleigh-Gans-Debye approximation is used for an analytical description with taking into account the difference in refractive indices of the medium corresponding to the frequencies of the exciting and generated radiation. The limiting forms of functions are obtained, with the use of which the electric field strength of the generated radiation is expressed. The order of dependence of these functions on the linear dimensions is found, when the lengths of the semiaxes of the particle are small compared to the wavelength of the exciting radiation and their ratio remains constant. It was found that the power density of the generated radiation in this case is determined to a greater extent by the chiral components of the nonlinear dielectric susceptibility tensor and is proportional to the fourth power of the length of the semiaxis of the particle, if the shape of the spheroidal particle differs significantly from the spherical one. The solution of this problem, obtained by other authors, is supplemented for the possibility of applying to the description of generation in the surface layer of a dielectric particle not only in the form of a prolate, but also in the form of an oblate spheroid. Corrections of inaccuracies and misprints made in similar works by other authors are proposed. The relationships between the formulas used in these works are found, taking into account the corrections and the formulas used in this work. Keywords: second-harmonic generation, dielectric spheroidal particle, generalized Rayleigh-Gans-Debye model, small particle approximation, chiral component.

Генерация второй гармоники в поверхностном слое диэлектрической сфероидальной частицы. I. Аналитическое решение

The problem of second-harmonic generation by a plane elliptically polarized electromagnetic wave in a thin optically nonlinear surface layer of a dielectric particle shaped as an ellipsoid of revolution is solved. The generalized Rayleigh–Gans–Debye approximation is used for an analytical description with taking into account the difference in refractive indices of the medium corresponding to the frequencies of the exciting and generated radiation. The limiting forms of functions are obtained, with the use of which the electric field strength of the generated radiation is expressed. The order of dependence of these functions on the linear dimensions is found, when the lengths of the semiaxes of the particle are small compared to the wavelength of the exciting radiation and their ratio remains constant. It was found that the power density of the generated radiation in this case is determined to a greater extent by the chiral components of the nonlinear dielectric susceptibility tensor and is proportional to the fourth power of the length of the semiaxis of the particle, if the shape of the spheroidal particle differs significantly from the spherical one. The solution of this problem, obtained by other authors, is supplemented for the possibility of applying to the description of generation in the surface layer of a dielectric particle not only in the form of a prolate, but also in the form of an oblate spheroid. Corrections of inaccuracies and misprints made in similar works by other authors are proposed. The relationships between the formulas used in these works are found, taking into account the corrections and the formulas used in this work.