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ImportanceMeibomian gland dysfunction (MGD) is a leading cause of evaporative dry eye disease (DED). Medical and surgical management for DED is limited; therefore, new treatment options are sought.ObjectiveTo evaluate the efficacy and safety of SHR8058 (perfluorohexyloctane) eye drops in Chinese patients with DED associated with MGD through 57 days.Design, Setting, and ParticipantsThis was a randomized, multicenter, double-masked, saline-controlled, phase 3 clinical trial conducted from February 4, 2021, to September 7, 2022. Patients were recruited from the departments of ophthalmology in 15 hospitals in China. Patients with DED associated with MGD were enrolled between February 4 and July 1, 2021. The diagnosis was based on patient complaint of DED symptoms, an ocular surface disease index of 25 or higher, tear film break-up time of 5 seconds or less, Schirmer I test without anesthesia results of 5 mm or more at 5 minutes, total corneal fluorescein staining (tCFS) score of 4 to 11, and an MGD score of 3 or higher.InterventionsEligible participants were randomly assigned 1:1 to receive perfluorohexyloctane eye drops or 0.6% sodium chloride [NaCl]) 4 times per day.Main Outcomes and MeasuresThe primary end points were the changes from baseline in tCFS and eye dryness scores at day 57.ResultsA total of 312 participants were included in the analysis: 156 (mean [SD] age, 45.4 [15.2] years; 118 female [75.6%]) in the perfluorohexyloctane group and 156 (mean [SD] age, 43.7 [15.1] years; 127 female [81.4%]) in the NaCl group. Both primary end points were achieved, ie, changes from baseline at day 57 of tCFS score (mean [SD], −3.8 [2.7] vs −2.7 [2.8]) and eye dryness score (mean [SD], −38.6 [21.9] vs −28.3 [20.8]) in the perfluorohexyloctane group were superior to the control group, with estimated mean differences of −1.14 (95% CI, −1.70 to −0.57; P P P = .003), awareness of DED symptoms (mean [SD] tCFS score, −38.1 [25.1] vs −23.7 [27.6]; P < .001), and frequency of dryness (mean [SD] tCFS score, −43.3 [23.8] vs −29.1 [24.8]; P < .001). Treatment-emergent adverse events occurred in 34 participants (21.8%) and 40 participants (25.6%) in the perfluorohexyloctane and control groups, respectively.Conclusions and RelevanceResults of this randomized clinical trial demonstrate that perfluorohexyloctane eye drops significantly ameliorated the signs and symptoms of DED associated with MGD with a rapid efficacy as well as satisfactory tolerability and safety through 57 days. Findings support the use of these eye drops if results can be confirmed independently and over longer time periods.Trial RegistrationClinicalTrials.gov Identifier: NCT05515471

Analytical formulas for the cross-spectral density matrix of a partially coherent radially polarized Laguerre–Gaussian vortex (PCRPLGV) beam in anisotropic atmospheric turbulence are derived based on the extended Huygens-Fresnel principle. The evolution laws of statistical properties of a PCRPLGV beam in turbulence, such as the average intensity, degree of coherence (DOC) and degree of polarization (DOP), are investigated in detail. It is found that the atmospheric turbulence induces degeneration of the intensity distribution of a PCRPLGV beam on propagation, and some new properties, such as self-shaping and self-rotating, will appear on propagation due to vortex phase. In addition, in order to verify our theoretical results, we combined the complex screen method and multi-phase screens method to simulate the propagation of PCRPLGV beam in atmospheric turbulence. And the studies indicate that the simulation results are consistent with the theoretical predictions. Our results will be useful in some potential applications, such lidar detection, remote sensing and free-space optical communications.

Coupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C4-factor) is introduced to describe t...

BACKGROUND The aim of this study was to explore the role of MIAT (myocardial infarction related transcripts) in diabetic optic neuropathy and its underlying mechanism. MATERIAL AND METHODS QRT-PCR (quantitative real-time polymerase chain reaction) was performed to detect the mRNA levels of MIAT and HSPA5 (heart shock protein 5) in diabetic rat model and high-glucose cultured Muller cells. After the intracellular MIAT level was increased by lentivirus transfection, the proliferation, cell cycle, and apoptosis of Muller cells were measured using the CCK-8 (Cell Counting Kit-8) assay, flow cytometry, and TUNEL (terminal deoxynucleotidyl transferase (TdT)-mediated dUTP nick-end labeling) assay, respectively. Mechanisms underlying the MIAT-related apoptosis were explored by Western blot analysis. The binding condition of microRNA-379 to MIAT and HSPA5 was confirmed by luciferase reporter gene assay. RESULTS Both MIAT and HSPA5 levels were remarkably increased in high-glucose cultured Muller cells. After transfected with LV (lentivirus)-MIAT, Muller cells showed a decreased proliferation and an enhanced apoptosis with the increased expressions of pro-apoptotic proteins. However, no remarkable changes were observed in cell cycle. Further mechanistic studies found that MIAT regulated HSPA5 expression by directly binding to microRNA-379. CONCLUSIONS MIAT was overexpressed in the diabetic optic nerve. MIAT overexpression remarkably promoted the apoptosis of Muller cells by adsorbing microRNA-379 and thus regulating HSPA5, which was a direct target of microRNA-379.

Statistical properties of an electromagnetic anomalous vortex (EAV) beam with orbital angular momentum (OAM) through a turbulent atmosphere are studied. Analytical formulae for the average intensity (AI) and degree of polarization (DOP) of EAV beam in a strong turbulence are derived. Accurate analytical formulae (without any approximations) for M2-factor of EAV beam under all turbulence conditions are also derived based on the second-order moments of the Wigner distribution function. Numerical results show that the transverse distributions for AI of EAV beam depend mainly on topological charge, beam order and structure constant of turbulence. An anomalous result is found that the on-axis intensity is larger for an EAV beam in a stronger turbulence (i.e., larger structure constant and smaller inner scale). Inner scale effects of DOP of the EAV beam in strong turbulence are also investigated. Off-axis DOPs of an EAV beam will appear oscillation near the propagation axis. It can be also found that M2-factor of an EAV beam propagating through the strong and weak turbulence are smaller for smaller transverse coherent length and structure constant of turbulence, larger beam order, topological charge and inner scale of turbulence.

An analytical formula that relates the molecular constants of the Herzberg expression and experimental transition lines is developed herein with a difference algebraic approach (DAA) model. Based on the data-driven strategy, the DAA model is able to deal with the tiny uncertainties that exhibit behind the experimental transition lines, which is applied to the P branch emission spectra of some first overtone bands of the ground electronic state of 12C16O. The relationship can be used to generate transition lines with sufficient accuracy, as evident from the high J of agreement with the HITRAN database, Velichko data, Goorvitch data and quantum-mechanical data. In addition, line intensities, absorption oscillator strengths and Einstein A coefficients of these lines, which are introduced to enhance the dataset and are in good agreement with those of other authors, are also reported to validate our results. These various comparative results show that the proposed data-driven strategy based on the DAA model is expecting to be a good algorithm that relies on relatively limited data for training.

Based on the model- and data-driven strategy, a spectroscopy learning method that can extract the novel and hidden information from the line list databases has been applied to the R branch emission spectra of 3–0 band of the ground electronic state of 12C16O. The labeled line lists such as line intensities and Einstein A coefficients quoted in HITRAN2020 are collected to enhance the dataset. The quantified spectroscopy-learned spectroscopic constants is beneficial for improving the extrapolative accuracy beyond the measurements. Explicit comparisons are made for line positions, line intensities, Einstein A coefficients, which demonstrate that the model- and data-driven spectroscopy learning approach is a promising and an easy-to-implement strategy.

The structural, electronic and magnetic properties of AgnSc (n = 1-16) clusters have been studied on the basis of density functional theory and the CALYPSO structure prediction method. The optimized geometry exhibits that the growth process of Sc-doped silver clusters have a periodic structural change. The Ag atom grows around a basically invariant cluster core in each growth cycle. The Sc atom has a tendency to occupy the most highly coordinated position in the ground state. The infrared spectra, Raman spectra and photoelectron spectra of AgnSc clusters are forecasted and can be used to identify the structures of these clusters from experiments. The global maxima of the dissociation energy, the averaged binding energy and the gap of the energy level occur at n = 15 for the most stable AgnSc clusters, implying that the Ag15Sc can be perceived as a superatom. The magnetism analysis indicates that the magnetic moment of the Sc atom in AgnSc clusters decreases with the increase of the cluster. The change of the magnetic moment is proportional to the charge transfer between the Sc and Ag atoms.

The structural, electronic, and magnetic properties of Ag n V (n = 1–12) clusters have been studied using density functional theory and CALYPSO structure searching method. Geometry optimizations manifest that a vanadium atom in low-energy AgnV clusters favors the most highly coordinated location. The substitution of one V atom for an Ag atom in Ag n + 1 (n ≥ 5) cluster modifies the lowest energy structure of the host cluster. The infrared spectra, Raman spectra, and photoelectron spectra of Ag n V (n = 1–12) clusters are simulated and can be used to determine the most stable structure in the future. The relative stability, dissociation channel, and chemical activity of the ground states are analyzed through atomic averaged binding energy, dissociation energy, and energy gap. It is found that V atom can improve the stability of the host cluster, Ag2 excepted. The most possible dissociation channels are Ag n V = Ag + Ag n − 1V for n = 1 and 4–12 and Ag n V = Ag2 + Ag n − 2V for n = 2 and 3. The energy gap of Ag n V cluster with odd n is much smaller than that of Ag n + 1 cluster. Analyses of magnetic property indicate that the total magnetic moment of Ag n V cluster mostly comes from V atom and varies from 1 to 5 μ B. The charge transfer between V and Ag atoms should be responsible for the change of magnetic moment.

The evolution law of arbitrary order moments of the Wigner distribution function, which can be applied to the different spatial power spectra, is obtained for partially coherent general beams propa...

The main purpose of this paper is to study the beam spreading and M 2 -factor of electromagnetic Gaussian Schell-model (EGSM) beam through inhomogeneous atmospheric turbulence. The analytical formulas for the root-mean-square (rms) spatial width, rms angular width, M 2 -factor of EGSM beam in turbulence are derived by using the second-order moments of the Wigner distribution function and extended Huygens-Fresnel integral. Our results show that the relative M 2 -factor of EGSM beam decreases with decreasing of zenith angle, initial coherence lengths and initial degree of polarization and with increasing of beam widths and inner scale. It is also shown that as the zenith angle is equal to π/6, the saturated propagation distances of the relative rms angular width, the relative rms spatial width, and the relative M 2 -factor are about 0.3 km, 3 km and 20 km, respectively. And it also can be found that the relative M 2 -factor becomes small when the initial degree of polarization closes to 0.

The effects of different micro-vibrational motions of sulfur oxide on its thermodynamic properties have been carried out. The theoretical full set of vibrational levels {Eυ} and the maximum vibrational quantum number υmax of the ground electronic state X3Σ− of SO molecule are obtained using the variational algebraic method (VAM) for vibrational motions. In the temperature range of 300–4000 K, the molar internal energies, the molar entropy and the vibrational heat capacities are studied by implementing the VAM vibrational energies to the classical statistical thermodynamic formulae. Compared with credible experimental data, the VAM thermodynamic results are better consistent with the experiment than the traditional simple harmonic oscillator (SHO) model and the configuration interaction (CI) calculations.

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence paramet...

Process errors of dielectric gratings are divided into two classes: shape errors and dimension errors. A theoretical model of dielectric gratings with process errors has been proposed, and a beam propagation model of a transmission spectral-beam-combining (T-SBC) system has further been developed based on the process error model. Beam characteristics such as intensity distribution, beam width, beam quality, and combined power in T-SBC systems have been calculated and analyzed. The results show that shape errors make output power oscillated but have little impact on beam qualities of combined beams. The combined power for equal fill factor error yields the highest tolerance among shape errors. Dimension errors degrade both the power and beam quality of the combined beam.

The role that zerovalent nickel plays in catalyzing the trimerization of butadiene to 1,5,9-cyclododecatriene conveys interest in the properties of the tris(butadiene)metal complexes (C4H6)3M. In this connection the complexes (C4H6)3M (M = Ti-Ni) of the first-row transition metals have been investigated by density functional theory. The intermediate C12H18Ni which has been isolated in the nickel-catalyzed trimerization of butadiene but is too unstable for X-ray crystallography is suggested here to have an open-chain hexahapto η3,3-C12H18 ligand rather than the octahapto such ligand suggested by some investigators. The lowest energy (C4H6)3M structures of the other first-row transition metals from vanadium to cobalt are found to have related structures with open-chain C12H18 ligands having hapticities ranging from four to eight with hexahapto structures being most common. The nickel and cobalt (C12H18)M derivatives favor low-spin singlet and doublet spin states, respectively, whereas the manganese derivative (C12H18)Mn favors the high-spin sextet state corresponding to the half-filled d5 shell of Mn(II). A (C4H6)3Cr structure with three separate tetrahapto butadiene ligands analogous to the very stable (η4-C4H6)3M (M = Mo, W) with the favored 18-electron metal configuration is found to be a very high energy structure relative to isomers containing an open-chain C12H18 ligand.

We skillfully combined the cosine theorem with the second moment theory and the Wigner distribution function and derived the analytical expressions of the propagation factor ( M 2 -factor) of a partially coherent radially polarized vortex beam (PCRPVB) in atmospheric turbulence. Then, we comparatively studied the propagation factors of a PCRPVB and a partially coherent electromagnetic vortex beam (PCEVB) in atmospheric turbulence. The results show that a PCRPVB has a smaller value of a relative M 2 -factor than a PCEVB, which means that a PCRPVB has a stronger ability to resist atmospheric turbulence than a PCEVB. To confirm our theoretical studies, the hyperbolic fitting method is combined with the random phase screen (RPS) to simulate the M 2 -factor of a PCRPVB and a PCEVB through atmospheric turbulence. The study results indicate that the theoretical values agree well with the simulated values. Our results may find applications in free-space optical communications and remote sensing.

Propagation formulae for M2-factor and beam wander of partially coherent electromagnetic hollow Gaussian (PCEHG) beam in non-Kolmogorov turbulence are derived based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function. Our results indicate that the normalized M2-factors of PCEHG beam with larger beam order, waist width, inner scale of turbulence, the generalized exponent parameter, and smaller transverse coherent widths, outer scale of turbulence, the generalized structure parameter are less affected by the turbulence. The root mean square beam wander and relative beam wander are more obvious for PCEHG beam with smaller beam order, larger inner and outer scales of turbulence, exponent parameter, transverse coherent widths, and the generalized structure parameter. What is more, the beam wander properties of PCEHG beam in non-Kolmogorov turbulence are very different from M2-factor and spreading properties of beam in turbulence.

Analytical formulae are derived for the propagation factors (M2-factors) of standard Laguerre Gaussian (SLG) beam and elegant Laguerre Gaussian (ELG) beam in non-Kolmogorov turbulence based on the extended Huygens-Fresnel principle and second order moments of the Wigner distribution function. The M2-factors of SLG beam and ELG beam in non-Kolmogorov turbulence have been discussed numerically and comparatively. It is shown that the relative M2-factors of ELG beam are more affected by the turbulence and keep the better beam quality in comparison with that of SLG beam. Furthermore, the normalized M2-factors of SLG beam and ELG beam with higher orders, longer wavelength, larger waist width, larger inner scale of turbulence and the generalized exponent parameter, smaller outer scale of turbulence and smaller the generalized structure parameter are less affected by the non-Kolmogorov turbulence.

Based on the extended Huygens-Fresnel principle (EHFP) and the definition of the Wigner distribution function (WDF), the propagation properties of partially coherent standard Hermite-Gaussian beams (SHGBs) and elegant Hermite-Gaussian beams (EHGBs) in inhomogeneous atmospheric turbulence have been investigated. The M2-factor, the curvature radius and the root-mean-square (rms) angular width of partially coherent SHGBs and EHGBs have been explored numerically and comparatively. It can be found that the saturation propagation distances (SPDs) of the M2-factor and the rms angular width of EHGB and SHGB in inhomogeneous turbulence with a small zenith angle of π/6 are about 20 km and 0.3 km, respectively. What’s more, the M2-factor and the curvature radius of the partially coherent EHGB are smaller than that of the partially coherent SHGB in inhomogeneous turbulence. It can be shown that the M2-factor and curvature radius depend on the zenith angle, coherence width, inner scale of the turbulence, beam order, wave number and waist width in inhomogeneous turbulence. Furthermore, it is found that the partially coherent SHGB and EHGB have the same rms angular width in inhomogeneous turbulence.

Based on the extended Huygens–Fresnel principal and the Wigner distribution function, the root mean square (rms) angular width and propagation factor (M2-factor) of partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam propagating through atmospheric turbulence along a slant path are studied in detail. Analytical formulae of the rms angular width and M2-factor of PCAEHG beam are derived. Our results show that the rms angular width increases with increasing of wavelength and zenith angle and with decreasing of transverse coherence length, beam waist sizes and inner scale. The M2-factor increases with increasing of zenith angle and with decreasing of wavelength, transverse coherence length, beam waist sizes and inner scale. The saturation propagation distances (SPDs) increase as zenith angle increases. The numerical calculations also indicate that the SPDs of rms angular width and M2-factor for uplink slant paths with zenith angle of π/12 are about 0.2 and 20 km, respectively.

The propagations of a partially coherent dark hollow beam (PC-DHB) through the atmospheric turbulence along a slant path (i.e., inhomogeneous atmospheric turbulence) are investigated. Analytical propagation formulae for the average intensity and spreading of PC-DHB in inhomogeneous turbulence are derived based on the extended Huygens-Fresnel integral. It is shown that the dark area of PC-DHB in inhomogeneous turbulence will drop more rapidly with the increase of propagation distance, and the evolution from a DHB to Gaussian beam becomes quicker for a smaller waist width, lower beam order, smaller inner scale of the turbulence and transverse coherence length, and larger zenith angle. Furthermore, PC-DHB spreads in inhomogeneous turbulence more rapidly than the free space, and the saturation propagation distance (SPD) of relative spatial spreading for uplink slant paths with zenith angles of 45° or less is about 5 km. The relative spreading becomes quicker for the larger waist width and zenith angle, lower beam order, smaller parameter p and inner scale of the turbulence.

Propagation properties including mean-squared beam width, mean-squared angular spreading, beam propagation M 2 -factor and turbulence distance of partially coherent Sinh-Gaussian (ShG) beams in non-Kolmogorov atmospheric turbulence have been investigated. With a non-Kolmogorov spectrum, the analytical formulas for the mean-squared beam width, angular spreading and M 2 -factor have been derived in non-Kolmogorov turbulence. The impact of the turbulent parameter (spectral index, inner scale and outer scale) and the decentered parameter on partially coherent ShG beams is discussed by numerical methods. It can be shown that the mean-squared beam width, angular spreading and M 2 -factor increase then decrease with increasing spectral index from 3 to 4; and they decrease with increasing inner scale and decreasing outer scale. The turbulence distance decreases then increases with increasing spectral index, and increases with increasing inner scale and decreasing outer scale. In addition, the mean-squared beam width and the M 2 -factor decrease then increase and exist a minimum values with increasing decentered parameter, while the turbulence distance increases monotonously.

The spreading and M 2 -factor of partially-coherent anomalous hollow (PCAH) beam in the turbulent atmosphere are studied in detail based on the extended Huygens – Fresnel principle. Analytical formulae of the root-mean-square (rms) spatial width, rms angular width, curvature radius of wave plane and propagation factor (M 2 -factor) of PCAH beam in turbulent atmosphere are obtained, respectively. It is found that the spatial and angular sizes of PCAH beam spreads rapidly in the strong turbulence than the weak turbulence and the free space. Beam spreadings and curvature radius of PCAH beam depend on initial beam widths, coherence length, wavelength and turbulence. The smaller M 2 -factor depends on the larger transverse coherence length, wavelength and inner scale of turbulence, and the weak turbulence.

Propagation properties of a partially coherent dark hollow beam (PC-DHB) in inhomogeneous atmospheric turbulence are studied in detail. Analytical formulae for the root-mean-square (rms) spatial width, rms angular width, M2-factor of PC-DHB in inhomogeneous turbulence are derived based on the extended Huygens–Fresnel integral. It is found that PC-DHB spreads in inhomogeneous turbulence more rapidly than the free space, and the saturation propagation distances (SPDs) of relative spatial and angular spreadings for uplink slant paths with zenith angles of 45° or less are about 5 and 0.6 km, respectively. M2-factor of PC-DHB in turbulence depends on beam order, waist width, inner scale of the turbulence and the SPD of the normalized M2-factor for the propagation with zenith angles of 45° or less is about 30 km. Our results are useful for the free space optical communications and the beam propagation in the slant path.

The properties of standard Laguerre–Gaussian beam (sLGB) and elegant Laguerre–Gaussian beam (eLGB) through the misaligned complex hard edge apertures (MCHEAs) are investigated. Analytical formulae for the far field distributions of sLGBs and eLGBs through the different hard edge apertures are derived based on the generalized Huygens–Fresnel diffraction integral equation. The propagation properties and beam qualities of sLGBs and eLGBs are studied comparatively. It is shown that the divergence angle of sLGBs with the low order modes is less than that of eLGBs. However, the energy distributions of eLGBs with the high order modes after through the multiple hard edged apertures are more convergent in comparison with sLGBs, and eLGBs have the better beam quality than sLGBs. The study results are useful for the propagations and applications of sLGBs and eLGBs through the complex optical systems.

Statistical properties of partially coherent vector beams propagating through anisotropic non-Kolmogorov atmospheric turbulence have attracted a large quantity of interest in recent years. Here, we show that the partially coherent vector Gaussian Schell-model (PCVGSM) beams for different initial correlation lengths will appear splitting phenomenon in turbulence, and the distribution of degree of coherence gradually evolves into circularly symmetric distribution with increasing propagation distance. We find that the distribution of degree of polarization of PCVGSM beam displays four petals pattern. It can also be found that the PCVGSM beam still keeps linearly polarized through turbulence without initial phase difference. In spite of this, it will gradually evolve into an elliptically polarized beam in turbulence by controlling the initial correlation lengths and the correlation coefficient. Our results are of great significance to detect and image for atmospheric lidar.

The calculation results of the R-branch transition emission spectra of (0–0) band of the A 2 1 → X 2 1 transition system of SbNa molecule are presented in this paper. These R-branch high-lying transitional emission spectral lines are predicted by using the difference converging method (DCM). Our results show excellent agreement between DCM spectral lines and the experimental values, and the deviations are controlled within 0.0224 cm−1. What is more, based on the principle of over-determined linear equations, the prediction error is quantified in this work, which provides reliable theoretical support for our predicted DCM calculations. This work provides a lot of useful information for understanding the microstructure of SbNa molecule.

Based on the diffraction theory, the diffraction properties of the beam generated by Gaussian mirror through the misaligned optical system with aperture are studied in detail. Two methods are used for solving the light field of the beam generated by Gaussian mirror through the misaligned optical system. Two analytical expressions derived by two different methods are consistent approximately when the diffraction aperture is very small. The numerical examples show that the diffraction beam will deviate obviously from the beam center when the misalignment line deviation and angle deviation are too large. M2-factor of the beam generated by Gaussian mirror is given by the numerical calculations. Therefore, the results can provide the references for studying the optical properties of the beam generated by Gaussian mirror.

The line deviations and angle deviations of the injected beam at the resonator mirrors in the large area discharge CO2 laser (LADCL) are changed when the output mirror and the phase-locking mirror (PLM) are misaligned. The equiphase surfaces excited by the injected beam are different in the laser resonator and the effect of phase-locking will be influenced. It is shown that the misalignment of PLM is the main cause of phase-locking range reduction. The misalignment of the output mirror will mainly result in the deviation of the output beam, and the misalignment of the PLM will mainly cause decrease of the light intensity. And the maximum misaligned angle should not exceed 20 s in order to obtain the ideal effect of phase-locking. The calculated results can provide references for studying deeply the misalignment of LADCL.

A concise and convenient analytical formula without any spectral constant is derived from the conventional expression of R-branch transitional energies for calculating the R-branch high-lying rovibrational emission spectral lines of diatomic molecule. This is based on the thought of Sun's difference converging method (DCM) in 2011. This formula can correctly predict the high-lying transitional emission spectral lines only using 11 known experimental transition lines and a set of physical criteria when any spectral constants of the system are not available. Furthermore, a new method for analyzing the accuracy of prediction with the improved formula is proposed, which point out the core problem of the predicted spectrum and give a quantitative conclusion on the reliability of our work. In this work, the new method is applied to study the R-branch transitional emission spectra of the (0–0) band of the A20+ → X10+ and A20+ → X21 transition systems of BiLi molecule. A series of experimental and theoretical comparisons and discussions show that under the condition of lack of any spectral constants, our method can still use 11 known experimental transition spectral data to reproduce the R-branch emission spectral lines reliably including the high excited rovibrational transition spectral lines.

Analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M2-factor of partially coherent standard Laguerre Gaussian beams (PC-SLGBs) and partially coherent elegant Laguerre Gaussian beams (PC-ELGBs) in inhomogeneous turbulent atmosphere have been derived. The propagation properties of PC-SLGBs and PC-ELGBs in inhomogeneous atmospheric turbulence are studied numerically and comparatively. It can be found that the propagation of laser beams in inhomogeneous turbulence is different from that in homogeneous turbulence. It is also shown that relative rms spatial widths and M2-factors of PC-ELGBs are more affected by inhomogeneous turbulence than those of PC-SLGBs. Moreover, the relative rms spatial widths and M2-factors of PC-SLGBs and PC-ELGBs in inhomogeneous turbulent atmosphere are closely related with waist widths, coherence widths, zenith angles, inner scales, and beam orders. Furthermore, the saturation propagation distance of the relative M2-factor and rms angular width with zenith angles of π/6 are 20 km and 0.5 km, respectively.

Msup2/sup-factor and root-mean-square (rms) angular width of partially coherent flat-topped (PCFT) beams propagating through inhomogeneous atmospheric turbulence are studied based on the extended Huygens-Fresnel principle and the Wigner distribution function (WDF). It is shown that the effect of turbulence on the PCFT beams can be neglected as the vertical height increases, which is different from the homogeneous turbulence. Analytical formulae of the Msup2/sup-factor and rms angular width of PCFT beams have been given. The saturation propagation distances (SPDs) increase with increasing zenith angle. It can be seen that the SPDs of the Msup2/sup-factor and rms angular width of PCFT beams propagating through inhomogeneous atmospheric turbulence are about 30 km and 0.5 km, respectively, when the zenith angle is π/4. It can be found that the Msup2/sup-factor increases with increasing beam order and zenith angle, and with decreasing waist width, inner scale, wavelength, and transverse coherence length. The rms angular width increases with increasing beam order, wavelength, and zenith angle, and decreasing waist width, inner scale, and transverse coherence length.

Nitric oxide (NO) is one of atmospheric molecules of interest and has attracted considerable attention due to its important role in the chemical process taking place in a flow field of hypersonic vehicle, in which the thermodynamic properties are required in the calculation of the aerothermodynamic flow field. Moreover, the total internal partition function is the key to calculating the thermodynamic properties of high-temperature gases. For diatomic molecules, according to the product approximation, the total internal partition function is split into three parts: electronic, vibration and rotation partition function. In this paper, by using the quantum statistical ensemble theory based on some classical thermodynamic and statistical formulae, the thermodynamic properties of NO are analyzed and discussed.Firstly, in order to obtain an accurate energy of molecule, the variational algebraic method (VAM) is employed to calculate the full vibrational energy, the resultis in good agreement with the experimental result and thus yielding the realistic predictions of the unobserved higher vibrational energy that converges to the dissociation limit. Secondly, an attempt is to use the full VAM vibrational energy, the Rydberg-Klein-Rees (RKR) vibrational energy, the simple Harmonic oscillator (SHO) model and the quantum-mechanical vibrational energy obtained by the multiconfiguration self-consistent-field (MCSCF) to calculate the vibrational partition function. Then, with the rotational contributions from the Müller-McDowell formula, the internal partition function can be determined by combining the product of electronic, vibration and rotation partition functions. Thirdly, according to the thermodynamic and statistical formulae, it is easy to calculate the internal energy, entropy and heat capacity for the NO molecule in a range of 1000－5000 K. Comparison of different calculated heat capacities with the experimental ones reveals the heat capacity, of which vibrational contributions determined by the full VAM vibrational energy accord better with the experimental ones, with the maximum relative error being no more than 2.4%, whereas it can be seen that those thermodynamic results evaluated from the SHO model attest to a failure for the summation of infinite vibrational energy. The thermodynamic results of NO may have proper applications in areas that can be of great importance in theoretical and (or) experimental aspects.

The phase-locking of the radial array CO 2 laser (RAL) is introduced based on the injection-locking principle. The characteristic parameters of laser beams used in the phase-locking are described, and the coupling coefficient c 00 between the injected mode and the eigenmode of RAL is calculated. The laser modes from RAL are the low-order Hermite Gaussian modes due to the diffraction loss. The analytical formula for the output beam through an ABCD optical system is derived according Collins formula. The numerical examples are given to illustrate our analytical results.