[Progress on historical evolution, clinical application, and pharmacological effects of Dachaihu Decoction and predictive analysis of its quality markers].

Dachaihu Decoction is a classic prescription with the function of harmonizing Shaoyang and purging away internal stasis of heat, which was specially developed by Master ZHANG Zhongjing for the concurrent disease of Shaoyang and Yangming. A large number of international studies have shown that Dachaihu Decoction has liver protection, gallbladder benefit, anti-inflammatory, and other pharmacological effects and is mostly used in modern clinical treatment of acute pancreatitis, acute cholecystitis, cholelithiasis, and other digestive diseases. This paper combined bibliography and statistics and selected the ancient book database and CNKI database to search the relevant literature on Dachaihu decoction, verify the composition and dosage, processing method, main diseases, and modern clinical application, and predict its quality markers(Q-markers) based on the "five principles" of Q-markers. The results suggest that saikosaponin a, baicalin, and 6-gingerol can be selected as potential Q-markers for Dachaihu Decoction, so as to provide a basis for the clinical research of traditional Chinese medicine and the development and application of compound preparations.

Focusability of coherently combined beams propagating downwards in the turbulent atmosphere.

The focusability of coherently combined beams (CCBs) propagating from orbit through the turbulent atmosphere to the ground is studied, where the diffraction, self-focusing and turbulence effects are considered. It is shown that the spot size on the ground of CCBs is much smaller than that of incoherently combined beams (ICBs). The analytical expression of the B integral of CCBs propagating in the turbulent atmosphere is derived, and an effective design rule for the CCB power transportation without filamentation is presented. It is found that the focusability of CCBs propagating in the turbulent atmosphere can be improved by the gradient power distribution method, and the spot size on the ground can always be reduced below the diffraction limit. Furthermore, the optimal gradient power distribution to reach the highest focusability on the ground without filamentation is presented.

Analytical propagation formulae of spectrally combined laser beams in nonlinear Kerr media.

The analytical propagation formulae of spectrally combined laser beams (SCLBs) in nonlinear Kerr media are derived, and the analytical expression of the ratio of the effect of the photorefractivity to the diffraction of SCLBs propagating in nonlinear Kerr media is also obtained. The validity of the analytical propagation formulae of SCLBs in nonlinear Kerr media is confirmed, and the error of the analytical propagation formulae is also discussed. It is shown the calculation time is reduced greatly by using the analytical propagation formulae. Therefore, a useful method is presented to study the propagation of SCLBs in nonlinear Kerr media.

Rotating anisotropic rectangular hollow Gaussian array.

A new class of partially coherent sources that can produce stable rotating anisotropic rectangular hollow Gaussian array profiles in the far field is presented. The cross-spectral density function and the spectral density of this kind of source on the propagation are derived, and its propagation characteristics, which are quite different from twisted Gaussian Schell-model beams, are discussed. The results show that each hollow lobe in the array tends to rotate around the axis during propagation. In addition, the dimension of the array, the distance between the lobes of the array, and the number of rows and columns of the rectangular array can be flexibly manipulated by adjusting the source parameters. Our work may provide a method to generate rotating anisotropic array beams with hollow lobes, which could have certain reference values in optical manipulation.

Equivalence theorem for the spectral density of light waves scattered from different types of anisotropic media.

The spectral density equivalence theorem of light waves on scattering from different types of anisotropic media is discussed. The possibility of producing identical spectral density distribution as light waves are scattered by different anisotropic media is also discussed. Moreover, the conditions under which a determinate anisotropic medium and random anisotropic medium may produce identical spectral densities are obtained. It is shown that the complete equivalence theorem in whole space or the partial equivalence theorem in some special planes can be realized under particular conditions.

Degree of paraxiality of a twist electromagnetic Gaussian Schell-model beam.

The definition of the degree of paraxiality (DOP) for a stochastic electromagnetic field is applied to a twist stochastic electromagnetic field. As an illustrative example, DOP for a wide class of model stochastic fields, i.e., twist electromagnetic Gaussian Schell-model (TEGSM) fields, is discussed. The dependence of the DOP of the light source on its properties is also studied in detail. The numerical results show that the DOP of a TEGSM beam is determined by the rms widths of auto-correlation functions and the twist factor as well as by the degree of polarization. To explain the behavior of DOP, the far-field divergence angle of this beam source is also discussed.

Hollow rectangular multi-Gaussian Schell-model array source.

A partially coherent light source called a hollow rectangular multi-Gaussian Schell-model array (HRMGSMA) is introduced. The relations between the spectral density of the far field and the characteristics of the source are discussed in detail. It is shown that the characteristics of the arrays, including the hollow size, shapes of the arrays and lobes, quantities of rings and lobes, and directions of lobes, can be adjusted flexibly by changing the related parameters of the HRMGSMA source.

Influence of Kerr nonlinearity on propagation characteristics of twisted Gaussian Schell-model beams.

The analytical propagation formulae of twisted Gaussian Schell-model (TGSM) beams through nonlinear Kerr media are derived. It is found that a TGSM beam is less sensitive to Kerr nonlinearity than a Gaussian Schell-model (GSM) beam. Furthermore, the propagation characteristics of TGSM beams with stronger twist and worse spatial coherence are less affected by Kerr nonlinearity. The self-focusing effect enhances the beam twist, but degrades the beam spatial coherence. In the atmosphere (one kind of self-focusing media), a TGSM beam has greater resistance to self-focusing effects and atmospheric turbulence effects than a GSM beam or an ideal Gaussian beam.

Hard-aperture effect on self-focusing of high-power laser beams propagating in the atmosphere.

The hard-aperture effect on self-focusing of high-power laser beams propagating from the ground through the atmosphere to space orbits is studied. It is shown that the spot size on the target increases as the truncation parameter decreases and the beam power increases. However, as the truncation parameter decreases, the apertured laser beam is less affected by self-focusing. On the other hand, two effective design rules are presented to optimize the intensity on the target, i.e., the optimal power and the optimal focal length. It is proven that the self-focusing effect and the hard-aperture effect both can be compensated by applying the optimal initial beam defocusing. It is also found that the higher maximum intensity on the target will occur by applying the optimal focal length rather than the optimal power.

Degree of paraxiality of an electromagnetic fractional multi-Gaussian Schell-model beam.

The degree of paraxiality (DOP) of an electromagnetic fractional multi-Gaussian Schell-model (EM-FMGSM) beam is discussed, and the effect of the properties of the light source on its DOP is also studied. It is shown from the numerical results that the DOP of an EM-FMGSM beam is determined by the rms widths of the auto-correlation functions, the truncated parameter, the degree of polarization, and the boundary characteristics of its source. Moreover, the far-field divergence angle of the beam source is also investigated to illustrate the behaviors of the DOP.

Self-focusing effect on the beam quality of Hermite-Gaussian beams propagating upwards through the inhomogeneous atmosphere.

The self-focusing effect on the beam quality of Hermite-Gaussian beams propagating upwards through the inhomogeneous atmosphere is studied. The analytical formula of the beam width is derived, and its validity is confirmed. Furthermore, the analytical formulas of the actual focal length and M2-factor are also derived. It is found that the self-focusing effect in the inhomogeneous atmosphere results in beam quality degradation. Under the same initial beam width and the same beam power, as the beam order m increases, the actual focal length is farther away from the target, and the spot size on the target and the M2-factor increase; namely, the beam quality degrades further. In addition, it is shown that the beam quality can be improved by the phase compensation.

Characteristics of high-power partially coherent laser beams propagating upwards in the turbulent atmosphere.

The characteristics of high-power partially coherent laser beams propagating upwards in the turbulent atmosphere are studied, where the principal features of diffraction, nonlinear self-focusing and turbulence are considered. Based on the "thin window" model, the analytical propagation formulae are derived by using the quadratic approximation of the nonlinear phase shift. It is found that the turbulence effect plays an important role in beam propagation characteristics. But the turbulence and self-focusing effects can be suppressed by increasing the laser elevation. Furthermore, the influence of laser elevation on the turbulence effect is stronger than that on the self-focusing effect, and influence of laser elevation on the self-focusing effect is stronger than that on the diffraction effect. In particular, the optimal focal length and wavelength are proposed to decrease the beam spot size on the target.

Manipulating far-zone scattered field by convolution of different types of weight function.

A method of convolution of two weight functions to design new types of scattering medium is proposed, and two novel media models are illustrated in detail. The first one is that the two functions involved in convolution are the same type with different parameters. In this case, the far-zone scattered spectral intensity will maintain a stable shape, but the profile size can be controlled by changing the value of parameters. The second one is that the two functions involved in convolution are different types. In this case, the profile of far-zone scattered spectral intensity depends not only on the type of the weight functions but also on the value of the parameters in each weight function. By examining the scattered property of these media, we demonstrate that various far-zone scattered spectral density, such as rectangular distribution and circular distribution, can be achieved. The method proposed in this manuscript may have potential applications in the manipulation of the far-zone scattered field.

Theory of the quasi-steady-state self-focusing of partially coherent light pulses in nonlinear media.

The quasi-steady-state (QSS) self-focusing of partially coherent light pulses (PCLPs) in nonlinear media is studied. The analytical formulas of the QSS self-focusing of PCLPs in nonlinear media (e.g., the beam width, spatial coherence width, and focal length) are presented. The effect of spatial coherence on the focal length and focus moving is investigated in detail. In particular, it is found that a PCLP has more advantages to avoid the optical damage of materials than a fully coherent light pulse.

Propagation characteristics of Gaussian-Schell model beams through optical systems in Kerr media.

For the beam spreading case, the propagation formulae of Gaussian-Schell model (GSM) beams through general optical systems in Kerr media are derived, and the propagation characteristics of GSM beams through an ideal thin lens in Kerr media are studied in detail. It is shown that the size and position of the beam waist can be controlled by the Kerr effect. Furthermore, the formula of the focal shift of the GSM beams focused by an ideal thin lens in Kerr media is also derived. It is found that in self-focusing media the focal shift decreases as the beam power or the beam coherence degree increases. In addition, there exists a maximum of the focal shift, and the formula of the focal shift maximum is derived. On the other hand, for the beam self-focusing case, the focusing characteristics of GSM beams focused by an ideal thin lens in Kerr media are also investigated.

Hollow rectangular multi-Gaussian Schell-model source.

We introduced a new class of a partially coherent source that can generate a field with a hollow rectangular profile, named the hollow rectangular multi-Gaussian Schell-mode source. The dependence of distribution of far-zone spectral density on the properties of the proposed source was analyzed. The results show that one can control the distribution properties of the far-zone intensity profile, including the thickness of the hollow edge, the shape of the hollow, the size of the hollow, and the orientation of the hollow, by adjusting the corresponding structural parameters of the source.

Degree of paraxiality of an anisotropic hollow multi-Gaussian Schell-model beam.

Degree of paraxiality (DOP) of an anisotropic hollow multi-Gaussian Schell-model (HMGSM) beam is discussed, and the influence of parameters of the beam source on its DOP is studied. It is shown that the parameters of the beam source, including the anisotropy, boundary characteristic, beam waist width, and beam coherence width, may play an important role in its DOP. Moreover, in order to illustrate the behaviors of DOP, the far-field divergence angle of this beam source has also been investigated.

Ring-shaped twisted Gaussian Schell-model array beams.

A new partially coherent source which can generate a beam field with a ring-shaped twisted array profile is presented, and the distribution characteristics of spectral density and degree of coherence of the field are discussed. It is shown that both the spectral density and degree of coherence will rotate along the propagating direction, but in opposite rotating directions. Furthermore, we find that the distribution properties of the ring-shaped array of the spectral density, including the number of the rings, the number of the lobes of each ring, and the distance of all adjacent lobes, can be properly controlled by adjusting structural parameters of the source.

Influence of thermal blooming on the beam quality of an array of Hermite-Gaussian beams propagating in the atmosphere.

The influence of thermal blooming on the quality of an array of Hermite-Gaussian (H-G) beams propagating in the atmosphere is studied, where the incoherent combination is considered. An analytical expression of the equivalent distortion parameter of such an array is derived and validated. As the mode order or the inverse radial fill factor of an array of H-G beams increases, the thermal blooming effect weakens, requiring more time to reach steady-state thermal blooming. The focal shift of an array of H-G beams in the atmosphere is also investigated. Owing to the thermal blooming effect in the atmosphere, the actual focus moves away from the geometric focus as the mode order decreases, which is different from the behavior in free space. Additionally, for an array of multimode beams, the actual focus moves away from the target as the weighting factor of TEM00 increases.

Kerr effect on propagation characteristics of Hermite-Gaussian beams.

The analytical propagation formulae of Hermite-Gaussian (H-G) beams propagating in Kerr media are derived by using the variational approach. The analytical formulae of the self-focusing critical power, the Rayleigh range and the beam quality factor of H-G beams propagating in Kerr media are also derived. It is demonstrated that the ABCD law is valid if a new complex parameter is introduced, which presents a simple method to study the propagation of H-G beams through an optical system in Kerr media. It is shown that, as the beam order increases, the self-focusing critical power of H-G beams increase and H-G beams are less affected by the Kerr nonlinearity. Finally, it is found that the focus point of H-G beams never appears in self-focusing media, and the focal length is not suitable for characterizing the self-focusing effect of H-G beams.