TE Terms Research Articles

Impact of an Aerobic Thermophilic Sequencing Batch Reactor on Antibiotic-Resistant Anaerobic Bacteria in Swine Waste

The introduction of antibiotics to animal feed has contributed to the selection of antibiotic-resistant bacteria in concentrated animal feeding operations. The aim of this work was to characterize the impact of an aerobic thermophilic biotreatment on anaerobic antibiotic-resistant bacteria in swine waste. Despite 162- to 6,166-fold reduction in antibiotic-resistant populations enumerated in the swine waste at 25 degrees C and 37 degrees C, resistant populations remained significant (10(4) to 10(5) most probable number per milliliter) in the treated swine waste. Five resistance genes were detected before [tet(LMOS) erm(B)], and six resistance genes were detected after [tet(LMOSY) erm(B)] biotreatment. However, the biotreatment decreased the frequency of detection of resistance genes by 57%. Analysis by denaturing gradient gel electrophoresis of polymerase chain reaction-amplified 16 S ribosomal DNA (rDNA) fragments showed that the biotreatment reduced the bacterial diversity of resistant populations enumerated at 37 degrees C. Cloning and sequencing of the 16 S rDNA of these populations revealed that most clones in the treated swine waste were closely similar to some of the clones retrieved from the untreated swine waste. This study revealed that the aerobic thermophilic biotreatment developed in our laboratory does not prevent the introduction of facultatively anaerobic antibiotic-resistant bacteria and their resistance genes into agricultural ecosystems. Horizontal transfer of ecologically advantageous genes within microbial communities are likely to prevent thermophilic biotreatments from completely eliminating antibiotic-resistant bacteria and their resistance genes in animal wastes.

Analytical vectorial structure of controllable dark-hollow beams in the far field

Based on the vector angular spectrum representation of electromagnetic beams and the method of stationary phase, the analytical vectorial structure of the controllable dark-hollow beam in the far field is derived. Analytical expressions of the energy flux for the TE term, the TM term, and the controllable dark-hollow beam in the far field are presented. The normalized energy flux distributions of the TE term, the TM term, and the controllable dark-hollow beam in the far field are illustrated and analyzed with numerical examples, and the effects of the different parameters on the normalized energy flux distributions are discussed in detail.

Vectorial structure of helical hollow Gaussian beams in the far field

The analytical vectorial structure of helical hollow Gaussian beam (HHGB) is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HHGB in the far-field, which is composed of TE term with the electric field transverse to the propagation axis, and TM term with the magnetic field transverse to the propagation axis, are demonstrated. The physics pictures of HHGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HHGB propagation.

Analytical vectorial structure of a Lorentz–Gauss beam in the far field

A description of a Lorentz–Gauss beam is made directly starting with the Maxwell equations. Based on the vector angular spectrum representation of the Maxwell equations and the method of stationary phase, the analytical TE and TM terms of a Lorentz–Gauss beam have been presented in the far field. The TE and TM terms are orthogonal to each other in the far field. The energy flux distributions of a Lorentz–Gauss beam and its TE and TM terms are depicted in the far field reference plane. The influences of the different parameters on the energy flux distributions of a Lorentz–Gauss beam and its TE and TM terms are discussed. Moreover, the vectorial structure of a Lorentz–Gauss beam is also compared with that of a Gaussian beam. This research is useful to the descriptions and applications of highly divergent laser beams.

The structural properties of cosine-Gaussian beam in the far field

A description of the cosine–Gaussian (CoG) beam is made directly starting with Maxwell's equations. By means of the full vector angular spectrum method and the method of stationary phase, the analytical expressions of the TE and TM terms of the CoG beam have been presented in the far field. The influences of the cosine parameter on the energy flux distributions of the whole beam and its TE and TM terms are investigated. The physical process of evolvement of internal structure is depicted in the far field. This research reveals the internal vectorial structure of the CoG beam in the far field and enriches the cognition of the CoG beam.

Investigation in hollow Gaussian beam from vectorial structure

The description of hollow Gaussian beam is directly started from the Maxwell’s equations. Based on the vector angular spectrum representation of Maxwell’s equations, hollow Gaussian beam is decomposed into the TE and TM terms. The analytical expressions of TE and TM terms are presented by means of mathematical techniques in the near field. By means of the method of stationary phase, the concise expressions of TE and TM terms in the far field have been also derived. The TE and TM terms are shown to be orthogonal to each other in the far field. According to the analytical representations of TE and TM terms, the light intensity distributions of the TE term, the TM term and the whole beam are depicted in the near and the far fields, respectively. The result obtained here is also compared with already known solutions. This research reveals the vectorial composition of hollow Gaussian beam, which is beneficial to enhance the applications of hollow Gaussian beam.

Far-field structure of a linearly polarized plane wave diffracted by a rectangular aperture

A description of a linearly polarized plane wave diffracted by a rectangular aperture is directly derived from the Maxwell's equations. Based on the vector angular spectrum representation of the Maxwell's equations, the diffracted plane wave is decomposed into the TE and TM terms. By means of the method of stationary phase, the analytical expressions for the TE and TM terms are presented in the far field. As the TE and TM terms are orthogonal to each other in the far field, their sum constitutes the physical pattern of Fraunhofer diffraction. The influence of the linearly polarized angle on the far field structure is also investigated with a numerical example.

Analytical vectorial structure of hollow Gaussian beams in the far field

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation.

Investigation in the far field characteristics of Lorentz beam from the vectorial structure

The description of a Lorentz beam is directly obtained from Maxwell's equations. Based on the vector angular spectrum representation of Maxwell's equations and the method of stationary phase, the analytical TE and TM terms of the Lorentz beam have been presented in the far field. The TE term is located at the y axis, and the TM term the x axis. The light intensity distributions of the Lorentz beam and its TE and the TM terms are depicted in the far field reference plane. The influences of the inequality of the transverse beam waists on the light intensity distributions of the Lorentz beam, its TE and TM terms are also analyzed. Moreover, the vectorial structure of the Lorentz beam is compared with that of the Gaussian beam. Due to the relatively small diffraction effect, the beam spot of the Lorentz beam is smaller than that of the Gaussian beam. This research reveals the vectorial composition of the Lorentz beam.

爱里斑的结构

The description of a plane wave diffracted by a circular aperture is directly started from the Maxwell's equations. Based on the vector angular spectrum representation of Maxwell's equations, the diffracted plane wave is decomposed into the TE and TM terms. The analytical TE and TM terms in the far field are presented by stationary phase. As the TE and TM terms are orthogonal to each other in the far field, their sum constitutes the so-called Airy disc pattern. Therefore, this research reveals the composition of Airy disc, which is beneficial to deepen and enhance the recognition of the classical diffraction problem.

Vectorial structure of Hermite–Laguerre–Gaussian beam in the far field

Starting from Maxwell's equations, a Hermite–Laguerre–Gaussian (HLG) beam is decomposed into the TE and TM terms by using the vector angular spectrum representation. By means of the method of stationary phase, the analytical TE and TM terms are presented in the far field. The energy flux distributions of the TE and TM terms are also investigated and depicted in the far field. The influences of the additional angle parameter and Gaussian waist width on the vectorial structure and energy flux pattern of HLG beam are also investigated. This research reveals the internal vectorial structure of HLG beam and may provide a new approach to the manipulation of laser beams.

Vectorial structure of Ince–Gaussian beam in the far field

By means of the vector angular spectrum representation of the electromagnetic beam and the method of stationary phase, the analytical vectorial structure of the Ince–Gaussian beam has been presented in the far field. The amplitude distributions of the Ince–Gaussian beam and its TE and TM terms are investigated in the far field. The extreme cases of the ellipticity parameter tending to infinity or zero are also considered. Although the vectorial structures of different Ince–Gaussian beams are apparently distinct, the ratios of the amplitude distributions of the TE and TM terms to the whole beam amplitude are independent of the parity and the values of the radial and angular elliptic mode numbers. This research reveals the abundant and interesting internal details of the Ince–Gaussian beam in the far field.

Structural polarization properties of vector Gaussian beam in the far field

Based on the vector angular spectrum representation of optical beam and the method of stationary phase, the analytical TE and TM terms of vector Gaussian beam have been presented in the far field. By using the local polarization matrix, the polarization properties of the TE and TM terms in the far field are investigated, and it is found that the degree of their polarization is only determined by the spatial location. When the source is completely polarized, the TE and TM terms are both completely polarized in the far field. When the source is completely unpolarized, the TE and TM terms in the far field are partially polarized. The whole beam is also partially polarized except on the propagating axis. Moreover, the degrees of polarization of TE and TM terms are both larger than that of the whole beam.

Investigation in the propagation of non-paraxial TE vector Gaussian beam from vectorial structure

Based on the vectorial structure of non-paraxial electromagnetic beam and the non-paraxial vectorial moment theory of light beam propagation, the beam waists, the divergence angles and the beam propagation factors of TE and TM terms have been presented for non-paraxial TE vector Gaussian beam. The formulae obtained are further discussed at the highly non-paraxial and paraxial cases. Their respective maximum divergence angles are given at the highly non-paraxial case. When reducing to the paraxial case, the beam propagation factors of TE and TM terms are smaller than unity, which results from their special energy flux distribution. As TE and TM terms can be detached in the far field, they can be applied in the optical storage and collimation domains.

Analytical structure of the TE and TM terms of paraxial Gaussian beam in the near field

The description of paraxial Gaussian beam is directly started from the Maxwell’s equations. According to the vector plane wave spectrum representation of Maxwell’s equations and the vectorial structure of electromagnetic beam, the analytical TE and TM terms of paraxial Gaussian beam are presented by means of mathematical techniques in the near field. The influence of linearly polarized angle on the components of the TE and TM terms is investigated. The structural light intensities are depicted in the near field. As the vectorial structures are not orthogonal in the near field, there is a crossed light intensity in the paraxial Gaussian beam. This research reveals the abundant internal structure of paraxial Gaussian beam in the near field.

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM 00 mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM 00 mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM 00 mode.

Analytical vectorial structure of non-paraxial nonsymmetrical vector Gaussian beam in the far field

Based on the vectorial structure of non-paraxial electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of non-paraxial nonsymmetrical vector Gaussian beam in the far field are presented. According to the analytical electromagnetic fields of the TE and TM terms, the energy flux distributions of the whole beam, its TE and TM terms are investigated. Moreover, the influences of non-symmetries on the energy flux distributions of the whole beam, its TE and TM terms are also analyzed, respectively. This research reveals the internal vectorial structure of non-paraxial laser beam in the far field and is useful to the propagation of non-paraxial laser beam.

Analytical vectorial structure of Laguerre-Gaussian beam in the far field

Based on the vector angular spectrum of the electromagnetic beam and the method of stationary phase, the analytical vectorial structure of the Laguerre-Gaussian beam has been presented in the far field. According to the analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam are investigated in the far field, respectively. The formulas obtained are applicable not only to the paraxial case, but also to the nonparaxial case. The physical pictures of Laguerre-Gaussian beams are well illustrated from the vectorial structure, which may provide a new approach to manipulate laser beams.

Vectorial Structure of Non-Paraxial Linearly PolarizedGaussian Beam in Far Field

According to the vectorial structure of non-paraxial electromagneticbeams and the method of stationary phase, the analytical TE and TMterms of non-paraxial linearly polarized Gaussian beam are presented inthe far field. The influence of linearly polarized angle on therelative energy flux distributions of the whole beam and its TE and TMterms is studied. The beam spot of the TE term is perpendicular to thedirection of linearly polarized angle, while that of the TM termcoincides with the direction of linearly polarized angle. The wholebeam spot is elliptical, and the long axis is located at the directionof linearly polarized angle. The relative energy flux distribution ofthe TE term is relatively centralized in the direction perpendicular tothe linearly polarized angle. While that of the TM term is relativelycentralized in the direction of linearly polarized angle. To obtain theisolated TM and TE terms, a polarizer should be put at the long and theshort axis of the whole beam spot, respectively.

Vectorial structures of non-paraxial linearly polarized Gaussian beam and their beam propagation factors

Abstract Based on the vectorial structure of non-paraxial electromagnetic beam and non-paraxial vectorial moment theory, the relationship of the beam waists, the divergence angles and the beam propagation factors among non-paraxial linearly polarized Gaussian beam, its TE and TM terms have been presented, respectively. The analytical beam propagation factors are given and further discussed at the highly non-paraxial case. The maximum divergence angles in the x -direction of non-paraxial linearly polarized Gaussian beam, its TE and TM terms are all 54.7°, and those in the y -direction are limited to be 63.4°, 67.7° and 39.2°, respectively. As TE and TM terms are orthogonal and can be detached at the far field, the potential applications of the isolated TE and TM terms are deserved further investigation.