Four-petal Gaussian Beams Research Articles

Vectorial structure of the far-field of an apertured four-petal Gaussian beam

Based on the theorem of vectorial structure and the method of stationary phase, an analytical vectorial structure of the far-field of an apertured four-petal Gaussian beam has been derived without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured four-petal Gaussian beam are also presented in the far-field reference plane, respectively. The energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam are graphically demonstrated in the far-field plane. The dependences of the energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam on the f-parameter, the truncation parameter, and the beam order are also examined.

四瓣高斯光束经过偏心圆孔限制的矢量非傍轴传输

四瓣高斯光束经过偏心圆孔限制的矢量非傍轴传输

Analytical vectorial structure of non-paraxial four-petal Gaussian beams in the far field

Abstract The analytical vectorial structure of non-paraxial four-petal Gaussian beams (FPGBs) in the far field has been studied based on vector angular spectrum method and stationary phase method. In terms of 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 derived in the far field, respectively. According to our investigation, the FPGBs can evolve into a number of small petals in the far field. The number of the petals is determined by the order of input beam. The physical pictures of the FPGBs are well illustrated from the vectorial structure, which is beneficial to strengthen the understanding of vectorial properties of the FPGBs.

Vectorial structure of a hard-edged-diffracted four-petal Gaussian beam in the far field

Based on the vector angular spectrum method and the stationary phase method and the fact that a circular aperture function can be expanded into a finite sum of complex Gaussian functions, the analytical vectorial structure of a four-petal Gaussian beam (FPGB) diffracted by a circular aperture is derived in the far field. The energy flux distributions and the diffraction effect introduced by the aperture are studied and illustrated graphically. Moreover, the influence of the f-parameter and the truncation parameter on the non-paraxiality is demonstrated in detail. In addition, the approximate formulas obtained in this paper can degenerate into un-apertured case when the truncation parameter tends to infinity. This work is beneficial to strengthen the understanding of vectorial properties of the FPGB diffracted by a circular aperture.

Vectorial structural characteristics of four-petal Gaussian beams in the far field

Based on the vector angular spectrum theory of electromagnetic waves and the method of stationary phase, analytical vector structures of four-petal Gaussian beams (FPGB) in the far field are derived. The energy flux for the TE term, TM term and the whole beam are represented and illustrated with numerical examples. Effects of beam orders and paraxial degrees on energy flux distributions are discussed in detail, and the corresponding analytical explanations are also given. These results may provide a new approach to manipulate other higher-order laser beams in the far field.

Diffraction properties of partially coherent electromagnetic four-petal Gaussian beams

The concept of existing scalar coherent four-petal Gaussian (FPG) beam is extended to the more general partially coherent electromagnetic four-petal Gaussian (PCFPG) beam, and the cross-spectral density matrix of the latter is derived in analytical expressions. Intensity distributions and degree of polarization in free space are investigated by numerical examples. Results show that propagation properties of the PCFPG beam are different from their scalar coherent and scalar partially coherent counterparts. Both intensity distributions and polarization strongly depend on transversal coherence lengths. When the propagation distance increases to a large value, intensity distributions of PCFPG beams convert into the Gauss profile. Polarization of PCFPG beams shows an oscillating characteristic upon propagation, and the oscillation would enhance with the increase of coherence lengths. These results may find potential applications in beam shaping and free space optical communications.

AVERAGE INTENSITY AND SPREADING OF PARTIALLY COHERENT FOUR-PETAL GAUSSIAN BEAMS IN TURBULENT ATMOSPHERE

The concept of partially coherent four-petal Gaussian (PCFPG) beam is introduced and described in analytical forms. Based on the Huygens-Fresnel integral formula, average intensity and beam spreading in turbulent atmosphere are derived in analytical expressions. Efiects of beam parameters and atmospheric structure constant on intensity distributions and efiective beam sizes are investigated in detail, respectively. Results show that PCFPG beams carrying larger coherence lengths or higher beam orders would be less afiected by turbulence. It is also indicated that, when the propagation distance increases, the PCFPG beam would convert into the Gauss- like proflle sooner or later, but this degradation can be reduced by modulating beam parameters. Results in this paper may provide potential applications in free-space optical communications.

Propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media

The propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media has been studied. The analytical solution and the analytical second-order moment beam width are obtained. For the off-waist incident and the waist incident cases, the intensity pattern evolves periodically during propagation in strongly nonlocal nonlinear media. Under the off-waist incident condition, the second-order moment beam width varies periodically during propagation, whatever the input power is. But under the waist incident condition, there exists a critical power. When the input power equals the critical power, the second-order moment beam width remains invariant, otherwise the second-order moment beam width varies periodically. Numerical simulations based on the nonlocal nonlinear Schrödinger equation are carried out for comparison with the theoretical predictions. The results show that the numerical simulations are in good agreement with the analytical results in the case of strong nonlocality.

Propagation of four-petal Gaussian beams in apertured fractional Fourier transforming systems

Based on the Collins diffraction integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation of a four-petal Gaussian beam passing through an apertured fractional Fourier transform (FRFT) optical system has been studied in detail. Some typical numerical examples are given to illustrate the properties of the four-petal Gaussian beam in the FRFT plane. The results indicate that the intensity distributions of the beam in the FRFT plane are closely related to not only the fractional order but also the beam parameters and the aperture parameters.

M2 factor of four-petal Gaussian beam

Based on the second-order moments, this paper derives an analytical expression of the M2 factor of four-petal Gaussian beam. The results show that the M2 factor is only determined by the beam order n. The corresponding numerical calculations are also given. As the beam order increases, the augment of M2 factor is disciplinary. As the expression of M2 factor is expressed in series form and becomes more complicated, a new concise formula of M2 factor is also presented by using curve fitting of numerical calculations. When 3 ≤ n ≤ 200, the maximum error rate of fitting formula will not exceed 2.6% and the average error rate is 0.28%. This research is helpful to the applications of four-petal Gaussian beam.

Propagation of Four-Petal Gaussian Beams in Turbulent Atmosphere

An analytical expression for the average intensity of four-petal Gaussian beams in turbulent atmosphere is derived. Studies show that in turbulent atmosphere, the contour lines of four-petal Gaussian beams with lower order N evolve into a number of petals with the increase in propagation distance, the contour lines with higher order N can reserve four-petal distribution at longer propagation distance than that with lower order N. These properties are similar to those in free space. However, with further increases of the propagation distance, the contours lines in turbulent atmosphere are different from those in free space.

Four-petal Gaussian光束在单轴各向异性晶体中的衍射特性

Propagation properties of polarized four-petal Gaussian beams along the optical axis of uniaxially anisotropic crystals were investigated. Based on the paraxially vectorial theory of beam propagation, analytic expressions of the diffraction light field were obtained. The effects of the anisotropy on the polarization properties of the diffracted four-petal Gaussian beams have also been explained by numerical method. The results elucidate that the linear polarization state and the symmetry of the incident beams cannot be kept during propagation in anisotropic crystals.

Vectorial Nonparaxial Four-Petal Gaussian Beams and TheirPropagation in Free Space

The vectorial nonparaxial four-petal Gaussian beam (FPGB) isintroduced. The closed-form propagation expressions for the free-spacepropagation of FPGBs are derived and their more general applicableadvantages are illustrated analytically and numerically. Some specialinteresting cases, in particular the paraxial one, are discussed. Itis found that the parameter f = 1/kw0 with the kbeing the wave number and w0 being the waist width playsa crucial role in determining the nonparaxiallity of FPGBs. For smallvalues of the f parameter the paraxial approximation isallowable. In the nonparaxial regime the beam order nadditionally affects the vectorial and nonparaxial behaviour of FPGBs.

Four-petal Gaussian beams and their propagation

A new form of laser beams called four-petal Gaussian beams is introduced. Based on the Collins integral, two kinds of analytical propagation expressions for this new kind of beams through a paraxial ABCD optical system are derived. The propagation properties of the four-petal Gaussian beams are studied and illustrated with numerical examples. At the source plane the beam has four-petals; the space among the petals is determined by the beam order. In the far field the beam evolves into a number of mirror symmetric petals and the petals of higher order beams can be equally spaced.