Polychromatic Gaussian beams emitted by dispersive laser resonators

In-vacuum propagation of a polychromatic Gaussian beam emitted by a dispersive laser resonator and its passage through thin plates are studied under following assumptions: optical fields are stationary and plane-polarized, the paraxial wave equation is valid for each monochromatic component of the beam, the waist position and the Rayleigh range depend on wavelength and diffraction edge effects are negligible. Mathematical expressions for beam radius, divergence, beam parameter product and beam propagation factor are obtained. The use of thin plates for waist position achromatization is analyzed.     

A high-efficient method for generating radially and azimuthally polarized Bessel beams using biaxial crystals

As was shown previously, in propagation of a circularly polarized Bessel light beam along the optical axes of a biaxial crystal, there takes place the conversion of the order of Bessel function. In this paper, a new result is presented which is obtained by varying the polarization state of an input beam. Namely, a linearly polarized beam can be transformed into a beam with the radial or azimuthal polarization state. At that the order-transformation also occurs. The switching between radial and azimuthal polarization states of the output beam is performed by the proper switching between two orthogonal linear polarization states of the input beam. The efficiency of polarization conversion is high and can be practically full at an appropriate choice of the cone angle of the input beam or crystal length.     

Axial intensity distribution and focal shifts of focused partially coherent conical Bessel–Gauss beams

Based on the generalized Huygens–Fresnel diffraction integral and the theory of partially coherent light, the axial intensity distribution and the focal shifts of focused partially coherent conical Bessel–Gauss beams are investigated. The dependence of the maximum on-axis intensity and the associated focal shift on the Fresnel number and the coherence parameter are examined and illustrated numerically. The results related to the J ₀-correlated beams and the fully coherent Bessel–Gauss beams are obtained as particular cases of this study.     

Hollow elliptical Gaussian beams generated by a triangular prism

Based on the tensor method, an analytical formula for hollow Gaussian beams (HGBs) generated by a triangular prism has been derived, and the propagation properties have been studied. It is shown that hollow elliptical Gaussian beams (HEGBs) can be obtained in the near field after the prism, and that the eccentricity of the output beam is affected by parameters such as the incidence angle, refractive index of the prism and the order of the HGB. It shows that by using a triangular prism one can conveniently obtain HEGBs.     

The degenerating diffraction far-field propagation properties of the conical double half-Gaussian hollow beams

The far-field propagation properties of conical double half-Gaussian hollow beams in the condition of Collins formula are studied. Because of the cone angle of this kind of hollow beams, the diffraction is compensated and the inner diameter is turning bigger by the rule of geometric optics as the propagation distance is increasing, whereas the degenerating diffraction phenomenon is turned out. The far-field intensity distribution of the conical double half-Gaussian hollow beams in the condition of in-Collin...     

Axial superposition of Gaussian spherical beams

A novel model of beam formed by coherent superposition of two correlated Gaussian spherical beams with different centers is presented. This kind of beam has a transverse spreading smaller than a fundamental Gaussian beam. The beam quality factor is smaller than one.     

Optical quality measurements on beams generated by a stable multipass resonator and a hybrid stable–unstable resonator

Using the same radio-frequency excited slab device, we have comparatively studied two different optical schemes defining a stable multipass resonator and a hybrid stable–unstable resonator. A thorough analysis of the beams extracted from the two laser setups shows that the stable folded resonator can produce a quasi-TEM₀₀ output, at a variance with the hybrid stable–unstable resonator which always generates undesired low-power side lobes.     

Colored conical emission in BBO crystal induced by intense femtosecond pulses

We present the experimental and theoretical study of colored conical emission (CCE) during intense femtosecond pulses propagating in a β-barium borate (BBO) crystal. CCE revealed special nonlinear dynamics of the strong coupling between the fundamental and second harmonic pulses due to the spatiotemporal modulation instability (MI). The underlying physics of CCE involve three three-photon processes, according to which the beam angular spectra was calculated on the phase-matching conditions and accords with the experimental observation.     

Focal shifts in focused Hermite-cosh-Gaussian laser beams

A closed-form propagation equation of Hermite-cosh-Gaussian beams passing through an unapertured thin lens is derived. Focal shifts are analyzed by means of two different methods according to the facts that the axial intensity of some focused Hermite-cosh-Gaussian beams are null and that of some others are not null but the principal maximum intensity may be located on the axis or off the axis. Optimal focusing for the beams is studied, and the condition of optimal focusing ensuring the smallest beam width is also given.     

Experimental and numerical study of a conical turbulent partially premixed flame

The structure and dynamics of a turbulent partially premixed methane/air flame in a conical burner were investigated using laser diagnostics and large-eddy simulations (LES). The flame structure inside the cone was characterized in detail using LES based on a two-scalar flamelet model, with the mixture fraction for the mixing field and level-set G-function for the partially premixed flame front propagation. In addition, planar laser induced florescence (PLIF) of CH and chemiluminescence imaging with high speed video were performed through a glass cone. CH and CH₂O PLIF were also used to examine the flame structures above the cone. It is shown that in the entire flame the CH layer remains very thin, whereas the CH₂O layer is rather thick. The flame is stabilized inside the cone a short distance above the nozzle. The stabilization of the flame can be simulated by the triple-flame model but not the flamelet-quenching model. The results show that flame stabilization in the cone is a result of premixed flame front propagation and flow reversal near the wall of the cone which is deemed to be dependent on the cone angle. Flamelet based LES is shown to capture the measured CH structures whereas the predicted CH₂O structure is somewhat thinner than the experiments.     

Transformation of pulsed Gaussian beams in a four dimension domain

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Anisotropic light diffraction in a biaxial crystal of alpha-iodic acid

A program for calculating characteristics of acousto-optic interaction in biaxial crystals is developed and used to analyze light diffraction by ultrasound in an iodic acid crystal. Crystal cuts with maximum acousto-optic figures of merits are found. It is shown that in the region of the optical axes the frequency dependences of the Bragg angles under anisotropic diffraction are substantially different from those in uniaxial crystals.     

Elegant Inceben Gaussian beams in a quadratic-index medium

Elegant Ince—Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince—Gaussian beams and they display better symmetry between the Ince-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince—Gaussian beams are discussed.     

Propagation of vectorial Gaussian beams behind a circular aperture

Based on the vectorial Rayleigh diffraction integral and the hard-edge aperture function expanded as the sum of finite-term complex Gaussian functions, an approximate analytical expression for the propagation equation of vectorial Gaussian beams diffracted at a circular aperture is derived and some special cases are discussed. By using the approximate analytical formula and diffraction integral formula, some numerical simulation comparisons are done, and some special cases are discussed. We find that a circular aperture can produce the focusing effect but the beam becomes the shape of ellipse in the Fresnel region. When the Fresnel number is equal to unity, the beam is circular and the focused spot reaches a minimum.     

Focal shift in focused off-axial Hermite-cosh-Gaussian beams

Based on the encircled-power criterion, the focal shift of off-axial Hermite-cosh-Gaussian beams passing through an apertured lens is studied and illustrated with detailed numerical examples. The dependence of focal shift on the beam and optical system parameters is discussed.     

A peculiarity of diffraction measurements using a Gaussian laser beam

Numerical modelling of the Gaussian beam diffraction by a wire near the Fraunhofer limit is presented. Two cases are considered: the case of the wire being on the axis of the beam and the case of the wire being off-axis. For the case where the wire is on the axis, the displacements of the diffracted minima are calculated. For the off-axis case, the changes in the positions of the maxima and minima and the power density are calculated. The conditions are determined at which the measurements made using a Gaussian beam can be calculated using the formula for plane waves. This work arises in connection with research being performed into the Doppler spectrum of big particles.     

高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

Propagation properties of hollow conical double half-Gaussian beams

In this paper, we present a new hollow beams - hollow conical double half-Gaussian beams - and deduce the analytical equation of propagation and transformation of these through the paraxial optical system by using the Collins formula. By using the formula deduced, we calculate and analyze the propagation properties of these in free space. In an experiment, we have obtained hollow conical double half-Gaussian beams, which are cone-angle controllable by using the combinational optical system of the spherical reflector, reflecting positive-axis cone and zoom lens, and we obtain the beam loop of far field in different distances. The results show good coherence between theory and experiment. This paper will play a guiding role in the practical application of hollow conical double half-Gaussian beams.