Convergent Gaussian Beam Research Articles

Characteristics of Light Field Near Focal Line of One-Dimensional Nonparaxial Convergent Gaussian Beam

Characteristics of Light Field Near Focal Line of One-Dimensional Nonparaxial Convergent Gaussian Beam

Spatial self-phase modulation of a Gaussian beam transmitted through a ferrofluid

We report on the experimental observation of the diffraction pattern formed in the far-field region when a high-power continuous-wave laser convergent or divergent Gaussian beam passes through a cuvette with ferrofluid. Two different types of diffraction rings with opposite light-intensity distribution are shown in the far field. The difference between the diffractive patterns is attributed to the interaction of the strong spatial self-phase modulation caused by the refractive index change of the medium with wavefront curvature of the input Gaussian beam. The observed behavior of the diffraction pattern dynamics is interpreted theoretically based on the Fresnel-Kirchhoff integral. The negative polarity of nonlinear refraction can be identified by the central interference profiles and the diffraction pattern. At the same time, the self-defocusing phenomena of the ferrofluid can be determined by the type of pattern. The nonlinear refraction coefficients of the ferrofluid were estimated to be ∼-2.89×10-5cm2/W (convergent Gaussian beam) and ∼-3.53×10-5cm2/W (divergent Gaussian beam). In addition, the corresponding third-order nonlinear optical susceptibility of the sample was also estimated as ∼1.43×10-5esu and ∼1.75×10-5esu, respectively. The experimental results imply a novel potential application of ferrofluid in nonlinear phase modulation devices.

微细光成型的加工分辨率研究

Micro stereo lithography is a kind of technology utilizing the solidified effect that photo curable polymer will appear under ultraviolet (UV) laser exposure. It is widely used in three-dimensional (3D) micro fabrication. We get the experimental values of a pair of UV laser curing coefficients, absorption coefficient and critical curing energy, of curable resin by fitting the calculation results of the Gaussian beam theory and experimental curing results. The theoretical relation between the curing unit's shape and the exposure features of time and intensity of convergent Gaussian beam is presented. The calculation and experimental results of curing unit under different conditions agree well with each other. This research offers a steady base for further research about the improvement of resolution.

Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media

The formation and the evolution of the far-field patterns of the Gaussian beams passing through a thin self-focusing medium and a thin self-defocusing medium are studied using the Fresnel–Kirchhoff diffraction theory, and the effects of the different Kerr media and the different Gaussian beams on the far-field pattern formation and evolution are analysed by taking into consideration both the change in the additional phase shift induced by the refractive index and the change in the sign of the radius of wavefront curvature of the laser beam passing through the nonlinear medium. Our results show that, when either the divergent Gaussian beam passes through the self-defocusing medium or the convergent Gaussian beam passes through the self-focusing medium, the far-field intensity distribution pattern is a series of thick diffraction rings with a central dark spot; while, when either the divergent Gaussian beam traverses the self-focusing medium or the convergent Gaussian beam traverses the self-defocusing medium, the far-field intensity distribution pattern is a series of thin diffraction rings with a central bright spot. Our results also show that whether the central dark spot or the central bright spot occurs depends mainly on the sign of the product of the additional phase shift and the radius of the wavefront curvature. When the sign is negative, that is, when the divergent Gaussian beam passes through the self-defocusing media, or the convergent Gaussian beam passes through the self-focusing media, the central dark spot surrounded by the thick diffraction rings will emerge in the far field; while, when the sign is positive, that is, when the divergent Gaussian beam traverses the self-focusing media, or the convergent Gaussian beam passes through the self-defocusing media, the central bright spot with the thin diffraction rings will occur in the far field. The difference between the diffraction patterns is attributed to the interplay of the strong spatial self-phase modulation caused by the refractive index change of the medium and the changes in sign of the radius of the wavefront curvature of the incident Gaussian beam. The results obtained in this paper are of significance to the design of practical nonlinear optical limiters for the eye or sensor protection and many other applications.

Scintillation of initially convergent Gaussian beams in the vicinity of the geometric focus

As an initially convergent Gaussian beam enters the vicinity of the geometric focus, weak fluctuation theory predicts a drop in the longitudinal component of the log-irradiance variance and an increase in the radial component off the beam center. The phenomenon intensifies as the beam nears the geometric focus, also with decreasing magnitude of the focusing parameter. Precisely at the geometric focus, first-order weak fluctuation theory further predicts that as the initial beam size continues to increase, the longitudinal component of the log-irradiance variance decreases toward zero, while the radial component increases without bound. This eventually entails a rapid change in scintillation across the beam surface that has yet to be verified experimentally, to our knowledge. We demonstrate that when diffractionlike effects produced by optical turbulence are introduced, predicted log-irradiance variance exhibits such extremes in behavior only in the case of weak turbulence. Also, at the exact geometric focus, scintillation does not vanish with increasing initial beam size but achieves a value determined by and growing with turbulence strength and nearly independent of initial beam size. The radial component of log-irradiance quickly loses significance as turbulence strength increases. In fact, general extremal behavior of the log-irradiance variance in the vicinity of the geometric focus is drastically curtailed. Differences across the diffractive beam surface become small and exhibit only a modest dependence on the initial beam size.

Effective beam parameters and the turbulent beam waist for convergent Gaussian beams

Expressions are developed for the location and the size of the beam waist for a convergent Gaussian beam in statistically homogeneous and isotropic atmospheric turbulence. Subsidiary expressions are presented that lead to the maximum distance from the transmitter at which the beam waist can be located under given optical turbulence conditions and the optimal initial radius of curvature required for placing the beam waist at a desired location. The free-space beam radius W of a Gaussian beam satisfies the relationship ∂W/∂z = - W/R, where z represents the path length and R is the phase-front radius of curvature at z. By enforcing this relation on the effective beam spot size in turbulence W(e), we can define an effective radius of curvature R(e). In addition to specifying the beam waist, R(e) leads to a pair of effective beam parameters θ(e) and Λ(e) that provide a natural extension to the complex amplitude plane. Within this context, general propagation characteristics may be described, including the coherence properties of a Gaussian beam in both weak and strong optical turbulence.