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Sevruk, B. B.

doi:10.1023/a:1026186112013

Journal of Applied Spectroscopy

2003

DOI: 10.1023/a:1026186112013

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B. B. Sevruk

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“…The intensity distribution of the Bessel-Gaussian beam is also not preserved in the far zone. The results of numerical modeling have shown that conical modulation at the laser radiation wavelength is observed in stimulated Raman scattering of Bessel light beams [8]. The effect of formation of the narrowest possible angular spectrum of the signal due to conical modulation occurs with azimuthally matched three-frequency parametric interaction of orthogonally polarized BesselGaussian beams under conditions when there is strong energy exchange in a crystal with quadratic nonlinearity [9][10][11].…”

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Self-modulation of Bessel-Gaussian wave beams in a medium with cubic nonlinearity

Sevruk

2006

J Appl Spectrosc

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A semi-discrete dynamic model has been developed for the formation of the spatial structure of wave fields in a medium with cubic nonlinearity. The characteristic features of self-focusing and conical modulation of intense Bessel-Gaussian light beams of different orders have been studied in different stages of their evolution during propagation. It has been shown that as a result of nonlinear refraction, in the far zone wave structures are formed consisting of three spatially separated conical beams. Increasing the cone angle of the wave vectors leads to a decrease in the effect of conical modulation of the radiation, and improves the structural stability of the beam. The considered self-modulation effects can be used for passive limiting of the laser radiation power.Key words: numerical modeling, self-focusing of radiation, medium with cubic nonlinearity, formation of wave beams and diffraction, Bessel-Gaussian light beams, spatial soliton.Introduction. Self-modulation of the amplitude and phase has a substantial effect on the spatial structure of intense wave beams during their propagation in a nonlinear medium. It has been shown that self-focusing of the medium can support the existence of helical light beams with a phase singularity [1]. Formation of such cylindrical beams is associated with conical modulation or emission of converted radiation, which arises due to nonlinear refraction as a direct consequence of the spatial and temporal dynamics of the wave fields described by the nonlinear Schrodinger equation [2]. A sign of conical modulation of the wave front is the characteristic ring structure of the image of the light beams in the far zone after passing through a medium with cubic nonlinearity. The effect of redistribution of the intensity profile of Gaussian beams in the far field due to conical modulation can be used for highspeed optical switching and limiting the power of laser radiation pulses [3], and also for the formation of diffraction-free Bessel beams with a limited aperture [4], having unique properties and important applications. Nonlinear Bessel-Gaussian beams (self-trapping spatial solitons) are a convenient tool for inducing controllable waveguides which can guide another light beam, creating a completely optical circuit [5]. Vortical Bessel-Gaussian beams, containing dark regions with zero field amplitude, are used for trapping particles, and also for exact tracing of a trajectory [6].The dynamic properties of Bessel-Gaussian beams have been studied analytically and numerically by solving the nonlinear Schrodinger equation in a Kerr medium [7]. Owing to the balance between the self-focusing and linear spreading effects, a diffraction-free situation is possible in the sense of preserving the mean-square width of the beam, but there is strong distortion of the steady-state radial profile in the near zone during nonlinear conversion. The intensity distribution of the Bessel-Gaussian beam is also not preserved in the far zone. The results of numerical modeling have shown that conical modula...

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confidence: 99%

“…The system of ordinary differential equations (7), (8) can be solved by using standard numerical methods. After finding the Fourier-Bessel coefficients b l…”

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confidence: 99%

Self-modulation of Bessel-Gaussian wave beams in a medium with cubic nonlinearity

Sevruk

2006

J Appl Spectrosc

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“…Semianalytical models of the processes of transformation based on the use of the Galerkin spectral method for numerical integration of coupled differential equations of electrodynamics [10][11][12] have been developed. It is shown that during coordinated interaction in crystals with quadratic nonlinearity phenomena of the formation of self-channeling spatial wave structures are observed.…”

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confidence: 99%

“…where ρ = r/r 0 [0, 1] and γ l are the roots of the Bessel functions J ν (x) [10][11][12]. In a single-mode interaction regime, the radial and angular profiles of the time-modulated amplitudes of input beams are represented in the form of circular harmonics of the simplest kind:…”

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confidence: 99%

Numerical Simulation of Bessel-Gauss Light Beams in Crystals with Quadratic Nonlinearity

Sevruk

2005

J Appl Spectrosc

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With the developed method of numerical simulation, the dynamics of formation of the spatial structure of interacting wave fields in the process of generation of the sum-frequency radiation was investigated. Radial intensity profiles and angular spectra of diffracting light beams with varied restriction and focusing parameters at different stages of energy exchange in the KTP crystal have been calculated. It is shown that with weak focusing, a self-channeling wave structure of soliton type with angular divergence of the second-harmonic component at the level close to the diffraction limit is formed in the field of the wide Bessel-Gauss pumping beam. Moreover, in the far-field zone complete spatial separation of the light fluxes corresponding to the fundamental and second harmonics occurs. Comparison of the efficiencies of conversion on pumping by Gauss and Bessel-Gauss light beams is made. Keywords: numerical simulation, generation of sum-frequency radiation and of a medium with quadratic nonlinearity, formation of wave beams and diffraction, Bessel-Gauss light beams, spatial solitons.Introduction. The Bessel-Gauss wave beams limited in space and possessing a finite energy are described by a family of solutions of the Helmholtz equation which contains both Bessel and Gauss beams as the limiting cases. The Bessel-Gauss light beams behave like the raylike ones if the annular divergence of the Gauss component is smaller than half the angle of the cone of the wave vectors of the Bessel component [1]. Such wave fields have been realized in a variety of experiments. In particular, they can be obtained as a result of redistribution of the intensity profile of Gauss beams in the Kerr medium [2]. The unique properties as well as potential applications of narrow conical wave beams have stimulated the development of methods for a theoretical analysis of the processes of their nonlinear transformation.In order to explain the experimentally observed transverse distribution of the intensity of the second harmonic [3] as well as the cumulative effects in parametric generation of light [4] in crystals, geometrical-optical models are suggested that take into account the influence of the conditions of the transverse phase self-matching of plane-wave components on the value of nonlinear polarization and of the overlapping integrals of interacting Bessel beams in the approximation of the given transverse distribution of the field of the pumping wave. The concept of transverse-phase self-matching with the use of the mode properties of interacting wave beams was used as the basis for describing the space structure of the transformed radiation field [5,6]. On the assumption of weak energy transfer between interacting waves, an optimum angle of the cone of an incident Bessel-Gauss beam that ensures the greatest efficiency of the generation of harmonics in a gas medium with an arbitrary density profile was found [7]. In [8], it is shown with the aid of a linearized perturbation analysis that diffractionless propagation in the process of g...

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Untitled

Cited by 2 publications

References 4 publications

Self-modulation of Bessel-Gaussian wave beams in a medium with cubic nonlinearity

Self-modulation of Bessel-Gaussian wave beams in a medium with cubic nonlinearity

Numerical Simulation of Bessel-Gauss Light Beams in Crystals with Quadratic Nonlinearity

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