Feasibility of remote focusing of a curvilinearly scanning beam in a moving defocusing medium

The thermal blooming of a collimated parabolically scanning beam in a defocusing medium moving across the beam is modeled. It is shown by numerical analysis that the maximum intensity in the beam within a specified portion of the path can be increased significantly by proper selection of the parameters of the scanning trajectory.Preliminary results of the present study have been reported at the Thirteenth All-Union Conference on Radio Wave Propagation [1] and at the Sixth All-Union Symposium on the Propagation of Laser Radiation in the Atmosphere [2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 27, No. 1, pp. 41–47, January, 1984.The authors are indebted to the editors for useful comments, which have contributed greatly to the improvement of certain aspects of the article.     

Adaptive correction of a tightly focused, high-intensity laser beam by use of a third-harmonic signal generated at an interface

By using the third-harmonic signal generated at an air-dielectric interface, we demonstrate a novel way of correcting wavefront aberrations induced by high-numerical-aperture optics. The third harmonic is used as the input physical parameter of a genetic algorithm working in closed loop with a 37-actuator deformable mirror. This method is simple and reliable and can be used to correct aberrations of tightly focused beams, a regime where other methods have limitations. Improvement of the third-harmonic signal generated with an f/1.2 parabolic mirror by 1 order of magnitude is demonstrated.     

Local heating of a liquid-like medium by a phase-conjugate ultrasound beam with self-adaptive focusing

Local heating of a liquid-like medium by means of self-adaptive focusing of a high-power phase conjugate ultrasound wave has been experimentally implemented. A sample of organic silicon polymer with a reflecting inhomogeneity was placed in water and exposed to a plane ultrasound beam so as to make the reflected acoustic field partially to enter the phase conjugation device. A parametrically amplified and conjugate wave was self-adaptively focused back to the inhomogeneity. Thermocouple measurements revealed ultrasound heating, which was localized near the inhomogeneity and depended weakly on its position within the aperture of the incident ultrasound beam. Themaximum heating value was about 6.5°C in 120 s with a frequency of ultrasound of 4.75MHz and a mean power of phase conjugate wave of about 0.1W.     

Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.     

On a Gaussian beam in an amplifying medium

The model of a Gaussian beam in an amplifying medium is analyzed within the framework of the paraxial (quasi-optical) approximation. Upon violation of the obtained restrictions, the model leads to a physically inconsistent conclusion about an infinitely high radiation power after a passage of an ordinary Gaussian beam through a layer of the amplifying medium. The importance of a limitation on the transverse dimensions of the amplifying medium or of the introduction of intracavity angular selection is demonstrated. The fundamental mode in the form of a Gaussian beam appears in the model with a quadratic dependence of the gain on the transverse coordinates.     

Distribution function of an electron beam in a focusing magnetic field

The distribution function of electrons moving in an axially symmetric focusing magnetic field is constructed. The macromotion and self-field of the beam are taken into account. The nonrelativistic and relativistic limits are discussed. Upon switching off the magnetic field the distribution functions obtained change into the Maxwell-Boltzmann distribution. The motion of charged particles in a focusing magnetic field is the simplest model for investigation of a beam of particles, for example, electrons, in storage or accelerator rings. In accordance with the well-known theorem of N. Bohr, a magnetic field has no effect on the distribution function for a one-dimensional distribution of electrons with respect to the momenta. However, the situation is altered if macromotion occurs in a static system, for example, the revolution of electrons in storage or accelerator rings. Maintaining the focusing of the beam in an equilibrium orbit, the magnetic field thereby affects the electron distribution function. For an actual electron beam the distribution function is determined by the initial conditions of formation of the beam; however, as a result of scattering processes it will approach some steady-state equilibrium distribution function. We will discuss the problem of finding such a distribution function in the nonrelativistic and relativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 35–40, July, 1978.The author thanks Professor I. M. Ternov of Moscow University for his constant interest in this research and Professor V. G. Bagrov of Tomsk University for help in the research.     

One-dimensional focusing of an atomic beam by a flat reflector

One-dimensional focusing of an atomic beam from a flat reflector is experimentally demonstrated. Focusing occurs because gravity changes the momentum transfer perpendicular to the surface depending on the height of the reflecting point. Theoretical analysis shows that, for a certain parametric range, diffraction-limited focusing of an atomic beam is possible. PACS 03.75.Be; 03.75.-b; 34.50.Dy; 32.80.Pj     

Generation of bottle beam by focusing a super-Gaussian beam using a lens and an axicon

This study explores the characteristics of the bottle beams that are formed by super-Gaussian beams that impinge through an axicon and a positive lens. Analytical solutions for the on-axial intensity of Gaussian and apertured-plane beams were obtained. The barrier around the dark region has a larger variation of intensity for higher-order super-Gaussian profiles. Flattening the tops of the profiles increases the bottle lengths for a fixed second-order moment width or distance between the axicon and the lens.     

Vircator with ballistic focusing of an electron beam

A high-power microwave oscillator (vircator) is built around an ironless induction linac. The feature of this device is ballistic focusing of an electron beam in a diode-type system with a concentric spherical cathode and anode. The possibility of the vircator to generate high-power microwave pulses is demonstrated.     

Explosionlike boiling of a viscous liquid in a high-intensity ultrasonic beam

The effect accompanying the propagation of high-intensity focused ultrasound in a viscous liquid, namely, medical gel, is studied. It is found that, under the action of continuous focused ultrasound (with an intensity of about 13000 W/cm²), in the area close to the waist of the caustic of the ultrasound beam, gas bubbles 10–15 mm in diameter periodically arise in an explosionlike way and then collapse with a lifetime of about 2 ms. The emergence of bubbles is accompanied by short pops with a duration of about 1 ms. An increase in the sound intensity leads to an increase in the frequency of the bubble generation (a decrease in the period from several seconds to fractions of a second) with practically the same shape of formations and the same dynamics of their development and collapse. Theoretical estimates adequately describe the size of the bubbles. The comparison of the effects produced by an intense focused ultrasonic beam on a gel and on biological tissue shows that the development of caverns (cavities) in tissues under the action of intense focused ultrasound is the manifestation of the effect of explosionlike boiling of the liquid.     

Interaction between multiple spatial solitons in the diffraction catastrophe region upon focusing a high-power laser beam in a nonlinear medium

When a high-power laser beam is focused in a nonlinear Kerr medium, beam self-diffraction by induced inhomogeneities of the refractive index is observed. A method for calculating the field amplitude and phase in the focal region with regard for self-diffraction by self-induced inhomogeneities is developed. Computer analysis of saturable Kerr media showed that the optical-field region with the least cross section of the focal pattern is followed by that of chaotically radiating “splashes” and long filaments. The latter radiate outward from the region of the caustic waist over long distances. They represent bright spatial solitons, which channel a significant portion of the primary beam energy. No less than 8–12 clear-cut solitons traveling in the positive z direction and moving apart in the transverse (x, y) plane are observed in the cross section. The field amplitude oscillates along each of the solitons. Various parameters of the saturable Kerr medium are taken into account.     

Investigation of a channeling high-intensity laser beam inunderdense plasmas

The interaction of an intense short pulse laser (>5×10 ¹⁸ Wcm^-2) with underdense plasma was extensively studied. The beam is found to be highly susceptible to the forward Raman scattering instability. At sufficiently high growth rates, this can lead to wavebreaking with the resultant production of a high flux of accelerated electrons (>10¹¹ for E>2 MeV). Some electrons are found to be accelerated well above the dephasing energy, up to 94 MeV. Self-scattered images intimate the presence of high-intensity channels that extend more than 3.5 mm or 12 Rayleigh lengths. These filaments do not follow the axis of laser propagation, but are seen to be emitted within an f4 cone centered around this axis. Spectra of the self-scattered light show that the main contribution of the scattering is not from light captured within these filaments. But there is evidence for self-phase modulation from effects such as ionization and relativistic self-focusing. However, no clear correlation is observed between channel length and the number or energies of accelerated electrons. Evidence for high intensities within the channels is given by small-angle Thomson scattering of the plasma wave generated therein, with this method, the intensity is found to be of the order of 10¹⁸ Wcm^-2 greater than 12 Rayleigh lengths from focus     

Propagation of a light beam in an absorbing medium with large-scale inhomogeneities

A method of solving the radiative transfer equation is proposed; it enables one to take into account the influence of absorption on the angular and spatial distributions of radiation under conditions of sharply anisotropic multiple scattering. For phase functions that decrease with an increase in the scattering angle by the power law, the total flux attenuation and profiles of the angular and spatial distributions in a strongly absorbing medium are studied. The obtained analytical dependences exhibit a good agreement with results of numerical solution of the radiative transfer equation.     

Longitudinal focusing and cooling of a molecular beam

A neutral polar molecule experiences a force in an inhomogeneous electric field. This electric field can be designed such that a beam of polar molecules is exposed to a harmonic potential in the forward direction. In this potential the longitudinal phase-space distribution of the ensemble of molecules is rotated uniformly. This property is used to longitudinally focus a pulsed beam of ammonia molecules and to produce a beam with a longitudinal velocity spread of 0.76 m/s, corresponding to a temperature of 250 mu K.     

Relativistic channel-coupling focusing enhanced nonlinear guiding of an intense laser beam in a plasma channel

We employ the variational method to study the optical guiding of an intense laser beam in a preformed plasma channel without using the weakly relativistic approximation. Apart from the dependence on the laser power and the nonlinear channel strength parameter, the beam focusing properties is shown also to be governed by the laser intensity. Relativistic channel-coupling focusing, arising from the coupling between relativistic self-focusing and linear channel focusing, can enhance relativistic self-focusing but its strength is weaker than that of linear channel focusing.     

Self-visualization and self-inversion effects of objects and structures upon focusing of an illuminating laser beam passing through them into an absorbing air medium

It is shown that effects of self-visualization of transparent objects and self-inversion of nontransparent ones are possible when an illuminating beam passing through them is focused into a (weakly) absorbing air medium at the initial stage of the thermal self-action of the beam. A model experiment was carried out in an optically thick cell with air at atmospheric pressure with addition of a small quantity of molecular bromine as a partial radiation absorber. The required power for the implementation of the processes was P = 200 mW at wavelength λ = 0.53 µm.     

Spin-dependent transverse force on a vortex light beam in an inhomogeneous medium

Spin-dependent effects on vortex light beams propagating in an inhomogeneous medium are demonstrated by solving the full three-component field Maxwell equations using the perturbation analysis. It is found that the hybrid Laguerre–Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams in a cylindrical graded-index medium is investigated. It is shown that the vortex light beam undergoes an additional transverse force acting differently on circular polarized beams with opposite handedness. The wave shape variation with distance taking into account the spin–orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated.     

Imaging and focusing of an atomic beam with a large period standing light wave

A novel atomic lens scheme is reported. A cylindrical lens potential was created by a large period ( 45 m) standing light wave perpendicular to a beam of metastable He atoms. The lens aperture (25 m) was centered in one antinode of the standing wave; the laser frequency was nearly resonant with the atomic transition 2³ S ₁–2³ P ₂ (=1.083 m) and the interaction time was significantly shorter than the spontaneous lifetime (100 ns) of the excited state. The thickness of the lens was given by the laser beam waist (40 m) in the direction of the atomic beam. Preliminary results are presented, where an atomic beam is focused down to a spot size of 4 m. Also, a microfabricated grating with a period of 8 m was imaged. We discuss the principle limitations of the spatial resolution of the lens given by spherical and chromatic aberrations as well as by diffraction. The fact that this lens is very thin offers new perspectives for deep focusing into the nm range.