Non-linear propagation of laser beam and focusing due to self-action in optical fiber: Non-paraxial approach

A somewhat more general analysis for solving spatial propagation characteristics of intense Gaussian beam is presented and applied to the laser beam propagation in step-index profile as well as parabolic profile dielectric fibers with Kerr non-linearity. Considering self-action due to saturating and non-saturating non-linearity in the refractive index, a general theory has been developed without any kind of power series expansion for the dielectric constant as is usually done in other theories that make use of paraxial approximation. Result of the steady state self-focusing analysis indicates that the Kerr non-linearity acts as a perturbation on the radial inhomogeneity due to fiber geometry. Analysis indicates that the paraxial rays and peripheral rays focus at different points, indicating aberration effect. Calculated critical power matches with the experimentally reported result.     

Waveguide propagation of laser beams in media with saturating non-linearity

The waveguide propagation of Gaussian laser beams in dielectric media with saturating non-linearity has been investigated analytically, using two profiles for the dependence of the dielectric constant on intensity. An expression for the radius of the uniform wave-guide, corresponding to a given power of the beam, has been obtained and the existence of a minimum radius, corresponding to an optimum power, has been predicted. For high power laser beams, oscillatory waveguides have been obtained; for very high powers the oscillations of the radius of the waveguide are small.Work supported by NOAA, USA.Work supported by CSIR, India.Work supported by NSF, USA; on sabbatical leave from IIT, Delhi.     

Stimulated Raman scattering of gaussian laser beam in relativistic plasma

This paper presents an investigation of Stimulated Raman Scattering of gaussian laser beam in relativistic Plasma. The pump beam interacts with a pre-excited electron plasma wave and thereby generate a back-scattered wave. Due to intense laser beam, electron oscillatory velocity becomes comparable to the velocity of light, which modifies the background plasma density profile in a direction transverse to pump beam axis. The relativistic non-linearity due to increase in mass of the electrons effects the incident laser beam, electron plasma wave and back-scattered beam. We have set up the non-linear differential equations for the beam width parameters of the main beam, electron plasma wave, back-scattered wave and derived SRS back-reflectivity by taking full non-linear part of the dielectric constant of relativistic plasma with the help of moment theory approach. It is observed from the analysis that self-focusing of the pump beam greatly affects the SRS reflectivity, which plays a significant role in laser induced fusion.     

Self-focusing of electromagnetic waves in a magnetoplasma

The steady state self-focusing of a Gaussian electromagnetic beam in a magneto-plasma has been studied. On a short time scale, a non-linearity in the dielectric constant of a plasma appears due to the ponderomotive force. This force in the case of the extraordinary mode has opposite signs forω>ω _c andω<ω _c, whereω _c is the electron cyclotron frequency. The self-focusing due to this effect is predicted at frequencies except forω _c /2<ω<ω _c . The focusing of the ordinary mode is adversely affected by the magnetic field. On a larger time scale, the non-uniform heating of electrons by the beam and the resulting redistribution of the electron density is a source of non-linearity. This non-local non-linearity is several orders of magnitude higher than the ponderomotive non-linearity. We predict self-focusing of the extraordinary mode only above the gyroresonance (ω>ω _c ), while the ordinary mode can be focused at all frequencies.     

Hot carrier diffusion induced instabilities of electromagnetic waves in plasmas and semiconductors

The stability of a plasma/semiconductor for small fluctuations in the intensity of plane electromagnetic beam has been studied when a non-linearity in the dielectric constant appears on account of the diffusion of non-uniformly heated carriers (due to fluctuations in the intensity of the beam). Fluctuations of optimum size and long duration have been found to grow at moderate powers. The effect of absorption is, however, to suppress this effect.Work supported by CSIR (India) and NSF (USA)     

Piezoelectric non-linearity in PbSc0.5Ta0.5O3 thin films

Epitaxial (001)-oriented PbSc_0.5Ta_0.5O₃ (PST) thin films were deposited by pulsed laser deposition. Local piezoelectric investigations performed by piezoelectric force microscopy show a dual slope for the piezoelectric coefficient. A piezoelectric coefficient of 3 pm/V was observed at voltages up to 0.8 V. However, at voltages above 0.8 V, there is a steep increase in piezoelectric coefficient mounting to 23.2 pm/V. This nonlinear piezoelectric response was observed to be irreversible in nature. In order to better understand this nonlinear behavior, voltage dependent dielectric constant measurements were performed. These confirmed that the piezoelectric non-linearity is indeed a manifestation of a dielectric non-linearity. In contrast to classical ferroelectric systems, the observed dielectric non-linearity in this relaxor material cannot be explained by the Rayleigh model. Thus the dielectric non-linearity in the PST films is tentatively explained as a manifestation of a percolation of the polar nano regions.     

Effects of electron temperature on dielectric function and localization of laser beams in underdense collisional plasma

Effects of electron temperature on dielectric function and localization of laser beams in underdense collisional plasmas are investigated. Simulation results show that the electron temperature has a strong effect on the dielectric constant and the laser beam localization. It is observed that due to the influence of the electron temperature, the dielectric function presents some interesting and complicated nonlinear variations, and gives rise to the laser beam localization. Moreover, the amplitudes of the beam width and the beam intensity are subjected to continuously oscillatory variation in the region of localization. In addition, the effects of several parameters on the dielectric function and the beam localization are discussed.     

Temperature dependence of dielectric behaviour of illuminated HgI2

The real part of the dielectric constant was studied in the temperature range of 340 to 10 K, and at frequencies that range from 1 to 10⁴ Hz. The dipole contribution to the dielectric constant has been found at temperatures lower than 110 K while the space-charge contribution due to the increase of crystal defects is dominant at temperatures higher than 290K.     

Nonlinear oscillatory waveguide propagation in a plasma

The presence of an intense Gaussian laser beam gives rise to a ponderomotive force on electrons in a collisionless plasma, leading to a redistribution of electron density along the wave-front and consequently to an intensity dependent dielectric constant which saturates with increasing intensity. The intensity dependent dielectric constant is responsible for beam propagation in an oscillatory waveguide. It is seen that (i) a beam of radiusr ₀ less thanr _0min (?c/ω _p) cannot be focused in the plasma regardless of its power, (ii) minimum dimension of oscillatory waveguide increases with increasing power of the beam. Similar results are also obtained for collisional plasma where nonlinearity arises due to nonuniform heating and consequent redistribution of carriers.     

利用激光冷却原子束测量氦原子精密光谱

⁴He原子2³S₁→2³P_0,1,2跃迁的精细结构分裂,目前在理论和实验上都能够达到10^-8水平的精度,并可被应用于测定精细结构常数α, 和对量子电动力学进行检验.该方面实验研究的关键, 是需要提高测量信噪比,并消除各种可能的系统偏差, 将这一精细结构分裂测量到亚kHz水平.在设计的这套实验方案中, 首次结合激光冷却原子技术,通过激光横向冷却来提高亚稳态氦原子束的束流强度,并对三态亚稳态氦原子进行偏折, 将其从原子束中分离,从而大幅降低测量背景,并利用频率锁定激光器的边带扫描的方式来进行光谱测量,以使得扫描测量中保持足够的频率精度. 在目前基本搭建成的实验装置上,实验方法的可行性已经获得验证,分析表明有望实现亚千赫兹水平的测量准确度.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity: Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity:Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated.An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field,with linear absorption and due to saturation effects for arbitrary large intensity.The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters.Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode.Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence.The beam is more focussed at lower intensity in both cases viz.extraordinary and ordinary mode.     

Miniature high-repetition-rate TEA CO2 laser with surface-wire-corona preionization

In this article, an experimental study of a miniature, sealed-off, high-repetition-rate transversely excited atmospheric-pressure (TEA) CO₂ laser with a kind of surface-wire-corona preionization (SWCP) is described. We have utilized an SWCP consisting of SiO₂ dielectric tube and a fine wire strained and attached to the dielectric surface. A BN ceramic material, which has an extremely low coefficient of thermal expansion of about 5 × 10⁻⁷/°C was employed as a supporter of the resonator. A measurement on emission spectra of SWCP has been reported. By applying SWCP to the TEA CO₂ laser, efficient laser operation at an overall efficiency of 9.8% with an output energy of 150 mJ has been achieved from a small discharge volume of 25 cm³ with an active length of 230 mm. At the pulse repetition frequency of 60 Hz, the TEM₀₀ mode of laser beam with pulse width of 60 ns was obtained.     

Critical (burst) electron emission from dielectrics, induced by injection of a dense electron beam

A dense pulsed electron beam and nanosecond pulse length has been used to inject negative electric charge into various dielectric materials (single crystals, glasses, composites, plastics) for initiation of electron field emission from the dielectric into a vacuum. It has been shown that upon reaching a critical electric field in the bulk and at the dielectric surface there is intense critical electron emission. The local current density from the emission centers reaches a record value (for dielectrics) of the order of 10⁶ A/cm². The emission occurs in the form of a single gigantic pulse. The measured amplitude of the emission current averaged over the emitting surface is the same order of magnitude as the injected electron current: 10–1000 A. the emission current pulse lages behind the current pulse of the primary electron beam injected into the sample. The delay time is in the range 1–20 nsec and decreases with increasing current density of the injected beam. Direct experimental evidence is found for intense generation of carriers (band or quasifree electrons) in the near-surface layer of the dielectric in a strong electric field due to the Frenkel-Poole effect and collisional ionization of traps, usually various donor levels. This process greatly strengthens the field emission from the dielectric. It has been shown experimentally that the emission is nonuniform and is accompanied by “point bursts” at the surface of the dielectric and ionized plasma spikes in the vacuum interval. These spikes are the main reason that the transition of the field emission into “bursts” is critical, similar to the current which has been previously observed in metals and semiconductors. However there are a number of substantial differences. For example the critical field emission current density needed for the transition into “bursts” is three orders of magnitude less than for metals. If we provide sufficient electron current at the surface or from the bulk of the dielectric to the emission centers, then the critical emission is always accompanied by a vacuum discharge between the surface of the dielectric and a metallic collector. A detailed computer model of the processes in the dielectric during injection of a high-density electron beam has been developed which allows one to understand the complex physical pattern of the phenomenon. Tomsk Polytechnic University. Institute of High-Current Electronics, Siberian Section, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 45–67, November, 1997.     

Experimental evidence of photoinduced valence change of Fe3+ in BaTiO3 and mechanism for growth of new grating in depleted pump condition: An EPR investigation

With a view to understanding the role of photo-induced valence changes of impurities in BaTiO₃ in the phenomena of photorefraction, EPR experiments were conducted under in situ He-Ne laser illumination. These experiments gave evidence for photoinduced valence change of Fe in BaTiO₃ at room temperature. The EPR signal due to trivalent iron was found to reduce in intensity with laser illumination The kinetics of the valence change has been investigated. Under large fringe width condition, the time constant of the decay is identified as the dielectric relaxation time τ_d. The changes in line shape on laser illumination to Dysonian form, appeared most predominantly in mechanically poled crystal compared to electrically poled single domain crystals. This demonstrated the possible role of domain walls and the defects there, as source or sinks of charge carriers on photo excitation. It is observed, that there is transient growth of Fe³⁺, when the laser illumination was put on, before its decay. This was attributed to charge transfer between electrons in oxygen vacancies and Fe⁴⁺. This predicted the growth of a transient grating under depleted pump condition in a two beam coupling experiment. This was experimentally proved by following the diffracted signal of the reading beam under the depleted pump condition.     

A slow gravity compensated atom laser

We report on a slow guided atom laser beam outcoupled from a Bose–Einstein condensate of ⁸⁷Rb atoms in a hybrid trap. The acceleration of the atom laser beam can be controlled by compensating the gravitational acceleration and we reach residual accelerations as low as 0.0027 g. The outcoupling mechanism allows for the production of a constant flux of 4.5×10⁶ atoms per second and due to transverse guiding we obtain an upper limit for the mean beam width of 4.6 μm. The transverse velocity spread is only 0.2 mm/s and thus an upper limit for the beam quality parameter is M ²=2.5. We demonstrate the potential of the long interrogation times available with this atom laser beam by measuring the trap frequency in a single measurement. The small beam width together with the long evolution and interrogation time makes this atom laser beam a promising tool for continuous interferometric measurements.     

Self-induced optical activity in crystals

We have observed non-linear rotation of the plane of polarization of a linearly polarized light beam in GaAs crystals ($\text{4}$3m). The effect has been investigated by means of YAG : Nd^3- laser and pulse polarimeter with accuracy to non-linear rotation angle 0.02°. Two mechanisms caused by the non-linearity of the spatial dispersion and the anisotropy of two-photon's absorption have been distinguished and corresponding susceptibilities have been calculated.     

Self-oscillating mode of electron beam generation in a source with a grid plasma emitter

Plasma processes and electron beam generation in an electron source with a grid plasma cathode are investigated. Experiments are conducted under the conditions of efficient electron extraction and an intense counter ion flux, which break grid stabilization. It is shown that a rise in the gas pressure and in the emitting plasma potential leads to the plasma potential modulation in the frequency range 10⁴–10⁵ Hz. Under the self-oscillation conditions, an electron beam is obtained with a constant current of up to 16 A and an electron energy modulated up to 100% of the accelerating voltage level (100–300 V). An explanation is given for relaxation self-oscillations arising when the plasma potential grows and for the system’s inertial non-linearity arising when the plasma potential induced by the space charge of the counter ion flux lags behind the current of electron-beam-generated ions.     

Visualization of the spatio-temporal structure of a pulsed photoelectron beam formed by femtosecond laser radiation

A method based on an original electron microscope created for investigating photoelectron beams is presented. It ensures a nanometer spatial resolution and picosecond time resolution. Electrons appearing when a metal needle is irradiated by femtosecond laser pulses are transmitted through a dielectric microcapillary and are subjected to a ponderomotive potential created by femtosecond laser radiation focused near the capillary tip. The position-sensitive detection scheme allows for the detection of the spatial profile of a photo-electron beam with a magnification of K ≅ 4 × 10⁴. The time structure of the photoelectron beam is visualized by scanning the delay time between laser pulses irradiating the needle and a laser pulse focused near the capillary tip.     

Specific features of the dielectric spectrum of CaCu3Ti4O12 in the low-frequency range

The dielectric spectra of CaCu₃Ti₄O₁₂ ceramics with giant values of the dielectric constant have been presented. The spectrum exhibits Debye dispersion with an activation energy of 0.075 eV in the high-frequency range of 10⁶–10⁷ Hz, and a characteristic plateau has been seen in the frequency dependence of the dielectric constant in the range of 10⁴–10⁵ Hz. A considerable increase in the loss factor ?″ has been observed in the low-frequency part of the spectrum and a capacitive-to-inductive impedance transition has been revealed in some samples at a frequency below 10^?2 Hz. The causes of this transition have been discussed.