Self-focusing of elliptically shaped high-power laser beams in a fully ionized plasma

The effect of self-focusing of a high-power light beam with an elliptical cross-section in a strongly ionised plasma has been evaluated. The mechanism of self-focusing considered is non-uniform heating of plasma by an electromagnetic wave having transverse variation of amplitude along its wave front. The heating causes redistribution of carriers which lead to a nonlinear relationship between the electron density and the electric vector and hence to a field-dependent effective dielectric constant. It is found that the beam gets focused at different focal points in different directions exhibiting the effect of astigmatism. There are several critical powers, below thex=0,y=0 planes; at higher powers one dimension focuses while the other defocusses, an oscillatory waveguide is formed in both dimensions. Above the highest critical power both dimensions self-focus, the dimensionless beam width parametersf ₁ andf ₂ forx andy focusing reach different minima corresponding to different self-focusing distances beyond which both dimensions continue diverging. The effect of energy loss through absorption from the beam has also been considered. It has been observed that absorption brings about a reduction in the extent of self-focusing and favours defocusing of the beam.     

Self-focusing of a laser beam in a strongly ionized plasma

In the presence of a strong Gaussian laser beam, the non-linearity in the dielectric constant of a strongly ionized plasma has been investigated. The non-linearity arises due to the heating and redistribution of the electrons; the loss of electron energy gained from the field has been assumed to be due to thermal conduction. This self-induced non-linearity causes a self-focusing and oscillatory waveguide propagation of the beam even when the non-linear dielectric constant does not fall in the saturating range. In a typical case of a 10¹⁰ W laser, the enhancement of axial intensity by a factor of 25 has been predicted in a length of 0.6 cm.Works supported by N.S.F. (USA).On leave from Malviya Regional Engeeniring College, Jaipur-4, India.     

Nonlinear electromagnetic propagation in plasma filled cylindrical waveguides

Using an appropriate expression for the field-dependent dielectric constant of a collisionless plasma, we have studied the field distribution of the TM₀₁ mode in a cylindrical waveguide. The wave equation has been solved by a Runge Kutta technique. It is seen that on account of redistribution of carriers from the high-field regions to low-field regions a beam of frequency lower than the average plasma frequency can be transmitted if its power is high. Work supported by NSF     

Microwave dielectric properties of Ba(Zn<Subscript>1/3</Subscript>Ta<Subscript>2 / 3</Subscript>)O<Subscript>3</Subscript> for application in high power waveguide window

Higher dielectric constant, low dielectric loss and good transmission characteristicshave been the goal for developing the ceramic waveguide window for high power windowapplications. The choice of materials having high k with low dielectric lossand reduced window size is key parameters to achieve maximum microwave transmissionwithout unleashing microwave dissipation. The microwave dielectric properties ofsynthesized Ba(Zn_1/3Ta_{2 /3})O₃ (BZT) ceramics have been studied for high power windowapplications. The structural studies are correlated with microwave dielectric propertiesof BZT. The maximum values of dielectric constant ?_r =30, Q ×f₀ = 102 THz and near zero temperaturecoefficient of resonance frequency were obtained for BZT ceramics sintered at thetemperature of 1550 °Cfor 4 h. The measured results are used to design a tapered transition from air filledwaveguide to narrow (reduced width and height) dielectric filled waveguide using Heckenslinear taper at a specific frequency. The simulation result shows that the lowerreflection loss is obtained for the tapered transition of the narrow BZT window ascompared to the standard waveguide BZT window. The return loss of –34 dB is obtained forS-bandwaveguide window with a bandwidth of 675 MHz. The return loss observed in the narrow BZTwindow is –46 dB with a bandwidth of 570 MHz at a center frequency of 3.63 GHz. Most ofthe disadvantages in conventional windows will be rectified using the design of the tapertransion employing narrow waveguide window in high power applications.     

Effect of self-fields on the electron cyclotron maser instability in a dielectric loaded waveguide

The influence of self-fields on the cyclotron maser instability in a hollow electron beam propagating parallel to a uniform axial magnetic field B ₀ ê _z in a dielectric loaded waveguide is investigated. The theoretical analysis is carried out within the framework of linearized Vlasov-Maxwell equations. It is assumed that the beam is thin with the radial thickness much smaller than the beam radius. A new dispersion relation for azimuthally symmetric electromagnetic perturbation is derived and analyzed numerically. The influence of self-fields on the cyclotron maser instability in a dielectric loaded waveguide for different dielectric medium is studied. It is found that unlike the hollow waveguide the growth rate is increased by increasing self-fields. The instability band width decreases due to the increasing self-fields. The maximum growth rate increases gradually as self-fields increase as regards a different dielectric medium.     

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.     

Distribution regimes of intense laser beam in a self-consistent plasma channel

In the present work, we investigate the distributed regimes of an intense laser beam in a self-consistent plasma channel. As the intensity of the laser beam increases, the relativistic mass effect as well as the ponderomotive expulsion of electrons modifies the dielectric function of the medium due to which the medium exhibits nonlinearity. Based on Wentzel–Kramers–Brillouin and paraxial ray theory, the steady-state solution of an intense, Gaussian electromagnetic beam is studied. A differential equation of the beamwidth parameter with the distance of propagation is derived, including the effects of relativistic self-focusing (SF) and ponderomotive self-channeling. The nature of propagation and radial dynamics of the beam in plasma depend on the power, width of the beam, and Ω _p, the ratio of plasma to wave frequency. For a given value of Ω _p (<1), the distribution regimes have been obtained in beampower–beamwidth plane, characterizing the regimes of propagation as steady divergence, oscillatory divergence, and SF. The related focusing parameters are optimized introducing plasma density ramp function, and spot size of the laser beam is analyzed for inhomogeneous plasma. This results in overcoming the diffraction and guiding the laser beam over long distance. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction studies.     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.     

Guided modes in slab waveguides with a left handed material cover or substrate

We study guided modes propagating along a dielectric slab waveguide with a left handed material (LHM) cover or substrate. The dispersion relation is derived by using normalized waveguide parameters. An analytical method is then proposed to calculate the universal dispersion curves. Different from a slab waveguide with a LHM core, we find that guidance properties are strongly dependent on dielectric permittivity ε and magnetic permeability μ of the substrate and cover layers. For oscillating guided modes, fundamental zero order mode is not always absence, sometimes it exists in a restricted range of normalized propagation constant. First order mode behaves as other higher order modes and exists up to infinite high frequency. Higher order modes have no double degeneracy in the case of LHM cover layer. For surface guided modes, the existence and the type of the mode solutions with respect to different parameters are classified systematically and discussed in detail. Unlike a slab waveguide with a LHM core where the dispersion curve of TE₁ surface mode continues with that of oscillating TE₁ mode, the dispersion curve of TE₁ surface mode continues with that of oscillating TE₀ mode. It seems that the two different kinds of modes compensate each other to form one whole mode. Both TE and TM guided modes are discussed.     

The fabrication of polymer-based evanescent optical waveguide for biosensing

A polymer waveguide was fabricated to amplify the evanescent optical field for biosensing. The structure of waveguide was designed to propagate a normal single mode at the input and output regions for low loss beam coupling and propagation. A sensing region was formed in the middle of the waveguide to activate the evanescent mode and to induce high birefringence by depositing a thin dielectric film with a high refractive index on a single mode waveguide. A polymer waveguide with the dimensions of 7 μm-width and 2.5 μm-thickness was fabricated by photolithography and dry-etching. The active region of the TiO₂ thin film was fabricated with the dimensions of 20 mm-length, 20 nm-thickness and 2 mm-tapered tail. A polarimetric interference technique was used to evaluate the evanescent waveguide biosensor, and biomaterial such as glycerol was tested. The sensitivity of the sensor increased with increasing TiO₂ film thickness. For the fabricated waveguide with a 20 nm-thick TiO₂ film, the measured index change to the lead phase variation of 2π was 1.8 × 10⁻⁴.     

Effect of Higher Order Axial Electron Temperature on Self-Focusing of Electromagnetic Pulsed Beam in Collisional Plasma

Effect of higher order axial electron temperature on self-focusing of electromagnetic pulsed beam in collisional plasma is investigated. It is shown that higher order axial electron temperature T_p4 is not trivial than T_p0 and T_p2, which can modify slightly radial redistribution of electron density and increases effective dielectric constant. As a result, on one hand, slightly reduce electromagnetic beam self-focusing in the course of oscillatory convergence, on the other hand, quicken beam divergence in the course of steady divergence, i.e., higher order axial electron temperature T_p4 can decrease the influence of collisional nonlinearity in collisional plasma.     

Self-focusing and defocusing of TEM0p Hermite-Gaussian laser beams in collisionless plasma

The authors have investigated the self-focusing and defocusing of first six TEM_0p Hermite-Gaussian laser beams in collisionless plasma. In case of collisionless plasma the nonlinearity in the dielectric constant is mainly due to the ponderomotive force. It is found that modes with odd p-values defocuses and that with even p-values exhibit oscillatory as well as defocusing character of beam-width parameters variation during their propagation in collisionless plasma. The entire theoretical formulation is established under parabolic wave equation approach. The numerical computation is completed by using fourth order Runge-Kutta method. Finally the behavior of beam-width parameters with the dimensionless distance of propagation is presented graphically.     

Numerical studies on wakefield excited by Gaussian-like microwave pulse in a plasma filled waveguide

Based on a differential equation derived analytically in terms of wakefield potential ?_MW in a plasma filled rectangular waveguide, we investigate the wakefield (E_MW) generated with the help of Gaussian-like microwave pulse under the effect of microwave frequency (f), pulse duration (τ), waveguide width (b), equilibrium plasma density (n₀) and microwave intensity (I). The study conducted for three cases of τ > 1/f_p, τ = 1/f_p and τ < 1/f_p, where f_p is the plasma frequency, reveals that the amplitude of the wakefield is increased for the large pulse duration and higher microwave intensity but is decreased with the waveguide width and microwave frequency for all these cases. The wakefield shows stronger dependence on the microwave frequency when the microwave with larger intensity is used. The wakefield decreases at a faster rate with the waveguide width for the case of τ > 1/f_p.     

Dielectric and piezoelectric properties of PZT–cement composites

Lead zirconate titanate (PZT) and cement composites of 0–3 connectivity were produced using PZT of 30–90% by volume. The effects of PZT on dielectric and piezoelectric properties of the composites were then investigated. The dielectric constant (ε_r) of the composites was found to increase with increasing PZT content. The ε_r value of 90% PZT composite obtained was 291 which is noticeably higher than that of PC sample (ε_r = 79). The dielectric loss (tan δ) was found to decrease with PZT content and the tan δ value was lowest at 0.63 for 90% PZT composite. Piezoelectric coefficient (d₃₃) was found to increase with PZT content as expected. However, the effects were most significant at two stages, first at 30% PZT volume content (14 pC/N) and then at very high PZT content (90% by volume) where d₃₃ value reached 43 pC/N.     

Percolation phenomenon in barium samarium titanate-silver composite

Ba₄Sm_9.33Ti₁₈O₅₄-Ag (BST-Ag) composites were prepared by a solid-state ceramic route and its dielectric properties were investigated in the vicinity of percolation threshold. The structure and microstructure of the composites were analyzed by X-ray diffraction along with optical and scanning electron microscopy observations. The effects of silver content and frequency on the dielectric properties of BST-Ag composites were studied using a LCR meter. The relative permittivity (ε_r) of the composite increases with silver content below the percolation limit and is in agreement with power law. A 0.14 volume fraction of silver loading increases the relative permittivity of the composite from 50 to 450 at 10 kHz. Addition of 0.15 volume fraction of silver increases the relative permittivity of the composite in the order of 10⁵. It is found that the giant relative permittivity is almost constant for frequencies from 1 kHz to 1 MHz. This high ε_r composite offers the perspectives for application in electromechanical devices.     

Defect structure and dielectric properties of Bi-based pyrochlores probed by positron annihilation

Positron annihilation lifetime (PAL) and Doppler broadening (DB) techniques have been performed to identify structural defects of the bismuth based pyrochlore systems with generic formula (Bi_1.5Zn_0.5)(Zn_0.5−x/3Ti_xNb_1.5−2x/3)O₇ (x = 0, 0.25, 0.5,1.0, 1.5). We found that all studied compounds contain substantial amount of the lattice vacancy defects, the variation of the annihilation lifetime suggests that the defects structure undergoes significant changes. The complex defects could be produced with increasing content of Ti, resulting in a drop in the intensity I₂ in the Ti-rich sample. At 1 MHz their dielectric constant (?′) varies from 150 for Ti-poor system to 210 for Ti-rich system and loss tangent (tan δ) remains rather low level. The high dielectric constant response of the BZTN ceramics is attributed to loosening state of cations located in the center of octahedral, so favor off-center displacement. The occurrence of complex defects help to enhance the dielectric constant.     

Enhancement of self focusing of laser beams in a degenerate magnetoactive solid state plasma

This paper presents an investigation of the enhancement of self focusing of high frequency EM waves in a compensated degenerate magnetoactive solid state plasma. The nonlinearity in the dielectric constant responsible for self focusing arises due to nonuniform heating and consequent redistribution Of carriers. A rigorous kinetic treatment valid beyond the perturbation limit has been presented assuming the carrier relaxation time to be energy dependent. The results show that the self-focusing of extraordinary waves is enhanced while that of ordinary waves is reduced with $\text{ω}{}_{\mathrm{c}}\text{ω}$ increasing. However the focusing of extraordinary waves is not possible when ω_c > ω. The effect of degeneracy is also found to enhance the self-focusing of the waves while that of the enhanced absorption is to suppress the self-focusing process.     

Relationship between oxide-ion conductivity and dielectric relaxation in the Ln2Zr2O7 system having pyrochore-type compositions (Ln=Yb, Y, Gd, Eu, Sm, Nd, La)

Ln₂Zr₂O₇ (Ln=Yb, Y, Gd, Eu, Sm, Nd, La) system changed from fluorite (F)-type to pyrochlore (P)-type phases when the ionic radius ratios, r(Ln³⁺)/r(Zr⁴⁺), were larger than 1.26. The oxide-ion conductivity showed sharp maximum at the vicinity of the phase boundary between the F- and P-type phases. The frequency dependence of dielectric constant () and dielectric loss factor () were successfully explained by the superimposition of Debye-type polarization due to dopant-vacancy associate and electrode-electrolyte interfacial polarization by the numerical calculation. The peak of dielectric loss tangent (tan δ) was ascribed to the dopant-vacancy associate. The ε_r(0) and dielectric constant of the associate (ε_r0) showed also the maximum values at the vicinity of the phase boundary between the F- and P-type phases.     

Unidirectional growth of l-lysine l-lysinium dichloride nitrate (l-LLDN) single crystals by the SR method

Bulk semi-organic single crystals of l-lysine l-lysinium dichloride nitrate (l-LLDN) were grown by Sankaranarayanan-Ramasamy (SR) method. The experimental parameters involved in the present work are discussed in detail. The cut-off wavelength and the transmittance of the crystal were determined by UV-vis-NIR spectral analysis. Mechanical stability of the crystal was determined by Vickers microhardness tester. Refractive index of the crystal was measured using Brewster’s angle method. A simple interferometric technique was used for measuring birefringence of the crystal. The frequency dependent dielectric constant (ε_r) and dielectric loss (tan δ) were also measured. The results were analyzed for the l-LLDN crystals grown by both conventional and unidirectional methods.     

Non-specular reflection of self-collimated beams in photonic-crystal-made prism and waveguide system

We demonstrate a dual-beam-reflection phenomenon for a Gaussian beam illuminating at a Kretschmann configuration composed of a photonic-crystal-made prism and a dielectric waveguide. One reflection beam has a positive shift and the other has a negative shift. The finite-difference time-domain (FDTD) shows that the specific phenomenon takes place only when the corresponding quasi-guided mode supported in the Kretschmann configuration is excited. Field profile of the quasi-guided mode demonstrates a strong localized stationary field in the dielectric waveguide. We found that the maximum positive lateral shift (LS) is 14.27a (where a is the lattice constant), corresponding to 3.07 times of the incident wavelength, which is 0.7135 times of the beam waist and much larger than that in some previous reports.