Nonlinear Ponderomotive Force Research Articles

Magnetic field enhanced terahertz generation from shape-dependent metallic nanoparticles

Abstract This communication deals with the analytical study of terahertz (THz) generation via frequency-difference mechanism using two circularly symmetric Gaussian laser beams with slightly different frequencies ω 1 and ω 2 and wave vectors k → 1 and k → 2 simultaneously propagating through a mixture of spatially corrugated noble-metal nanoparticles. The mixture, consisting of spherical nanoparticles (SNPs) and cylindrical nanoparticles (CNPs), is placed in a host medium under the influence of an externally applied static magnetic field. The two co-propagating laser beams impart a nonlinear ponderomotive force on the electrons of the NPs, causing them to experience nonlinear oscillatory velocity. Furthermore, the consequent nonlinear current density excites THz radiation at the beat frequency ω ( = ω 1 − ω 2 ) . Magnetic fields influence the surface plasmon resonance condition associated with electrons of the nanoparticles due to enhancement in ponderomotive nonlinearities, thereby causing an increment in the amplitude of the generated THz field. It is observed that the generated THz radiation has a strong dependence on the shape and size of the NPs in addition to the magnetic field strength. CNPSs provide greater THz amplitude than SNPs due to additional resonance modes, and combining both kinds of nanostructures further enhances the amplitude. THz radiation plays an important role in biomedical and pharmaceutical fields, communications, security and THz spectroscopy.

Magnetically enhanced THz generation by self-focusing laser in VA-MCNTs

Magnetically enhanced terahertz (THz) radiations are generated on account of the self-focusing of the laser beam in the bunch of anharmonic Vertically Aligned Metallic Carbon Nanotubes (VA-MCNTs) embedded on the non-conductive sapphire or silicon on sapphire (SOS) substrate. The high-power Gaussian laser beam gets self-focused in the bunch of VA-MCNTs as the initial power of the propagating beam is greater than its critical power. The resulting laser beam interacts with the bunch of VA-MCNTs and as a result, the electrons of MCNTs experience a nonlinear ponderomotive force to show oscillatory behavior with resonant nonlinear transverse velocity. It produces the nonlinear current which drives the THz radiation generation. Enhanced THz generation is noticed in the regions where self-focusing becomes stronger. We have observed that an applied magnetic field, anharmonic behavior of MCNTs, self-focusing, and dimensions of MCNTs also pave the way for the enhancement of the normalized THz amplitude. The anisotropic behavior of the dielectric tensor in the presence of an externally applied static magnetic field also helps to enhance the THz amplitude. The results shown (by the beautiful graphs and well supported by the numerical simulation) in the present scheme indicate that the bunch of VA-MCNTs can play a diverse and significant role in the important applications of THz medical photonics by varying the values of various parameters. The emitted THz radiation has the ability to detect changes in the DNA of human beings because the frequency of the emitted radiation is observed to lie in the frequency region of molecular spectra of DNA and the corresponding energy of THz radiation is not high enough to damage the DNA by ionization.

Terahertz generation by beat-wave mechanism of two Gaussian laser beams with corrugated noble-metal nanospheres in external magnetic field

An analytical model is presented that deals with THz generation by nonlinear mixing of two Gaussian laser beams with different frequencies ω1 and ω2 and wave vectors k1→ and k2→simultaneously propagating through an array of spatially corrugated noble-metal nanoparticles placed in the presence of a static magnetic field where ponderomotive nonlinearities are operative. The two co-propagating laser beams exert a nonlinear ponderomotive force on the plasma electrons, causing them to acquire nonlinear oscillatory velocity. This velocity leads to the generation of nonlinear macroscopic current density at the beat frequency ω (ω1-ω2) which further gives rise to strong terahertz radiation. The beat frequency lies in the THz region and density ripple provides the necessary phase-matching conditions. The externally applied magnetic field enhances the nonlinear coupling between the electric field of the lasers and causes resonant interaction of the laser beam with electrons of the NPs. THz radiations being non-invasive and biologically innocuous, play an important role in medical imaging, biomedical and pharmaceutical fields, and THz spectroscopy.

Generation of second harmonic terahertz surface plasmon wave over a rippled graphene surface

Abstract We propose a mechanism for the generation of second harmonic terahertz surface plasmon waves by incident terahertz electromagnetic radiation (ω, k 0) over a graphene surface deposited on the rippled dielectric substrate (SiO2). A p-polarized THz radiation incident obliquely on the graphene surface exerts a nonlinear ponderomotive force on free electrons in the rippled regime. This nonlinear ponderomotive force imparts oscillatory velocity to the electrons at frequency 2ω. Second harmonic oscillatory velocity couples with the modulated electron density and generates a nonlinear current density that drives second harmonic terahertz surface plasmon waves. Rippled surface provides an extra wave number for the phase matching condition to produce resonantly second harmonic at frequency 2ω and wavenumber (2k 0z + q). We examine the tunable response of second harmonic terahertz surface plasmon waves with respect to change in Fermi energy of graphene and laser incident angle. Second harmonic amplitude gets higher values by lowering the Fermi energy (E F) and increasing incident angle.

Nonlinear interaction of the fast magnetosonic wave with the extraordinary mode laser and ion-scaled turbulence generation in the magnetized plasma

This study introduces a nonlinear wave-wave coupling model to understand the nature of the turbulence generation at the ion scale observed in the interaction of high-intensity laser with plasma. For this nonlinear coupling of waves, the fast magnetosonic wave and the extraordinary mode laser are taken into account, along with the nonlinear ponderomotive force. The model dynamical equations have been developed for the extraordinary mode laser and the fast magnetosonic wave. Laboratory simulations have been employed to solve the obtained model equations utilizing the finite difference and pseudo-spectral methods. The simulation results show the initiation of the nonlinear progression of the laser beam at an early time and its turbulent nature at a later time. The background density perturbation, along with the cavity and hump caused by the ponderomotive force, has also been studied. The simulation results demonstrate that the propagation angle of the fast magnetosonic wave affects the magnitudes of the localization of the laser beam (pump wave) and the perturbed background density. The turbulent power spectra (ensemble-averaged) have also been studied for the different propagation angles of the fast magnetosonic wave. The turbulent spectra demonstrate that the plasma turbulence is MHD-type at small-scale lengths and ion-dominated at larger-scale lengths. This study also observed that the simulation results have some resemblance with the experimental results reported by Chatterjee et al.12 in the intense laser-plasma interaction experiment at a laboratory astrophysical scale.

Generation of High-Power Terahertz Waves in a Collisional and Magnetized Plasma by Two-Color Femtosecond Laser Beams

Terahertz (THz) radiation generation based on a nonlinear induced electron current density in the interaction of two-color femtosecond laser beams with collisional and magnetized plasma is investigated. The nonlinear electron current density that is responsible for THz radiation includes a share from nonlinear ponderomotive force and a part from relativistic term. In this work, relativistic effects along with the effects of variation of interacting plasma density, external magnetic field, and electron collision frequency on THz wave generation have been considered. The reduction of electron collision frequency along with rising in the magnitude of the external magnetic field generates more power without any deformation of radiation patterns. The angular distribution showing the radiation pattern of THz radiation in the forward direction is obtained and the effect of laser pulse second harmonic and variation of electric field on the directivity of generated waves is examined. The change in two-color laser beam intensities both in relativistic and nonrelativistic regimes leads to the generation of THz wave electric fields with different orders of magnitude. The numerical analysis indicated that the utilization of laser pulse second harmonic in a two-color scheme enhances the THz electric field leading to more intense radiation compared to single-color mechanism. The model also shows the effect of external magnetic field and electron collision frequency on the radiation efficiency of THz generation for linear and circular polarizations of two-color laser pulses.

Excitation of terahertz surface magnetoplasmons by nonlinear mixing of laser and its second harmonic on a rippled surface of n type semiconductor

We investigated the excitation of terahertz (THz) surface magneto plasmons (SMPs) by nonlinear mixing of laser and its second harmonic on a rippled surface of n-type semiconductor-free space interface. Obliquely incident p-polarized lasers exert a nonlinear ponderomotive force on free electrons of n-type semiconductor. Nonlinear ponderomotive force induces the oscillatory velocities at frequencies \(2\omega _{1}\) and (\(\omega _{1}-\omega _{2}\)). These oscillatory velocities beat the modulated electron density \(n_{q}\) to get the charge density perturbation at (\(2\omega _{1}, 2k_{1z}+q\)) and (\(\omega _{1}-\omega _{2}, k_{1z}-k_{2z}+q\)). Perturbed charge density couples with the linear oscillatory velocities to produce a nonlinear current density, which resonantly derives THz SMPs at frequency \(\omega =2\omega _{1}-\omega _{2}\) and propagation constant \(k_{z}=2k_{1z}-k_{2z}+q\). Here, q provides the extra wave number for the phase matching condition. The efficiency of THz SMPs wave amplitude was attained up to \(9\%\) and THz SMPs wave amplitude controlled by the electron cyclotron frequency \(\omega _{ce}\) and incident angle \(\theta\).

Excitation of terahertz surface magnetoplasmons by nonlinear mixing of two lasers on a rippled surface of magnetized n-InSb

We investigated the generation of terahertz (THz) surface magnetoplasmons (SMPs) over a rippled surface of magnetized n-type semiconductor (n-InSb) by using the nonlinear mixing of two p-polarized lasers with frequencies ω1, ω2 and wave numbers k1z, k2z, respectively. Incident obliquely from free space on the semiconductor surface with ripple wave number q exerts a nonlinear ponderomotive force on the free electrons at the frequency difference, ω=ω1−ω2. Ponderomotive force induces the nonlinear current that drives resonant terahertz surface magnetoplasmons at beat frequency with suitable wave number, kz=k1z−k2z+q. The amplitude of THz SMPs increases with the increase in applied external magnetic field. It also increases with increase the incidence angle of lasers and attains a maximum, and then drops to zero with further increase in the angle of incidence.

Spatiotemporal nonlinear evolution of the laser pulse and turbulence generation in laser produced plasmas

This study presents a model to understand the behavior of the turbulence generated in the magnetic field of mega gauss order during high-intensity laser interaction with magnetized plasma. The modified nonlinear Schrödinger (MNLS) equation is developed by contemplating the effect of the group velocity dispersion, diffraction, and nonlinearity induced by the relativistic variation of electron mass and the nonlinear ponderomotive force. Numerical simulation is carried out to solve the dimensionless MNLS equation. The simulation results show the generation of the solitary wave type coherent structures in the nonlinear spatiotemporal evolution of the laser pulse at the early stage, but subsequent turbulence generation has also been observed. The ensemble-averaged turbulent power spectrum has been studied and the power-law scaling is approximately ∼ k−1.85(a solid red line of scaling k−1.85 is given for reference). To get insight into the spatiotemporal nonlinear development of the laser pulse, while propagating in the plasma medium, a semi-analytical model has also been presented. The present study could be substantial in replicating astrophysical scenarios by laboratory simulations along with understanding the underlying quintessential physics of magnetic turbulence.

Electron Bernstein wave aided heating of collisional nanocluster plasma by nonlinear interactions of two super-Gaussian laser beams

In this present theoretical study, we investigate electron Bernstein wave (EBW) aided collisional nanocluster plasma heating by nonlinear interaction of two super-Gaussian laser beams. The interactions of laser beams electric field profiles with electronic clouds of nanoclusters cause the beat wave. The nonlinear ponderomotive force is generated through the beat wave. There may be good potential to excite the EBW aiding cluster plasma to lead electron heating via cyclotron damping of the Bernstein wave. An analytical scheme is proposed for the anomalous heating and evolution of electron temperature by using this mechanism. Graphical discussions were promised to achieve extreme heating rate via the spatial shape of super-Gaussian laser beams and the resonance condition of beat wave to surface plasmon frequency. The heating is controlled by tuning the laser beam width, mode index, collisional frequency, clustered radius, and density.

Numerical investigation of nonlinear current density and terahertz field induced by laser-plasma interaction

Unique characteristics of terahertz (THz) radiation can provide novel information in different fields of science and technology. In order to meet the demanding applications, the efficient THz radiations are highly needed. Therefore, in the present paper, we propose new schemes based on the interaction of nonrelativistic lasers with plasma. When an intense laser beam interacts with plasma, the electrons of plasma start oscillating and drives a nonlinear ponderomotive force results a nonlinear oscillatory velocity. By the beating of density ripple with this nonlinear velocity, a nonlinear current density appears. An efficient THz radiation is generated during laser-plasma interaction due to this nonlinear current density. The equations for terahertz field are derived with the help of Maxwell’s 3rd and 4th equations to obtain the normalized amplitude of terahertz radiation. Scheme offered here is the adapted one to achieve efficient THz radiation by optimizing the laser-plasma parameters.

Excitation of electron Bernstein waves by beating of two cosh-Gaussian laser beams in a collisional plasma

In this paper, a theoretical study has been proposed for excitation of electron Bernstein waves in collisional plasma with dc magnetic field by nonlinear interactions of two cosh-Gaussian laser beams. The beat wave with frequency and wave vector , exerts a nonlinear ponderomotive force on electrons. This nonlinear force has the potential to drive the electron Bernstein wave in collisional plasma with dc magnetic field. The convective loss of waves in plasma is also discussed. An analytical formalism is developed for power going into the electron Bernstein wave with respect to total laser power. The variation of normalized potential and power distribution profile as a function of beam direction, normalized beat wave frequency, and normalized collisional frequency is demonstrated to excite Electron Bernstein waves (EBWs) under resonance conditions. The spatial shape of laser beam, optimum laser beam width parameter, decentred parameter, extreme value of electron thermal velocity and cyclotron frequency is proposed for much more excitation. This proposed theory of electron Bernstein wave excitation may be applicable for plasma heating.

Nonlinear evolution of localized structures and turbulent magnetic field amplification by extraordinary laser beam in laser produced plasmas

In the present investigation, the nonlinear coupling of waves is evaluated to understand the turbulent magnetic field in the laser-produced plasma. The model equations are set up for the extraordinary (x-mode) laser and upper hybrid oscillations, incorporating the relativistic electron mass variation and the nonlinear ponderomotive force. The upper hybrid oscillations are excited due to the nonlinear ponderomotive force exerted by the x-mode laser. The nonlinear coupled system of x-mode laser and the upper hybrid oscillations were simulated numerically. Simulation results depict the evolution of localized structures with time. The ensemble-averaged turbulent power spectrum is obtained through numerical simulations. Furthermore, the frequency spectra associated with upper hybrid oscillation lie in the terahertz (THz) frequency range. A semi-analytical approach in the paraxial approximation has been studied to get a better perspective of the field localization process. Such studies of nonlinear wave-wave interaction are crucial to understand the turbulent magnetic field generation relating to various laboratory and astrophysical scenarios.

Second-harmonic generation of hollow Gaussian laser beams in inhomogeneous plasmas in the presence of wiggler magnetic field

Second-harmonic generation of hollow Gaussian laser beams (HGLBs) in inhomogeneous plasmas is investigated in the presence of an external wiggler magnetic field. The wiggler magnetic field and electric field of the laser pulse exert a ponderomotive force on electrons deriving electron velocity. Electron velocity, wiggler magnetic field and magnetic field of the laser pulse beat to exert a nonlinear ponderomotive force on electrons at the second-harmonic frequency. The nonlinear ponderomotive force can derive a nonlinear current density. Using linear and nonlinear current densities and wave equation in cylindrical coordinates, two equations obtaining different components of the electric field of second-harmonic wave (SHW) are derived. Results indicate that by increasing the external wiggler magnetic field, order of HGLB, rippled electron density, rippled wave number and initial intensity of the laser pulse, the amplitude of the excited SHW increases. Finally, it is found that by decreasing the initial width of the laser beam, the amplitude of SHW increases, attains a maximum and then decreases.

Electron Bernstein wave aided beat wave of Hermite-cosh-Gaussian laser beam absorption in a collisional nanocluster plasma

In this paper, we investigate the electron Bernstein wave aided beat wave of Hermite-cosh-Gaussian laser beam absorption in a collisional nanocluster plasma. The interactions of electric field profile of Hermite-cosh-Gaussian laser beams with electron clouds of nanoclusters cause the beat wave. The nonlinear ponderomotive force is generated through the beat wave of two Hermite-cosh-Gaussian laser beams. The time average power absorption per electron per unit area per unit time by electron Bernstein wave aided electric field of laser beat wave is derived. The graphical discussions were promised to achieve extreme absorption via spatial shape of Hermite-cosh-Gaussian laser beam and resonance condition of beat wave to surface plasmon frequency. The electron Bernstein waves parameters such as thermal velocity, cyclotron frequency and perpendicular component of wavenumber is also leading with beat wave for control and enhancement of absorption process in plasma embedded with nanocluster. The absorption is controlled by tuning the laser beam width, mode index, collisional frequency, clustered radius, and density.

Effect of pulse enhancement on beat wave THz generation in a ripple density magnetized plasma

Generation of terahertz pulse by the method of nonlinear mixing of two lasers in a plasma which is magnetized and have ripple density is studied permitting the effect of pulse enhancement. Due to nonlinear ponderomotive force, coupling of electron flow with density ripples occurs which leads to production of nonlinear current. Terahertz radiation are resonantly driven by this nonlinear current at beat frequency. Since here magnetic field is transverse to propagation of laser so we have transverse component of current density, while density ripples are responsible for phase matching. Thus, enhancement of pulse occurs due to the mismatch in group velocity of laser pulses and terahertz radiation, which further results in saturation of amplitude of terahertz waves.

The Whistler Traveling Wave Parametric Amplifier Driven by an Ion-Ring Beam Distribution from a Neutral Gas Injection in Space Plasmas

A new parametric amplifier model describes the observations of intensified whistler waves produced by a dedicated burn of the BT-4 engine on the Cygnus spacecraft during the NG-13 mission. Ground very low frequency (VLF) radio emissions at 25.2 kHz from a Navy NML transmitter in North Dakota were amplified by 20-30 dB during the Cygnus burn at 480-km altitude and recorded at 1060 km by the e-POP/RRI plasma wave receiver on the SWARM-E satellite. The amplification process starts with charge exchange between the exhaust molecules and the ambient O+ in the ionosphere to produce water vapor ions that spiral around the earth's magnetic field lines. This ion-velocity-ring distribution generates broadband, oblique-lower-hybrid (OLH) waves, which act as a pump for the parametric amplifier. The nonlinear ponderomotive force on the electrons causes the high-amplitude OLH pump to mix with the input whistler signal, yielding an OLH idler wave. Resonant mixing of the pump and idler electric fields promotes temporal growth in the amplitude of the whistler waves as they propagate through the exhaust cloud. The key features to rocket exhaust-driven amplification (REDA) process are broadband gain, bi-directionality along the magnetic field, pump depletion, phasing, and feedback. Pump depletion limits the intensity of the output whistler waves by wave energy conservation. The total wave energy is the electrostatic energy of the pump and idler lower hybrid waves plus the energy extracted by the propagating whistler signal. The whistler traveling wave parametric amplifier provides an efficient mechanism for active amplification of signals in space.

Terahertz radiation generation through nonlinear interaction of frequency chirped laser pulses with hot inhomogeneous plasmas

Terahertz (THz) radiation generation is investigated by nonlinear interaction of frequency chirped laser pulses with hot inhomogeneous plasmas. The plasma has a density ripple on its surface and linear inhomogeneity of the electron temperature. A high power laser obliquely incidents on a plasma and exerts a quasistatic nonlinear ponderomotive force on plasma electrons. This force oscillates electrons having a drift velocity with finite transverse component. The drift velocity beats with inhomogeneous density and temperature and consequently a nonlinear current density is produced which leads to the THz wave. The linear and nonlinear current densities are coupled with the wave equation and this equation is solved in the electrostatic and electromagnetic cases. In another case, the wave equation is solved numerically by considering both electrostatic and electromagnetic cases. The effects of frequency chirped parameter, incident laser intensity, and the inhomogeneities of electron density and electron temperature are studied on the amplitude of the THz wave. Results show that by increasing the THz frequency, the amplitude of the THz wave decreases. Moreover, by increasing frequency chirped parameter, incident laser intensity, and the inhomogeneities of electron density and electron temperature, the amplitude of the THz wave increases.

Magnetosonic shocklets in electron-positron-ion plasmas

The formation and propagation characteristics of the magnetosonic shocks are investigated in a three-component magnetoplasma, consisting of warm dynamical ions with hot inertialess electrons and positrons. By solving the well-known nonlinear magnetohydrodynamic equations within the framework of diagonalization method, a set of two exact nonlinear wave equations is derived, which permits for both analytical as well as numerical solutions. It is shown that coherent solitary structures are formed at time τ = 0, which transform into the magnetosonic shocklets with the passage of time (τ > 0) because of the rapid steepening of ion-fluid velocity and magnetic field perturbations. The nonlinear ponderomotive force could be the major responsible force behind the wave steepening and wave breaking in such plasmas. Furthermore, the variation of plasma β, the positron-to-electron density ratio p and the ion-to-electron temperature ratio σ significantly modifies the profiles of the ion-fluid velocity and magnetic field. The present study might be useful for understanding the nonlinear propagation of magnetosonic shocklets in interstellar medium and in laboratory plasma experiments, where an additional positron-component exist.

Production of Terahertz Radiations by Short Pulse Lasers

In this paper, we develop an analytical formalism for THz generation from Laser filaments in the presence of static electric field in the magnetized collisional plasma. Two femtosecond laser pulses with different frequencies undergo filamentation in magnetized collisional plasma to have non-linear coupling in the presence of transverse static electric field. This results in balancing action of static ponderomotive force with pressure gradient force and forms transverse density ripple and non-linear ponderomotive force couple with density ripple to provide strong non-linear transverse current which results in excitation of THz Radiations at resonance. This coupling is further enhanced by electric static field.