Hermite-Gaussian Laser Beam Research Articles

Second harmonic generation of self-focused Hermite-Gaussian laser beam in collisional plasma

This work presents a theoretical approach for self-focusing as well as second harmonic generation of a Hermite-Gaussian (HG) laser beam in collisional plasma. On incidence in plasma, high electric field of HG laser beam causes the nonuniform distribution of plasma electrons as a result of collisional nonlinearity and thus creates the refractive index gradient which causes the wavefront to collapse about the centre and form a tight focus. Moment theory approach has been used to derive the coupled differential equations governing the spot size of the HG laser beam in both the transverse directions x and y. Second harmonics of the HG laser beam is generated by the excitation of the electron plasma wave at pump frequency which further interacts with the pump beam to generate the radiation with double the frequency of the later. Different mode indices of HG laser beam have significant effect on the self-focusing as well as on second harmonic generation of the laser beam in plasma. It has been observed that for higher mode indices (TEM02) second harmonic yield (SHY) is greater.

Terahertz radiation generation through the nonlinear interaction of Hermite and Laguerre Gaussian laser beams with collisional plasma: Field profile optimization

The nonlinear interaction of Hermite-Gaussian and Laguerre-Gaussian (LG) laser beams with a collisional inhomogeneous plasma is studied, and the amplitude of the emitted terahertz (THz) electric field is evaluated. The effects of laser beams and plasma parameters, including the beams width, LG modes, the plasma collision frequency, and the amplitude of density ripple on the evolution of THz electric field amplitude, are examined. It is found that the shape of the generated THz radiation pattern can be tuned by the laser parameters. In addition, the optimum values of the effective parameters for achieving the maximum THz electric field amplitude are proposed. It is shown that a significant enhancement up to 4.5% can be obtained in our scheme, which is much greater than the maximum efficiency obtained for laser beams with the same profiles.

TEM modes influenced electron acceleration by Hermite–Gaussian laser beam in plasma

AbstractElectron acceleration by a circularly polarized Hermite–Gaussian (HG) laser beam in the plasma has been investigated theoretically for the different transverse electromagnetic (TEM) mode indices (m, n) as (0, 1), (0, 2), (0, 3), and (0, 4). HG laser beam possesses higher trapping force compared with a standard Gaussian beam owing to its propagation characteristics during laser–electron interaction. A single-particle simulation indicates a resonant enhancement in the electron acceleration with HG laser beam. We present the intensity distribution for different TEM modes. We also analyze the dependence of beam width parameter on electron acceleration distance, which effectively influences the electron dynamics. Electron acceleration up to longer distance is observed with the lower modes. However, the higher electron energy gain is observed with higher modes at shorter distance of propagation.

Optical trapping and manipulation of light-absorbing particles by means of a Hermite–Gaussian laser beam

This paper describes simultaneous optical trapping and displacement of several nonspherical light-absorbing microparticles in air by means of a focused Hermite–Gaussian laser beam (laser mode TEM10, radiation wavelength 457 nm). Agglomerations of carbon nanoparticles are displaced in three dimensions by distances of the order of a millimeter. The structure of the Hermite–Gaussian beam used here made it possible to displace microparticles simultaneously along two parallel trajectories in space.

Vortex Hermite-Gaussian laser beams.

We study elliptical vortex Hermite-Gaussian (vHG) beams, which are described by the complex amplitude proportional to the nth-order Hermite polynomial whose argument is a function of a real parameter a. At |a|<1, on the vertical axis of the beam cross section, there are n isolated optical nulls that produce optical vortices with topological charge +1(a<0) or -1(a>0). At |a|>1, similar isolated optical nulls of the vHG beams are found on the horizontal axis. At a=0, the vHG beam becomes identical to the HG mode of the order (0,n). We derive the orbital angular momentum (OAM) of the vHG beams, which depends on the parameter a and an ellipticity parameter of the Gaussian beam. The derived equation allows the transverse intensity of the vHG-beam to be changed without changing its OAM. The experimental and theoretical results are in good agreement.

Hermite-gaussian laser beams with orbital angular momentum

We consider vortex Hermite-Gaussian modes (VHG-modes) with their complex amplitude being proportional to an n-th order Hermite polynomial dependant on a real parameter a. When |a| &lt; 1, there are n isolated intensity nulls on the horizontal axis in the beam’s cross-section. These nulls generate optical vortices with a topological charge of +1 (a &lt;0) or -1 (a &gt; 0). If |a| &gt; 1, the VHB-mode has analogous isolated nulls on the vertical axis. When |a| = 1, all n isolated nulls appear on the optical axis in the center of the beam and generate an n-th order optical vortex. In this case, the VHG-mode coincides with a Laguerre-Gaussian mode of order (0, n). For a = 0, the VHG-mode coincides with a Hermite-Gaussian mode of order (0, n). We calculate the orbital angular momentum of the VHB-modes, which depends on a parameter a and varies from 0 (at a = 0 and a → ∞) to n (at a = 1).

Reflective terahertz imaging with the TEM01 mode laser beam

Reflective terahertz imaging with a first-order Hermite-Gaussian laser beam was experimentally investigated. High spatial resolution targets prepared by direct laser microprocessing were used to evaluate the performance. The reflection imaging system at 2.524 THz frequency demonstrated up to diffraction limited resolution using the single focusing mirror with the numerical aperture not smaller than 0.6. The TEM(01) mode laser beam was also applied for practical samples such as silicon solar cell terahertz (THz) imaging. It is shown that usage of appropriate optics enables us to obtain high-quality THz images with the multimode laser beam.

Orbital angular momentum of superposition of two generalized hermite–gaussian laser beams

We have obtained an expression for complex amplitude of the generalized paraxial Hermite-Gaussian (HG) beams. At certain parameters these beams become well-known HG modes and elegant HG beams. We calculated an orbital angular momentum (OAM) of linear combination of two generalized HG beams with transposed adjacent indices and with phase delay of p/2. It has been shown that for a sum of two HG modes the OAM is integer, while for two elegant HG beams it is always unitary and for two hybrid HG beams it is fractional.

Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp

Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp has been investigated. It is known that a laser beam shows an oscillatory self-focusing and defocusing behavior with the propagation distance. To overcome the defocusing, localized upward plasma density ramp is introduced, so that the laser beam attains a minimum spot size and maintains it with only a mild ripple. The density ramp could be important for the self-focusing of a Hermite–Gaussian laser by choosing the laser and plasma parameters appropriately. Self-focusing becomes stronger as the propagation distance increases. The behavior of beam-width parameters with the distance of propagation is presented graphically.

Self-focusing and defocusing of TEM 0p Hermite–Gaussian laser beams in collisionless plasma

The authors have investigated the self-focusing and defocusing of first six TEM 0 p 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.

Dependence of the electron energy gain on the field polarization of Hermite–Gaussian beam

The interaction of charged particles with a Hermite–Gaussian laser beam is numerically and analytically investigated for linear and circular polarizations. The electron final energy is obtained as a function of the laser parameter (polarization, waist and intensity) and the electron parameter (initial injection energy and initial coordinate, ( z 0 ) ). The energy gain increases with increase in laser beam waist and laser intensity. For relativistic electrons and laser intensities I 0 ∼ 10 20 – 10 21 W / cm 2 an increase in electron energy Δ ɛ ∼ ( 10 – 20 ) GeV can be attained.

Comment on “Field structure and electron acceleration in a laser beam of a high-order Hermite–Gaussian mode” [J. Appl. Phys. 101, 083113 (2007)

Wang et al. [J. Appl. Phys. 101, 083113 (2007)] investigated vacuum electron acceleration by high-order Hermite–Gaussian laser beams. However, we reveal that some of their explanations for their simulation results are not reasonable. We investigate their simulation in detail and discover that the injection momentum distributions in the longitudinal and transverse directions play an important role in inducing the valley that appears in the plot of the ejection energy as a function of the injection angle.

Direct acceleration of electrons by intense crossed Hermite–Gaussian laser beams

Abstract Electron acceleration by two crossed linearly polarized Hermite–Gaussian laser beams in vacuum has been proposed and investigated in the Letter. The laser fields have the same amplitude and frequency. To accelerate electrons along z -axis directly, the necessary conditions and energy gain expressions are given.

Direct acceleration of electrons using single Hermite–Gaussian beam and Bessel beam in vacuum

The longitudinal electric field E z of Hermite–Gaussian laser beam or Bessel laser beam, concentrating on the axis, is favorable for using to directly accelerate electrons. The general characteristics of intense laser beam used to accelerate electrons along axis, the necessary conditions and the energy gain relations are discussed.

Transverse Fourier analysis of squeezed light in diode lasers

The transverse properties of squeezed light are studied for a number-squeezed edge diode laser working in an external-cavity configuration. Light noise is analyzed as a function of the transverse wave vector transmitted by a single slit at the focal plane of a short focal lens. Noise measurements obtained by opening the slit centered at the kx=0 position show a minimum squeezing at the slit center that increases up to the full-beam noise-compression. Noise is also measured by displacing a single slit of fixed width at the focal plane. The results of this wave-vector dependence are compared with a theory in which the slit is treated as a beam splitter for the incoming Hermite–Gaussian laser beam. A summation of the noise contributions at each wave vector cannot give the obtained result with the slit being open, which indicates a possible noise correlation of light with distinct wave vectors.

Harmonic oscillator fiducials for Hermite-Gaussian laser beams

This paper exploits the identical functional forms of quantum mechanical harmonic oscillators and Hermite-Gaussian laser beams to investigate the probability densities of large-order modes. The classical limits of a two-dimensional harmonic oscillator provide corresponding integration limits for the photon probability densities of the laser-beam modes to determine the fraction of photons detected therein. The probabilities of detecting photons within the ‘classical limits’ of Hermite-Gaussian laser beams exhibit a power-law dependence in the limit of large-order modes and asymptotically approach unity, in agreement with the Correspondence Principle. The classical limits for large-order modes are shown to include all of the nodes and peaks for Hermite-Gaussian laser beams; Sturm's theorem provides a direct proof that is further illustrated by examination of the concavity and convexity of Hermite functions.

Polarization properties of Maxwell-Gaussian laser beams.

Gaussian beam solutions of Maxwell's equations are constructed in terms of the solutions of the paraxial scalar wave equation. Explicit expressions for the field components of Hermite-Gaussian laser beams are given and their polarization and propagation characteristics are discussed. Experimental evidence for the polarization structure of Hermite-Gaussian laser beams is presented.

Acceleration of particles by an asymmetric Hermite-Gaussian laser beam.

The application of a focused laser beam to accelerate particles using the longitudinal electric-field component is investigated one step beyond the paraxial-ray approximation. Vacuum acceleration to high energies along the axis of an asymmetric Hermite-Gaussian beam is in principle possible, but the interaction distance is short (one Rayleigh length on each side of focus). The use of a gas can increase the energy gain per focal passage by a factor of 2.4, while permitting arbitrary spacing of drift tubes and lenses of a lens waveguide. Drift tubes are therefore not needed. A beam loaded with a graded-index gas, in which phase and particle velocities are equal over the interaction trajectory, permits three-dimensionally stable particle trajectories. This property is explained by the anisotropy of the medium in a comoving reference frame. The functions of acceleration, focusing, and bunching of particles can thus be performed simultaneously by a single optical beam that is guided in a lens waveguide.

Hermite-Gaussian beam transformation by a shifted spherical lens at normal incidence

A solution of the problem of transformation of a general p1,p2-mode simple astigmatic Hermite-Gaussian laser beam due to its normal incidence on a shifted thin spherical lens is given. The treatment of the astigmatic laser beams at their off-axial incidence on a lens makes clear the distinction between the geometrical focus of the lens and the focal shifts of the two waists of the outgoing beam, whose presence is significantly felt when the lens is situated within the Rayleigh ranges of the incoming beam.