Laguerre-Gaussian Profile Research Articles

Laguerre-Gaussian and beamlet array as second generation laser heater profiles

The microbunching instability is known to be detrimental to x-ray free electron laser performance. At the Linear Coherent Light Source, the microbunching instability is suppressed with a laser heater, which increases the uncorrelated energy spread of e-beam in the injector. While the current system has been shown to improve x-ray brightness, other laser architectures could further enhance performance. In this study, we model the interaction between a laser and e-beam with arbitrary transverse profiles and examine the effect of various laser designs on the energy distribution of the electrons after the injector and laser heater, as well as their ability to suppress microbunching instability. This simulation incorporates random transverse jitter in order to reproduce physically representative operation of the Linac Coherent Light Source. We compare Gaussian and Laguerre-Gaussian modes, and explore composite beams in the form of an array of Gaussian beamlets. We conclude that the Gaussian laser profile is highly susceptible to e-beam ellipticity and random transverse jitter. The Laguerre-Gaussian profile, a mathematically ideal solution to suppressing microbunching, is less susceptible to these effects and can provide effective suppression even with a distorted e-beam, though performance can be improved by increasing stabilization. The array of beamlets presents a solution that produces consistent and smooth energy distributions with significantly less variance in heating than the Laguerre-Gaussian profile.

Coherent population transfer with Laguerre–Gaussian pulses

We report a scheme to achieve coherent population transfer in a four-level double- closed-loop atomic system by utilizing the coherent beams with Laguerre–Gaussian profiles. It is demonstrated that a maximal population transfer is achieved for a special value of the relative phase of the applied fields. We then compare the results with a similar configuration, but for the laser pulses with the usual Gaussian profiles and conclude that using the Laguerre–Gaussian modes can result in almost complete population transfer. Besides, the creation of a superposition between two lower states can be achieved through properly changing the relative phase. The suggested scheme may hold great practicality for the realization of the population transfer as well as creation of the superposition between states in the quantum systems with multiple states.

Light deflection by light: Effect of incidence angle and inhomogeneity

We study the angular deflection of the circular polarized components of a linearly polarized probe field in a weakly birefringent atomic system in tripod configuration. A spatially inhomogeneous control field incident obliquely onto an atomic vapor cell facilitates a large angular divergence between circular components. We show that the angular resolution can be dynamically controlled by optimally choosing the angle of incidence and the transverse profile of the control beam. For instance, by employing a Laguerre-Gaussian profile of the control field, one can impart a large angular divergence to the circular components close to the entry face of the atomic vapor cell. We further demonstrate how such a medium causes the focusing and refocusing of the probe field, thereby acting as a lens with multiple foci. The absorption in the medium remains negligible at resonance due to electromagnetically induced transparency (EIT).

Fluorescence correlation spectroscopy with a doughnut-shaped excitation profile as a characterization tool in STED microscopy.

The resolution of stimulated emission depletion (STED) microscopes is ultimately limited by the quality of the doughnut-shaped illumination profile of the STED erase beam. We show here that in the focal plane this illumination profile is well approximated by an analytical expression - a difference of Gaussian functions, which tends towards a first order Laguerre-Gaussian profile in the case of a well aligned beam with a true zero-intensity central minimum. We further show that along the optical axis the maximum intensity profile is reasonably approximated by a Gaussian decay away from the focal plane. The result is a fully Gaussian analytical approximation of the three-dimensional point-spread function of STED erase beams. This allows the derivation of an analytical form for the autocorrelation function of the fluorescence generated by fluorophore diffusion through the STED depletion volume. We verified this form to be correct by performing fluorescence correlation spectroscopy (FCS) experiments in solutions of the dye Alexa Fluor 532. Since the quality of the illumination profile is reflected in the shape of the autocorrelation function, we propose that fluctuation analysis can be used as a tool to assess the quality of STED erase beams.

On the exchange of orbital angular momentum between twisted photons and atomic electrons

We obtain an expression for the matrix element for scattering of a twisted (Laguerre–Gaussian profile) photon from a hydrogen atom. We consider photons incoming with an orbital angular momentum (OAM) of ℓħ, carried by a factor of eiℓϕ not present in a plane-wave or pure Gaussian profile beam. The nature of the transfer of +2ℓ units of OAM from the photon to the azimuthal atomic quantum number of the atom is investigated. We obtain simple formulas for these OAM flip transitions for elastic forward scattering of twisted photons when the photon wavelength λ is large compared with the atomic target size a, and small compared with the Rayleigh range zR, which characterizes the collimation length of the twisted photon beam.

Spatial modes of phase-sensitive parametric image amplifiers with circular and elliptical Gaussian pumps

We develop a method for finding the number and shapes of the independently squeezed or amplified modes of a spatially-broadband, travelling-wave, frequency- and polarization-degenerate optical parametric amplifier in the general case of an elliptical Gaussian pump. The obtained results show that for tightly focused pump only one mode is squeezed, and this mode has a Gaussian TEM(00) shape. For larger pump spot sizes that support multiple modes, the shapes of the most-amplified modes are close to Hermite- or Laguerre-Gaussian profiles. These results can be used to generate matched local oscillators for detecting high amounts of squeezing and to design parametric image amplifiers that introduce minimal distortion.

Nonlinear tubular Bragg diffraction and all-optical switching over Laguerre-Gaussian beams

In this paper we show the nonlinear diffraction of a weak beam on a Laguerre-Gaussian (LG) beam of high intensity, where a part of the weak beam is transformed to the shape of a LG beam. We also show the rotation of a second LG beam influenced by this LG beam until their petals overlap. It is, to our knowledge, the first time that a soliton interaction extends to beams of LG profile. This work can be useful in all optical switching and signal processing.