Laguerre-Gaussian Laser Modes Research Articles

Controllable experimental modulation of high-order Laguerre-Gaussian laser modes.

High-order helical and sinusoidal Laguerre-Gaussian (LG) laser modes have uneven energy distribution among their multiple concentric vortex core rings and lobes, respectively. Here, we explore an experimental method to reshuffle the optical energy among their multiple concentric vortex core rings and lobes of high-order LG modes in a controllable manner. We numerically designed a diffractive optical element displayed over a spatial light modulator to rearrange optical energy among multiple concentric vortex core rings. This changes outer low-intensity concentric vortex core rings into high-intensity vortex core rings of high-order helical LG modes at the Fourier plane. The precise generation of a high-order modulated helical LG laser mode has a maximum number of highly intense concentric vortex core rings compared to known standard helical LG modes. Further, this method is extended to high-order sinusoidal LG modes consisting of both low- and high-intensity lobes to realize modulated sinusoidal LG modes with a maximum number of highly intense lobes in a controllable manner. We envisage that the modulated helical and sinusoidal high-order LG modes may surpass standard LG modes in many applications where highly intense rings and lobes are crucial, as in particle manipulation of micro- and nanoparticles, and optical lithography.

Self-Q-switched Tm:YAP vortex laser by thermal-lensing effect

We demonstrated a self-Q-switched Gaussian laser mode and a Laguerre-Gaussian (LG0,1) laser mode at 1937.9 nm, which was directly generated by thermal lensing effect in a Tm:YAP laser. By building a Mach-Zehnder interferometer, the helical nature of the wavefront is checked. The experimental maximum output power of LG01 pulsed vortex laser was 83 mW with the repetition rate of 75.46 kHz and pulse width of 1.711 μs, corresponding to the peak power of 0.64 W and single pulse energy of 1.10 μJ. The self-Q-switched Tm:YAP vortex laser is compact and provides a convenient way to construct 2 μm pulsed vortex laser source.

Structured laser beams: toward 2-μm femtosecond laser vortices

Structured ultrashort-pulse laser beams, and in particular eigenmodes of the paraxial Helmholtz equation, are currently extensively studied for novel potential applications in various fields, e.g., laser plasma acceleration, attosecond science, and fine micromachining. To extend these prospects further, in the present work we push forward the advancement of such femtosecond structured laser sources into the 2-μm spectral region. Ultrashort-pulse Hermite– and Laguerre–Gaussian laser modes both with a pulse duration around 100 fs are successfully produced from a compact solid-state laser in combination with a simple single-cylindrical-lens converter. The negligible beam astigmatism, the broad optical spectra, and the almost chirp-free pulses emphasize the high reliability of this laser source. This work, as a proof of principle study, paves the way toward few-cycle pulse generation of optical vortices at 2 μm. The presented light source can enable new research in the fields of interaction with organic materials, next generation optical detection, and optical vortex infrared supercontinuum.

Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams.

While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to assess the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. Some of these approaches are limited to a certain alphabet, while others tend to fall short when considering optical beams with a nontrivial structure, such as Hermite-Gauss, Laguerre-Gauss, and other modes with a nontrivial structure. Here, we propose a new definition of the classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. Following this definition, we calculate the amount of information in Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition and experimentally validate it by reconstruction of the Wigner distribution function from the intensity distribution of structured laser beams. We experimentally demonstrate the technique that allows to infer field structure of the laser beams in singular optics to assess the amount of contained information. Given the generality, this approach of defining information via analyzing the beam complexity is applicable to laser modes of any topology that can be described by well-behaved functions. Classical Shannon information, defined in this way, is detached from a particular alphabet, i.e., communication scheme, and scales with the structural complexity of the system. Such a synergy between the Wigner distribution function encompassing the information in both real and reciprocal space and information being a measure of disorder can contribute into future coherent detection algorithms and remote sensing.

Interaction of Tungsten tips with Laguerre-Gaussian beams

Interaction of femtosecond laser pulses with metallic tips have been studied extensively and they have proved to be a very good source of ultrashort electron pulses. We present our study of interaction of Laguerre-Gaussian (LG) laser modes with Tungsten tips. We report a change in the order of the interaction for LG beams and the difference in the order of interaction is attributed to ponderomotive shifts in the energy levels corresponding to the enhanced near field intensity supported by numerical simulations.

Temporally shaped Laguerre–Gaussian femtosecond laser beams

Femtosecond vortex beams with adjustable temporal pulse shapes are generated. These shaped laser pulses are characterized in the spectral domain by determination of the spectral amplitude and phase as well as in the spatial domain by expansion of the beam profile in a superposition of Laguerre-Gaussian transversal laser modes. The experiments demonstrate that the temporal pulse shapes impressed with a pulse shaper based on a programmable liquid-crystal spatial light modulator are basically unaltered by subsequent transmission through a spiral phase plate, while a high-quality optical vortex is imposed. The combination of programmable pulse shapes and optical vortices in femtosecond laser beams opens new possibilities for applications in micromachining, high harmonic generation, and microscopy.

Generating laser transverse modes analogous to quantum Green’s functions of two-dimensional harmonic oscillators

We theoretically analyzed the relationship between quantum Green’s functions of two-dimensional harmonic oscillators and radial-order Laguerre–Gaussian laser modes of spherical resonators. By using a nearly hemispherical resonator and a tight focusing in the end-pumped solid-state laser, we successfully generated various laser transverse modes analogous to quantum Green’s functions. We further experimentally and numerically verified that the transverse order associated with quantum Green’s functions is noticeably raised with increasing the pump power induced by the thermal effect. More importantly, the high lasing efficiency and the salient structure enable the present laser source to be used in exploring the light–matter interaction.

High-order-harmonic generation by Laguerre-Gaussian laser modes: Control of the spectra by manipulating the spatial medium distribution

We study high-order-harmonic generation (HHG) by the incident laser beam in the Laguerre-Gaussian mode with a nonzero topological charge. We find that the harmonic signal in the central spot on the beam axis does not always vanish and depends on the distribution of the medium in the focal region of the incident laser beam. The HHG spectra on the beam axis can be controlled by changing the spatial medium distribution. General theoretical results are confirmed by calculations of HHG in the medium of argon atoms, with the single-atom response obtained by means of the time-dependent density functional theory.

Optimization of electromagnetically induced transparency by changing the radial size of Laguerre–Gaussian laser modes

We demonstrate electromagnetically induced transparency (EIT) in ultracold Rb87 with the control laser in a Laguerre–Gaussian mode and the probe laser in a Gaussian mode. The effects on EIT transmission spectra due to varying control mode sizes are explored and optimized. The narrowest EIT features that still exhibit large signal contrast occur when the control and probe laser have equivalent waists, despite the differences in the radial intensity profiles of the probe and control beams.

Laguerre-Gaussian beams with complex shift in cartesian coordinates

We studied a generalization of the family of Laguerre-Gaussian (LG) laser modes with asymmetrical intensity distribution. As the asymmetrical LG beam is propagating in a homogeneous medium, the asymmetry of its main (central) bright ring reduces, while the contrast of the rest rings increases. The number of bright rings coincides with that of a standard (symmetrical) LG mode. Using the expansion of the complex amplitude into the angular spectrum of plane waves, we calculated analytically the power of the asymmetrical LG beams and projection of their orbital angular momentum (OAM) on the optical axis. It is found that the normalized OAM (OAM per photon) is completely determined by the topological charge and the ratios between the shifts and the waist radius. We also found the conditions under which the normalized OAM coincides with the topological charge (as is the case for the optical vortices).

Laguerre-Gaussian beams with complex shift in cartesian coordinates

We studied a generalization of the family of Laguerre-Gaussian (LG) laser modes with asymmetrical intensity distribution. As the asymmetrical LG beam is propagating in a homogeneous medium, the asymmetry of its main (central) bright ring reduces, while the contrast of the rest rings increases. The number of bright rings coincides with that of a standard (symmetrical) LG mode. Using the expansion of the complex amplitude into the angular spectrum of plane waves, we calculated analytically the power of the asymmetrical LG beams and projection of their orbital angular momentum (OAM) on the optical axis. It is found that the normalized OAM (OAM per photon) is completely determined by the topological charge and the ratios between the shifts and the waist radius. We also found the conditions under which the normalized OAM coincides with the topological charge (as is the case for the optical vortices).

Angular spin-orbit coupling in cold atoms

We propose coupling two internal atomic states using a pair of Raman beams operated in Laguerre-Gaussian laser modes with unequal phase windings. This generates a coupling between the atom's pseudo-spin and its orbital angular momentum. We analyze the single-particle properties of the system using realistic parameters and provide detailed studies of the spin texture of the ground state. Finally, we consider a weakly interacting atomic condensate subject to this angular spin-orbit coupling and show how the inter-atomic interactions modifies the single-particle physics.

Confinement of ultracold atoms in a Laguerre–Gaussian laser beam created with diffractive optics

We report 2D confinement of 87Rb atoms in a Laguerre–Gaussian laser beam. Changing of the sign of the detuning from the atomic resonance dramatically alters the geometry of the confinement. With the laser detuned to the blue, the atoms are confined to the dark, central node of the Laguerre–Gaussian laser mode. This trapping method leads to low ac Stark shifts to the atomic levels. Alternatively, by detuning the laser to the red of the resonance, we confine atoms to the high intensity outer ring in a multiply-connected, toroidal configuration. We model the confined atoms to determine azimuthal intensity variations of the trapping laser, caused by slight misalignments of the Laguerre–Gaussian mode generating optics.

Dual-wavelength laser with topological charge

We demonstrate the simultaneous oscillation of different photons with equal orbital angular momentum in solid-state lasers for the first time to our knowledge. Single tunable Hermite-Gaussian (HG0,n) (0 ≤ n ≤ 7) laser modes with dual wavelength were generated using an isotropic cavity. With a mode-converter, the corresponding Laguerre-Gaussian (LG0,n) laser modes were obtained. The oscillating laser modes have two types of photons at the wavelengths of 1077 and 1081 nm and equal orbital angular momentum of nħ per photon. These results identify the possibility of simultaneous oscillation of different photons with equal and controllable orbital angular momentum. It can be proposed that this laser should have promising applications in many fields based on its compact structure, tunable orbital angular momentum, and simultaneous oscillation of different photons with equal orbital angular momentum.

Features of nonparaxial propagation of gaussian and bessel beams along the axis of the crystal

It is analytically and numerically shown that nonparaxial mode laser beams propagating along the axis of a crystal demonstrate the periodic change of intensity connected with an interference of ordinary and extraordinary beams. For Bessel beams the oscillation period inversely proportional to a square of spatial frequency of a laser beam and a difference of dielectric permittivity. For the linearly-polarized radiation there is a periodic redistribution of energy between two transversal components, and for beams with circular polarization energy is pumped from an initial beam into the vortex beam of the second order and vice-versa. The received dependence allows to select parameters of an incident beam with length of a crystal for full transformation to the vortex beam. For Gaussian beams similar periodic changes have nonlinear character. Laguerre-Gaussian laser modes with high radial order show a behavior close to Bessel beams on small distances. With increase of a distance the length of a period is increasing and the beam is astigmatically deforming.

Shaping Laguerre–Gaussian laser modes with binary gratings using a digital micromirror device

Laguerre-Gaussian (LG) beams are used in many research fields, including microscopy, laser cavity modes, and optical tweezing. We developed a holographic method to generate pure LG modes (amplitude and phase) with a binary amplitude-only digital micromirror device (DMD) as an alternative to the commonly used phase-only spatial light modulator. The advantages of such a DMD include very high frame rates, low cost, and high damage thresholds. We have shown that the propagating shaped beams are self-similar and their phase fronts are of helical shape as demanded. We estimate the purity of the resultant beams to be above 94%.

Gluon spin, canonical momentum, and gauge symmetry

It is well known that in gauge theories, the spin (and orbital angular momentum) of gauge particles is not gauge invariant, although the helicity is; neither are the canonical momentum and canonical angular momentum of charged particles. However, the simple appeal of these concepts has motivated repeated attempts to resurrect them as physical descriptions of gauge systems. In particular, measurability of the gluon-spin-contribution to the proton helicity in polarized proton scattering has generated many theoretical efforts in generalizing it and others as gauge-invariant quantities. In this work, we analyze the constraints of gauge symmetry, the significance of gluon spin in the light-cone gauge, and what is possible and natural in QCD parton physics, emphasizing experimental observability and physical interpretation in the structure of bound states. We also comment on the measurability of the orbital angular momentum of the Laguerre-Gaussian laser modes in optics.

Direct generation of optical vortex pulses

We demonstrate the direct generation of optical vortex pulses with stable energy and changeable orbital angular momentum. Single Laguerre-Gaussian (LG0,l) laser modes were directly generated using a laser diode with output intensity profile of doughnut distribution. With passive Q-switching, vortex pulses with stable energy were obtained. Moreover, the topological charge was changeable by variation of the pump power. By a mode-converter and second harmonic generation, the LG0,2l mode was identified. It can be proposed that this pulsed laser should have promising applications in various fields based on its compact structure, stable and high pulse energy, and changeable orbital angular momentum.

HG-LG Mode Conversion with Stressed 3-Mode Fibers under Polarization

We have coupled an upright HG mode into a fiber-optic waveguide and used the application of stress to generate a Laguerre-Gaussian laser mode. We have generalized previous results by McGloin et al. by using a polarized input beam, a true 3-mode fiber and by applying the stress on a stripped piece of the optical waveguide. These generalizations are necessary in order to perform quantum information experiments and obtain reliable information on the stress imposed on the optical fiber.

Bose–Einstein condensation transition studies for atoms confined in Laguerre–Gaussian laser modes

Multiply-connected traps for cold, neutral atoms fix vortex cores of quantum gases. Laguerre–Gaussian laser modes are ideal for such traps due to their phase stability. We report theoretical calculations of the Bose–Einstein condensation transition properties and thermal characteristics of neutral atoms trapped in multiply connected geometries formed by Laguerre–Gaussian (LG p l ) beams. Specifically, we consider atoms confined to the anti-node of a LG 0 1 laser mode detuned to the red of an atomic resonance frequency, and those confined in the node of a blue-detuned LG 1 1 beam. We compare the results of using the full potential to those approximating the potential minimum with a simple harmonic oscillator potential. We find that deviations between calculations of the full potential and the simple harmonic oscillator can be up to 3%–8% for trap parameters consistent with typical experiments.