Gaussian Beam Research Articles

Photonic spin Hall effect in twisted bilayer phosphorene

We investigate the photonic spin Hall effect of a linearly polarized Gaussian beam reflected on the surface of twisted bilayer phosphorene. The photonic spin shift depends strongly on optical resonance behavior, which is determined by the twist angle. The magnified spin shift near the Brewster angle is sensitive to the twist angle and can be fitted by numerical models. In particular, the spin shifts in the terahertz region of frequency are well within the current experimental detection precision. Our findings suggest that the photonic spin Hall effect is promising for precise characterization of the optical property and the structure of twisted bilayer phosphorene.

Improving the beam quality of single-grating spectrally combined fiber lasers with adaptive optics.

Spectral combination is promising for diffraction-limited beam quality and single aperture beams. Unfortunately, beamlet deviations, linewidth broadening, and thermal aberrations inevitably degrade the beam quality. Many high-power laser systems integrate adaptive optics systems to maintain beam qualities. However, owing to the nature of incoherent combination, there is no well-defined wavefront in the spectrally combined beam, and whether phase compensations can enhance beam quality has not been discussed yet. We present the feasibility of improving the beam quality of spectral combined fiber lasers by adaptive optics. Simulations indicate that common path aberrations can be effectively corrected by adaptive optics, while beam quality degraded by displacement deviations and linewidth broadening cannot be improved. Additionally, the combined beam could be directly used as the beacon light in the propagation tunnel. To our knowledge, this study is the first to demonstrate that adaptive optics can improve the beam quality of spectrally combined fiber lasers and enable a further step toward diffraction-limited beam quality.

Z-scan model for Laguerre-Gaussian excitation in mode-mismatched thermal lens spectrometry.

In this work, we have introduced a Z-scan thermal lens (TL) model based on Laguerre-Gaussian (LG) L G10 laser induced excitation in a mode-mismatched dual-beam configuration. The analytical expression of the TL signal and its dependence on sample to detector distance as well as the Z-scan have been derived. The theoretical analysis shows that the phase shift and TL signal are higher than the values obtained using an excitation with the T E M 00 Gaussian profile. The experimental demonstration of the theoretical approach has been performed using the L G10 and T E M 00 Gaussian beams, respectively. Experimental proofs of the model are presented and found to be in agreement, demonstrating that Laguerre-Gaussian induced excitation is more sensitive than the Gaussian one.

High-performance grating couplers on 220-nm thick silicon by inverse design for perfectly vertical coupling

Efficient grating couplers (GCs) for perfectly vertical coupling are difficult to realize due to the second-order back reflection. In this study, apodized GCs (AGCs) are presented for achieving perfectly-vertical coupling to 220 nm thick silicon-on-insulator (SOI) waveguides in the C-band. We compare the performance of the AGCs to that of uniform GCs (UGCs) and demonstrate the superiority of the former. The AGCs were obtained through inverse design using gradient-based optimization and were found to effectively suppress back reflection and exhibit better matching to the Gaussian beam profile. The design and measurement results show that AGCs have a 3 dB lower coupling loss than UGCs. We fabricated focusing AGCs by electron beam lithography with a single, 70 nm shallow etch and a minimum feature size of 100 nm, which makes them compatible with CMOS technology. The AGCs achieved a coupling efficiency of −5.86 dB for perfectly vertical coupling. Overall, our results demonstrate the potential of AGCs for achieving high-performance coupling in the C-band on the SOI platform.

Improvement of the reproducibility in LIBS single levitated aerosol particle analysis based on particle size-selectivity of photophoretic optical trap

To improve the reproducibility of single particle analysis with LIBS, we study the particle size selectivity of photophoretic optical trap. Firstly, the photophoretic force is theoretically simulated and size selectivity in a Gaussian trapping beam is analyzed. Then, the particle size is statistically examined under different power of the trapping Gaussian beam. The results indicate the larger particles are selected by the trap with higher laser power, which is in good agreement with the theoretical expectation. In addition, comparing the particle size distribution of hollow beam trapping with that of Gaussian beam, we found the particle size distribution in hollow beam trapping is broader, which is due to the larger freedom of radiating area on the particle in the hollow beam. Finally, the reproducibility of single particle LIBS is testified. The results show better reproducibility can be achieved with Gaussian beam as a narrower range in particle size is obtained by the trap. This work suggest optical trap can provide a useful tool to control the freedom of particle size and therefore improve the reproducibility of single particle analysis.

High-power and high-quality Gaussian beam in VCSEL via anisotropic modes control

Gaussian beam in the vertical cavity surface emitting laser (VCSEL) hasimportantapplicationin 3D sensing and optical communications, due to its concentrate energy at center and long propagation distance. However, its beam quality under high power tends to be serious degradation and become annular hollow distribution, severely limiting the use of VCSEL. Here, the anisotropic elliptical oxide aperture VCSEL (AEOA-VCSEL) was designed to achieve high-power Gaussian beam with high-quality via anisotropic modes control. The saturation output power reached up to 8.2 mW under low injection current, to our best knowledge, which was the highest power generated in single VCSEL device. Moreover, the AEOA-VCSEL can control the output beam profile only by adjusting injection current, and could also homogenize the mode spacing among adjacent high-order modes. The facile preparation process and low cost makes the device present great potential in augmented and virtual reality (AR/VR), 3D sensing and optical communications.

Beam profile analysis in magnetoplasma medium

In the current study, electromagnetic fields produced by a point source in a magnetoplasma medium under the steady external magnetic field are derived by using Maxwell equations. To obtain the general Gaussian beams complex source point method is used. The radiated fields are Gaussian beams when the complex values are assigned to the source coordinates in the derived expressions. Due to the analytic continuation between real and imaginary source points being performed directly in the high frequencies no further calculations are required to convert ray solutions to beam solutions. Thus, the obtained beam solutions are valid outside the paraxial region therefore better representation of fields is obtained. The derived beam profiles are investigated for different set of parameters numerically.

Fiber laser cutting of steel plate by twin spot beam setting in scanning direction

This study investigated the effects of laser beam intensity distribution on the reduction of dross height in fiber laser cutting of a steel plate with 3.2 mm thickness. A twin-spot beam was produced by splitting a single Gaussian beam into two beams using a special axicon lens, and these beams were set in the scanning direction for cutting experiments. The power ratio of two beams (R:F = Rear power:Front power) was varied to discuss the intensity balance for the effective reduction of dross. After cutting experiments, ray tracing analysis was conducted using an optical analysis to calculate the absorbed power density distributions in the kerf. A smaller dross height of 18 μm can be achieved at a power ratio of R:F = 8:2, and its value is lower than that by a single Gaussian beam. At a power ratio of R:F = 8:2, the front beam of lower power is irradiated at the upper part of the workpiece, and the rear beam of higher power is absorbed at the lower part of the workpiece. Thus, effective heat input to the lower part of the workpiece can contribute to a reduction of the dross height. Variation of power ratio in the rear and the front beams is effective in controlling the cutting front shape, and the uniformity of absorbed power in the thickness direction can be improved by setting the rear beam of about four times higher power to the front beam of lower power to obtain a smaller dross height in the case of a 3.2 mm steel plate.

Controlling beam dynamics with spectral quadratic phase modulation in the fractional Schrödinger equation.

The propagation dynamics of Gaussian beams and finite energy Airy beams with spectral quadratic phase modulation (QPM) modeled by the fractional Schrödinger equation (FSE) are numerically investigated. Compared with beam propagation in the standard Schrödinger equation, the focusing property of beams under FSE is influenced by the QPM coefficient and the Lévy index. For symmetric Gaussian beams, the focusing position increases and the focusing intensity decreases for the larger QPM coefficient or smaller Lévy index. For asymmetric Airy beams, multiple focusing positions occur, and the tendency of focusing intensity is opposite to that of Gaussian beams. Our results show the promising application of the FSE system for optical manipulation and optical splitting by controlling the QPM.

Nonlinear generation of an optical bottle beam in domain-engineered ferroelectric crystals.

Nonlinear wavefront shaping in periodically poled ferroelectric crystals has received great attention because it offers a convenient way to generate a structured light beam at new frequencies. In contrast to structurally uniform beams like Laguerre-Gaussian or Hermite-Gaussian modes, here we demonstrate the possibility to generate a spatially varied optical bottle beam via a frequency doubling process in a domain-engineered Sr0.61Ba0.39Nb2O6 (SBN) crystal. The nonlinear holography method was employed to design the modulation pattern of the second-order nonlinear coefficient χ(2), and the femtosecond laser poling was used to imprint the χ(2) pattern into the SBN crystal via ferroelectric domain inversion. The second harmonic bottle beam with zero intensity in its center that is surrounded in all three dimensions by light was observed with the incidence of a fundamental Gaussian beam. These results are useful for nonlinear generation and control of structured light at new frequencies, which has important applications in nonlinear photonics and quantum optics.

Sub-70 nm surface structures on femtosecond laser irradiated GaAs in distilled water and sensing application.

This study reveals the possibility of distinct ablation mechanisms at different radial positions of the ablated track on GaAs when ablated with femtosecond pulses in distilled water. From the center to the edges of the ablated track, fascinating features such as micron-sized cones, nano-pores, and nano-ripple trenches (average size of 60-70 nm) were observed. The requirement for simulations incorporating the variations in a Gaussian beam fluence and dynamics of the melt flow/surrounding media is discussed. Deep-subwavelength structures, i.e., nano-ripple trenches with a ripple size of ∼λ/11 are achieved on the GaAs surface in this study. Further, these GaAs surface structures acted as excellent hybrid surface-enhanced Raman spectroscopy platforms upon gold coating.

Bessel–Gauss Beams of Arbitrary Integer Order: Propagation Profile, Coherence Properties, and Quality Factor

We present a novel approach to generate Bessel–Gauss modes of arbitrary integer order and well-defined optical angular momentum in a gradient index medium of transverse parabolic profile. The propagation and coherence properties, as well as the quality factor, are studied using algebraic techniques that are widely used in quantum mechanics. It is found that imposing the well-defined optical angular momentum condition, the Lie group SU(1,1) comes to light as a characteristic symmetry of the Bessel–Gauss beams.

Improving the longitudinal and radial forces of optical tweezers: A numerical study

Usually, optical tweezers are based on the focusing a Gaussian laser beam giving rise to a diffraction-limited spot. An alternative has been proposed by several authors which consists to enlighten the trap by a high-order radial Laguerre-Gauss LGp0 beam. However, doing that leaves unchanged the longitudinal stability but improves several times the radial force with increasing the radial mode index p. In this paper, it is demonstrated, for a given power, that introducing a primary spherical aberration (SA) on the path of the incident LGp0 beam allows increasing several times both the longitudinal and transverse trapping effects. The best results are obtained for negative SA.

Cubic Nonlinearity of Graphene-Oxide Monolayer.

The cubic nonlinearity of a graphene-oxide monolayer was characterized through open and closed z-scan experiments, using a nano-second laser operating at a 10 Hz repetition rate and featuring a Gaussian spatial beam profile. The open z-scan revealed a reverse saturable absorption, indicating a positive nonlinear absorption coefficient, while the closed z-scan displayed valley-peak traces, indicative of positive nonlinear refraction. This observation suggests that, under the given excitation wavelength, a two-photon or two-step excitation process occurs due to the increased absorption in both the lower visible and upper UV wavelength regions. This finding implies that graphene oxide exhibits a higher excited-state absorption cross-section compared to its ground state. The resulting nonlinear absorption and nonlinear refraction coefficients were estimated to be approximately ~2.62 × 10-8 m/W and 3.9 × 10-15 m2/W, respectively. Additionally, this study sheds light on the interplay between nonlinear absorption and nonlinear refraction traces, providing valuable insights into the material's optical properties.

A comparative study of electromagnetically induced transparency (EIT) in Λ-, V-, and Ξ-type systems using Laguerre–Gaussian (LG) laser beams

In this paper, a theoretical investigation of electromagnetically induced transparency (EIT) using Laguerre–Gaussian (LG) beams has been carried out for the three canonical atom-laser coupled systems (e.g. [Formula: see text]-, V-, and [Formula: see text]-type) in [Formula: see text]Rb atom. The required optical Bloch equations (OBEs) are derived for each system. The OBEs are analytically solved in steady-state condition under the weak probe field approximation. We have used the iterative perturbative technique to obtain the probe coherence term. The probe response w.r.t. probe detuning for different orders of the orbital angular momentum (OAM) number of both the pump and probe LG beams has been studied. We have also studied the effect of the OAM number on probe response in both Doppler-free and Doppler-broadened mediums. It has been observed that the EIT signal is squeezed for nonzero OAM number of the pump beam with arbitrary OAM number of the probe beam. It is found that for higher-order OAM number, the EIT signal is further squeezed. The modification of the EIT signal is attributed because of the spatial-dependent Rabi frequency. Our study demonstrates that the dynamic of the probe field inside an atomic medium may be controlled by tuning the OAM number of the LG beam.

Experimental Investigations and Modeling of Interference Fringe Geometry in Line-Shaped Gaussian Beam Intersections for Laser Doppler Sensors

Line-shaped beam-based Doppler distance sensors enable 3D shape measurements of rotating objects, for instance for working lathe monitoring with a simultaneous, multipoint velocity, and distance measurement. The velocity and distance estimations are fundamentally referred to the interference fringe spacing of the sensors. In this case, the fringe spacing variation-caused measurement error is significant; however, a complete, accurate model of the fringe geometry distribution for the line-shaped fringe volume is still missing and required to identify and minimize the error. Therefore, this work presents a high-accuracy 3D model for the fringe spacing evaluation of the sensors with experimental investigations. The model is derived from the phase expression of Gaussian beams introducing extension ratio, and can be universally applied to describe fringe geometry distribution throughout the intersection volume of spherical and line-shaped beams. With an experimental setup of a laser Doppler sensor, a full-field fringe spacing estimation using a high-resolution matrix camera is performed with dual-wavelength beams. The numerical modeling and experimental results show an average relative difference below 0.6%.

Tailoring OAM spectrum of high-order harmonic generation driven by two mixed Laguerre–Gaussian beams with nonzero radial nodes

The extreme ultraviolet (XUV) light beam carrying orbital angular momentum (OAM) can be produced via high-order harmonic generation (HHG) due to the interaction of an intense vortex infrared laser and a gas medium. Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node (from 0 to 2) in the driving laser consisting of two mixed Laguerre–Gaussian (LG) beams. We find that due to the change in spatial profile of HHG, the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node. We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes. Through the map of coherence length and the evolution of harmonic field in the medium, we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node. We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.

High-order harmonic interferometry for the study of intensity-dependent dipole phase

Abstract High-order harmonics are ideal probes to resolve the attosecond dynamics of strong field recollision process. In this work, an easy-to-implement phase mask is utilized to covert the Gaussian beam to TEM01 transverse electromagnetic mode, allowing the realization of two source interferometry of high-order harmonics. We experimentally measured the intensity-dependence of dipole phase directly with high-order harmonic interferometry, in which the driving laser intensity can be precisely adjusted. The classical electron excursion simulations reproduce the experimental findings quite well, demonstrating that Coulomb potential plays subtle roles on the movement of electrons for harmonics near the ionization threshold. This work is of great importance for precision measurements of ultrafast dynamics in strong-field physics.

Developing a misalignment model for folded optical resonators and designing a kilowatt-class disk laser resonator with a short effective length

In this article, a formulation was developed for designing a stable disk laser resonator and achieving a high power and a beam quality close to the fundamental mode with a short effective length. In this regard, by taking a matrix approach and using Gaussian beam propagation based on the ABCD law for Gaussian beams, the fundamental-mode spot size inside a resonator and its sensitivity to misalignment, as well as dynamic stability in multiple folded resonators, were analyzed in order to achieve a short effective length. In the presented method, the optimal geometrical parameters of the resonator were obtained by applying the length limits, permissible level of sensitivity to misalignment, and range of dynamic stability with the help of MATLAB software coding. Using this design algorithm, a Z-shaped resonator with the arm length of 50 cm and fundamental-mode spot size of 2.4 mm on the active media was designed, while the resonator had a good dynamic stability and low sensitivity to misalignment. Considering these specifications, it was possible to design a compact disk laser with a power of 1 kW, which had a beam quality close to the fundamental mode.To the best of our knowledge, the laser disk resonator described in this paper, which is resistant to misalignment and has a short effective length, has not been previously documented in the literature. The model developed in this research is a general model that can be used in much more complex structures with any numbers of optical elements in other lasers.

Error estimates for Gaussian beams at a fold caustic

In this work we show an error estimate for a first order Gaussian beam at a fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For the caustic that we study the exact solution can be constructed using Airy functions and there are explicit formulae for the Gaussian beam parameters. Via precise comparisons we show that the pointwise error on the caustic is of the order O ( k − 5 / 6 ) where k is the wave number in Helmholtz.