Initial Beam Profile Research Articles

Four-dimensional dynamics of multirotational transition stimulated rotational Raman scattering in air

Stimulated rotational Raman scattering in air is a powerful parasitic process that degrades high intensity laser beams and pulses propagated over significant distances. Conversely, it is used beneficially in the context of Raman lasers. Through this inelastic scattering process, laser photons are converted to higher (anti-Stokes) or lower (Stokes) energies, according to rotational mode transitions in nitrogen and oxygen diatomic molecules. The full wave-mixing problem involves numerous frequencies, and it is consistently assumed that only one rotational mode contributes to the conversion process. We instead present a dynamic 4D multirotational model that is implemented in a parallelized manner within the Virtual Beamline++ optical modeling package allowing high-resolution 4D studies. We highlight the effect that spontaneous emission plays in large and small beam-width setups, even in the highly saturating regime. The weaker transition modes play a large role in the persistent dynamics and can lead to complex spatiotemporal coupling through nonlinear competition of the modes. We highlight how and why these weaker modes persist, how the size and shape of speckle patterns depends highly on the initial beam profile, and how weaker modes can transiently become stronger as a result of such competition.

Self-focusing effect analysis of a perfect optical vortex beam in atmospheric turbulence.

The correlation function and the detection probability of orbital angular momentum (OAM) of a perfect optical vortex beam (POVB) were obtained under atmospheric turbulence conditions and then used to estimate the POVB propagation model through atmospheric turbulence. The POVB propagation in a turbulence-free channel can be divided into anti-diffraction and self-focusing stages. The beam profile size can be well preserved in the anti-diffraction stage as the transmission distance increases. After shrinking and focusing the POVB in the self-focusing region, the beam profile size expands in the self-focusing stage. The influence of topological charge on the beam intensity and profile size differs depending on the propagation stage. The POVB degenerates into a Bessel-Gaussian beam (BGB)-like when the ratio of the ring radius to the Gaussian beam waist approaches 1. The unique self-focusing effect of the POVB enables higher received probability compared to the BGB when propagating over long distances in atmospheric turbulence. However, the property of the POVB that its initial beam profile size is not affected by topological charge does not contribute to the POVB achieving a higher received probability than the BGB in short-range transmission application scenarios. The BGB anti-diffraction is stronger than that of the POVB, assuming a similar initial beam profile size at short-range transmission.

Evolution of four-petal Lorentz–Gauss beams in the strongly nonlocal nonlinear media

In this paper, the properties of four-petal Lorentz–Gaussian beams (FPLGBs) during propagation in the strongly nonlinear nonlocal media (SNNM) are investigated by using the Collins formula. The impact of the beam and media parameters on the propagation of an FPLGB is investigated analytically. The intensity distribution of an FPLGB during propagation in the SNNM evolves periodically and the initial beam profile with four beamlets disappears for enormous values of the input power.

Evolution of rectangular and triangular initial beam profiles in positive Kerr local medium

The hyperbolic secant (Sech) shape, as the initial beam profile, is the well-know profile that compensates the diffraction and self-focusing effect during propagation in Kerr medium, and evolves as the bright spatial soliton. The Sech beam can be confined in the Kerr medium andinduces its own waveguide. In this work, two initial beam profiles, rectangular and triangular functions, that are different than Sech profile, are considered, and the propagation of these beam profiles in third-order nonlinear (Kerr) medium is investigated. As a result, the initialbeam-width played an important role in confining the beam profiles in direction of propagation. In addition, the intensity profiles change to the Sech profile after some initial step of propagation. All the calculations and simulations have been done by the Split-Step numericalmethod with MATLAB program.

Ionization-assisted refocusing of femtosecond Gaussian beams

Ionization occurs ubiquitously in intense laser-matter interaction and often leads to rapid decrease in laser intensity via plasma defocusing, shortening the effective interaction length of desired high-field processes. Refocusing of pulses may compensate for this adverse effect. However, it typically relies on Kerr-induced self-focusing and requires sufficiently high power. Here, we present simulations showing the refocusing of intense pulses with an initial Gaussian beam profile in atmospheric pressure gases at relatively low power. We attribute this refocusing to the formation of ring-structure plasmas. We find that tighter focusing leads to stronger refocusing, and the initial chirp of the pulse greatly affects its dynamics due to spatiotemporal coupling of focused broadband pulses. Our results highlight a novel aspect of complex pulse dynamics and can be relevant to applications involving tightly focused ultrafast Gaussian beams.

Dark spatial soliton and quasi-soliton by arbitrary initial beam profiles in negative Kerr local and nonlocal medium

In this paper numerically, generation of dark spatial solitons and quasi-solitons in negative Kerr medium which is described by the (1 + 1)-Dimensional local and nonlocal Nonlinear Schrodinger Equation, using arbitrary initial condition field distributions dissimilar to the analytical solution is demonstrated. In the local and nonlocal case, different initial beam profiles with different initial beam-widths are considered, while different response functions of medium and degrees of nonlocality are governing the nonlocality. For the local case extra (lack of) energy in the center of beam profile is released to (absorbed from) the symmetric transversal area of media respectively, until the beam profile self evolves to the fundamental dark soliton with its appropriate amplitude and beam-width of the analytical dark soliton hyperbolic tangent. In the nonlocal case, the beam profile finds some oscillation on beam-width and evolves to a Reversed-Gaussian function, regardless of the nonlocal response function and the degree of nonlocality. By increasing the degree of nonlocality, the evolved beam profile finds the wider beam-width. Analytical formulas for the propagated intensity profile in nonlocal media are given. All the numerical simulations are done by MATLAB program and Split-Step method.

Generation of bright spatial quasi-solitons by arbitrary initial beam profiles in local and nonlocal (1+1)-Dimensional nonlinear media

In this paper we demonstrate numerically that it is possible to generate bright spatial quasi-solitons, in media that are described by the (1+1)-Dimensional local and nonlocal Nonlinear Schrodinger Equation, using initial condition field distributions that are distinct from the analytical solution. In the local case different initial conditions were considered and in the nonlocal case different response functions and degrees of nonlocality were considered, obtaining the same behavior: at the beginning the initial profile is reshaped and after some distance, the beam propagates almost without change or in an small oscillatory way. The propagated intensity profile in the local case evolves to hyperbolic secant and in the nonlocal case to Gaussian, regardless of the degree of nonlocality. Analytical formulas for the propagated intensity profile are given.

The properties of anomalous hollow beam propagating in the slant atmosphere

The equations of anomalous hollow beam (AHB) in slant atmosphere have been derived, and the average intensity distributions have been illustrated and analyzed using numerical examples. The results shown that the AHB propagating in slant atmosphere will lose the initial dark hollow with a solid core profile and evolve into Gaussian beam as the propagation distance increases. The results also shown the AHB propagating in slant atmosphere with larger strength (larger C0 or small zenith angle α) will lose the initial beam profile faster at the same propagation distance L.

Propagation characters of multi-Gaussian beam with large eccentric displacement in collisionless plasma: Higher order paraxial theory

The multiple coherent identical Gaussian beams with symmetry distribution are abbreviated as multi-Gaussian beam, of which the propagation characters in collisionless plasma are studied with the WKB method and higher order paraxial theory. The initial beam profile presents the flat top like or hollow like distribution when the eccentric displacement is large enough. Based on the derived nonlinear propagation equations, the initial condition analyses are performed, and the impact of eccentric displacement on the free propagation effect and ponderomotive nonlinearity is thoroughly discussed. The propagation characters of dimensionless beam width parameter, spot intensity, and spatial distribution of plasma electron density are presented. Results show that the initial spot intensity is expanding outwards along the propagation and the ring structure of electron evacuation in plasmas is generated.

Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis

We derive an analytical propagation expression of the finite energy Airy-Hermite-Gaussian beam propagating in a uniaxial crystal orthogonal to the optical axis, and calculate numerical examples to investigate the influences of the propagation distance and the ratio of the extraordinary refractive index to the ordinary refractive index on the beam profile. In addition, we also examine the intensity distribution of the beam propagating in the uniaxial crystals at different observation sections. Our research shows that the initial beam profile of the beam remains nearly invariant for a short propagation distance in the crystal. However, as propagation distance continues to increase, the beam width will gradually enlarge, where the diffusion velocities of the beam in the X and Y directions are different. Moreover, both the ratio of the extraordinary refractive index to the ordinary refractive index and the Hermite order number also strongly affect the beam profile in a uniaxial crystal. Our work may find some potential applications in optical trapping and nonlinear optics involving in the special beam profile.

Angle-resolved conical emission spectra from filamentation in a solid with an Airy pattern and a Gaussian laser beam.

Filamentation dynamics in fused silica are investigated using an Airy pattern and a Gaussian laser beam. The angle-resolved conical emission spectra are measured and compared with the predictions of several models. Our experimental observations are consistent with the X-waves model in both cases. This indicates that both laser beams spontaneously evolve into nonlinear X-waves and suggests a universal evolution of filaments in fused silica, regardless of the initial laser beam profile.

Average intensity of four-petal Gaussian beams through paraxial optical system in atmosphere turbulence

The propagation properties of four-petal Gaussian beams through the paraxial ABCD optical system in atmosphere turbulence are investigated by numerical examples. It is found that the beam propagating through ABCD optical system in atmosphere turbulence can keep its initial four-petal beam profile almost invariant for a short propagation distance, the beam will converted to Gauss-like beam with several small petals with the propagation increasing, and the beam loses its initial profile slower than the beam propagating in atmosphere turbulence.

Residual Stress Extraction of Surface-Micromachined Fixed-Fixed Nickel Beams Using a Wafer-Scale Technique

This paper reports on the extraction of residual stress in surface-micromachined nickel thin films of electrostatically actuated fixed-fixed beams using a wafer-scale technique. The distribution of residual stress for 87 beams on a 4-in quarter wafer piece is presented. The residual stress ( $\sigma _{0}$ ) is determined from the best fit of the displacement-voltage curves predicted by a computationally efficient model to the experimental data. The nondestructive and automated measurements are taken at room temperature and directly at the beam itself without any additional test structures. The model employed incorporates the nonideal effects of inclined supports, nonflat initial beam profiles, and fringing fields. The extracted residual stress values vary between −12.8 and 13.6 MPa (negative values are for compressive stresses and positive ones for tensile stresses). The residual stresses for these 87 beams follow a nearly normal distribution with a mean value of −1.7 MPa and a standard deviation of 5.9 MPa, which represents the variability of the residual stresses across the wafer. Detailed uncertainty analysis has been conducted, and it reveals that inaccurate modeling of the nonideal effects will result in significant errors in the extracted residual stress. Although demonstrated on nickel thin films, this technique can be applied to other metallic thin films. [2014-0344]

Mechanism study of 2-D laser array generation in a YAG crystal plate.

We have reproduced the process of two-dimensional array generation by using two crossing laser beams in a YAG crystal plate based on numerical simulation considering cross-phase modulation (XPM) and self-focusing. Furthermore, we come to the conclusion that both XPM and the cylindrical symmetry breaking in the initial beam profile contributes to the generation of two-dimensional array. In addition, we have studied the threshold input laser beam power for the two crossing beams splitting in a YAG crystal plate. Our study could be valuable in various applications, such as 2-D all-optical switching devices or multicolor pump-probe experiments.

SU‐E‐T‐501: Initial Orthovoltage Beam Profile Analysis of a Small Brass MLC

PurposeTo create brass leaves for an orthovoltage MLC and take initial beam profile measurements.MethodsThe low‐energy MLC was designed in previous work. Brass was chosen for its self‐lubrication and low cost. Stock brass rectangles (30cm × 1.0cm × 0.5cm) were ordered with pre‐cut gear rack along the topmost long edges. Leaf designs were translated into G‐code, then cut with a Tormach CNC‐1100 mill. Intense bowing was observed in the beam direction, which required straightening via an in‐house jig. Straightened leaves were placed into MLC assembly and mounted to a 320 kVp orthovoltage tube. EDR2 film was irradiated in four situations: MLC open so one edge was isocentric, and MLC open more than isocentric, completely closed MLC, and an open field shot with the MLC removed. The first two scans tested penumbra for our rectangular edges due to unfocused design. The final two scans tested transmission and interleaf leakage. All four experiments were set to 120 kVp and 10 mA for two minutes.ResultsTransmission and interleaf leakage were found to be zero. Interleaf leakage is faintly visible on film, but undetected by our film scanner despite high spatial resolution. Penumbra at isocenter was found to be 0.72mm, which matched the penumbras of true field edges. Penumbra off‐isocenter was 1.1mm. Mechanically, leaves are moving smoothly once straightened.ConclusionBeam profiles through our brass MLC are acceptable. Leaves attenuate and move as designed. Looking forward, we intend to animate our MLC to deliver more complicated treatment plans.

Phase transition to spatial Bloch-like oscillation in squeezed photonic lattices

We propose an exactly solvable waveguide lattice incorporating an inhomogeneous coupling coefficient. This structure provides classical analogs to the squeezed number and squeezed coherent intensity distribution in quantum optics where the propagation length plays the role of a squeezed amplitude. The intensity pattern is obtained in a closed form for an arbitrary distribution of the initial beam profile. We have also investigated the phase transition to the spatial Bloch-like oscillations by adding a linear gradient to the propagation constant of each waveguide ($\ensuremath{\alpha}$). Our analytical results show that the Bloch-like oscillations appear above a critical value for the linear gradient of the propagation constant ($\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$). The phase transition (in the propagation properties of the waveguide) is a result of competition between discrete and Bragg diffraction. Moreover, the light intensity decays algebraically along each waveguide at the critical point while it falls off exponentially below the critical point ($\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$).

Self-focusing of profiled ultrashort-wavelength laser beams in air

We report on the results of laboratory experiments of filamentation of sharply focused gigawatt femtosecond laser radiation passed through various aperture diaphragms in air. For the multiple filamentation regime, the dependences of the length and spatial structure of the filamentation region on the initial beam profile are established. It is found that light beam profiling by a diaphragm leads in some cases to a displacement of the filamentation region and to repeated self-focusing of radiation behind the linear focal waist. In the beam of the same power in the absence of a diaphragm and in the regime of the formation of a single filament, this effect terminates in front of the geometrical focus. The experimental results are illustrated by numerical simulation data.

Cylindrical symmetry breaking leads to multiple filamentation generation when focusing femtosecond lasers with axicons in methanol

We demonstrate that multiple filaments could be generated when focusing femtosecond laser pulses into methanol solution with an axicon. These long multiple filaments are located on the central spot and ring structures of the quasi-Bessel beam created by the axicon. Further numerical simulation reproduces the key features of the experimental observation. The outcome of simulation suggests that the cylindrical symmetry breaking in the initial beam profile could be responsible for the occurrence of multiple filamentation by using an axicon as focusing optics. Since the quasi-Bessel profile is determined by the axicon properties, the axicon has been suggested as a simple optics component to control multiple filaments.

Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media

Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.

Level crossing statistics for optical beam wander in a turbulent atmosphere with applications to ground-to-space laser communications

Level crossing statistics is applied to the complex problem of atmospheric turbulence-induced beam wander for laser propagation from ground to space. A comprehensive estimate of the single-axis wander angle temporal autocorrelation function and the corresponding power spectrum is used to develop, for the first time to our knowledge, analytic expressions for the mean angular level crossing rate and the mean duration of such crossings. These results are based on an extension and generalization of a previous seminal analysis of the beam wander variance by Klyatskin and Kon. In the geometrical optics limit, we obtain an expression for the beam wander variance that is valid for both an arbitrarily shaped initial beam profile and transmitting aperture. It is shown that beam wander can disrupt bidirectional ground-to-space laser communication systems whose small apertures do not require adaptive optics to deliver uniform beams at their intended target receivers in space. The magnitude and rate of beam wander is estimated for turbulence profiles enveloping some practical laser communication deployment options and suggesting what level of beam wander effects must be mitigated to demonstrate effective bidirectional laser communication systems.