Intensity Distribution Of Beam Research Articles

Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system

Based on the Collins diffraction integral formula, an analytical expression of a general four-petal Gaussian vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution of a four-petal Gaussian vortex beam propagating in free space is graphically demonstrated. The influences of beam order and topological charge on the normalized intensity distribution are discussed in detail. This research is useful to the optical trapping, optical communications, and beam splitting techniques, etc.

A “comb” structure measurement of a micrometer displacement in laser plasma propulsion

A “comb” structure of beam intensity distribution is achieved to measure target displacements at the micrometer level in laser plasma propulsion experiments. Compared with single-beam and double-beam detection, the “comb” structure is more suitable for a thin film targets with a velocity lower than 10−2 m/s. Combined with a light-electric monitor, the “comb” structure can be used to measure a velocity range from 10−3 to 1 m/s. Using this “comb” structure, the coupling coefficient of aluminum ablated by nanosecond pulse laser in air is determined and compared. The results indicate that this “comb” structure is an effective experimental approach.

Two-photon polymerization of a three dimensional structure using beams with orbital angular momentum

The focus of a beam with orbital angular momentum exhibits internal structure instead of an elliptical intensity distribution of a Gaussian beam, and the superposition of Gauss-Laguerre beams realized by two-dimensional phase modulation can generate a complex three-dimensional (3D) focus. By taking advantage of the flexibility of this 3D focus tailoring, we have fabricated a 3D microstructure with high resolution by two-photon polymerization with a single exposure. Furthermore, we have polymerized an array of double-helix structures that demonstrates optical chirality.

Asymmetric Bessel-Gauss beams.

We propose a three-parameter family of asymmetric Bessel-Gauss (aBG) beams with integer and fractional orbital angular momentum (OAM). The aBG beams are described by the product of a Gaussian function by the nth-order Bessel function of the first kind of complex argument, having finite energy. The aBG beam's asymmetry degree depends on a real parameter c≥0: at c=0, the aBG beam is coincident with a conventional radially symmetric Bessel-Gauss (BG) beam; with increasing c, the aBG beam acquires a semicrescent shape, then becoming elongated along the y axis and shifting along the x axis for c≫1. In the initial plane, the intensity distribution of the aBG beams has a countable number of isolated optical nulls on the x axis, which result in optical vortices with unit topological charge and opposite signs on the different sides of the origin. As the aBG beam propagates, the vortex centers undergo a nonuniform rotation with the entire beam about the optical axis (c≫1), making a π/4 turn at the Rayleigh range and another π/4 turn after traveling the remaining distance. At different values of the c parameter, the optical nulls of the transverse intensity distribution change their position, thus changing the OAM that the beam carries. An isolated optical null on the optical axis generates an optical vortex with topological charge n. A vortex laser beam shaped as a rotating semicrescent has been generated using a spatial light modulator.

Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method

This paper presents a method for designing double freeform surfaces to simultaneously control the intensity distribution and phase profile of the laser beam. Based on Snell’s law, the conservation law of energy and the constraint imposed on the optical path length between the input and output wavefronts, the double surfaces design is converted into an elliptic Monge–Ampère (MA) equation with a nonlinear boundary problem. A generalized approach is introduced to find the numerical solution of the design model. Two different layouts of the beam shaping system are introduced and detailed comparisons are also made between the two layouts. Design examples are given and the results indicate that good matching is achieved by the MA method with more than 98% of the energy efficiency. The MA method proposed in this paper provides a reasonably good means for laser beam shaping.

Analysis of Behavior of Focusing Error Signals in Astigmatic Method in the Scheme of Land–Groove Recording

We present the behavior of focusing error signals in a land-groove-type optical disk by theoretical analysis. A gain difference between focusing error signals from a land and a groove occurs because the focusing error signal from the land does not coincide with that from the groove. We also report the dependence of the gain difference on some factors, which are related to the intensity distribution of a laser beam. The physical format of digital versatile disk random access memory is used as a land-groove-type optical disk model. The simulation results show that coma aberration that distorts the intensity distribution unidirectionally causes a large gain difference.

Laser guiding through an axially non-uniform collisional plasma channel

This paper presents an investigation of laser guiding through an axially non-uniform collisional plasma channel formed by ionizing laser prepulse. Due to self-defocusing of the ionizing prepulse, an axial non-uniform plasma channel is formed. When delayed second laser beam propagates through such preformed plasma channel, on account of non-uniform intensity distribution of laser beam, non-uniform heating of electrons takes place. Non-uniform heating diffuses the electrons away from the axis which further enhances the plasma channel. Unbalanced diffraction and refraction phenomenon through such an axial non-uniform collisional plasma channel results into periodic beam width variation with the distance of propagation. Second order ordinary differential equations for the beam width parameter of prepulse and the guided beam have been set up by using the moment theory approach. Laser guiding upto several Rayleigh lengths has been observed.

Reconstruction of phase trajectories of a laser beam propagated through a turbulent medium

The instrument of phase trajectories and phase portraits are used in the analysis of fluctuation processes in open-space optical transmission channels. Experimental time series of beam intensity distribution in the detection plane are used to reconstruct the dimension of embedding space for the first two spatial moments. Knowledge of the structure of phase trajectories reconstructed will allow one to forecast the dynamics of spatiotemporal fluctuation processes on different time scales.

Orbit-orbit interaction and photonic orbital Hall effect in reflection of a light beam

We examine the orbit—orbit interaction when a paraxial beam with intrinsic orbital angular momentum (IOAM) reflects at an air—glass interface. The orbital-dependent splitting of the beam intensity distribution arises due to the interaction between IOAM and extrinsic orbital angular momentum (EOAM). In addition, we find that the beam centroid shows an orbital-dependent rotation when seen along the propagation axis. However, the motion of the beam centroid related to the orbit—orbit interaction undergoes a straight line trajectory with a small angle inclining from the propagation axis. Similar to a previously developed spin-dependent splitting in the photonic spin Hall effect, the orbital-dependent splitting could lead to the photonic orbital Hall effect.

Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging

In this paper, we present a real-time measurement and adjustment method, based on scanning imaging, for optical transmitter which emits 90°×2° linear laser beam. This novel optical arrangement consists of an area array CCD and two linear array CCDs. According to the relationship between the positions, angles of transmitter optical components and the beam parameters of emergent laser, the system can help us to decide the real-time adjustment of optical transmitter by measuring the related beam parameters. In order to improve the measurement speed, avoid occlusion and ensure simultaneous measurement, the two linear array CCDs are placed at near field, far field and separated by a definite angle to acquire the beam intensity distribution through suitable nonlinear correction during the process of scanning. After a complete scanning, the beam parameters and the spot image are acquired by continuous measurement. The proof-of-principle experiments showed that the measurement results were in agreement with the analysis. The presented method was applied to direct fast adjustment for higher quality on the assembly of the optical transmitter. The presented procedure is highly advantageous for diverse laser beam emitted from the optical transmitter, such as elliptic, linear and so on.

Beam shaping characteristics of an unstable-waveguide hybrid resonator.

The unstable-waveguide hybrid resonator emits a rectangular, simple astigmatic beam with a large number of high-spatial-frequency oscillations in the unstable direction. To equalize the beam quality, in this paper, a beam shaping system with a spatial filter for the hybrid resonator was investigated by numerical simulation and experimental method. The high-frequency components and fundamental mode of the output beam of the hybrid resonator in the unstable direction are separated by a focus lens. The high-frequency components of the beam are eliminated by the following spatial filter. A nearly Gaussian-shaped beam with approximately equal beam propagation factor M² in the two orthogonal directions was obtained. The effects of the width of the spatial filter on the beam quality, power loss, and intensity distribution of the shaped beam were investigated. The M² factor in the unstable direction is changed from 1.6 to 1.1 by optimum design. The power loss is only 9.5%. The simulation results are in good agreement with the experimental results.

Nonparaxial propagation of Lorentz–Gauss beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of nonparaxial propagation of a polarized Lorentz-Gauss beam in uniaxial crystal orthogonal to the optical axis are derived and used to investigate its propagation properties in uniaxial crystal. The influences of the initial beam parameters and the parameters of the uniaxial crystal on the evolution of the beam-intensity distribution in the uniaxial crystal are examined in detail. Results show that the statistical properties of a nonparaxial Lorentz-Gauss beam in a uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal: the beam waist sizes-w(0), w(0x), and w(0y)-not only affect the size and shape of the beam profile in uniaxial crystal but also determine the nonparaxial effect of a Lorentz-Gauss beam; the beam profile of a Lorentz-Gauss beam in uniaxial crystal is elongated in the x or y direction, which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index; with increasing deviation of the ratio from unity, the extension of the beam profile augments. The results indicate that uniaxial crystal provides an effective and convenient method for modulating the Lorentz-Gauss beams. Our results may be valuable in some fields, such as optical trapping and nonlinear optics, where a light beam with a special profile and polarization is required.

Theory for optical assembling of anisotropic nanoparticles by tailored light fields under thermal fluctuations

In order to evaluate the assembling processes of arbitrary-shaped nanoparticles (NPs) by the irradiation of a tailored laser beam under thermal fluctuations, we have developed a “Light-induced-force Nano Metropolis Method (LNMM)” as a new theoretical method based on the stochastic algorithm in the energy region and the general formula of light-induced force. By using LNMM, we have investigated the change of configurations of silver NPs with anisotropic shapes under the irradiation of laser beams with various polarizations and intensity distributions (Gaussian beam and axially-symmetric vector beams) in an aqueous solution at room temperature. As a result, it has been clarified that silver NPs can be selectively arranged into a characteristic spatial configuration reflecting the properties of an irradiated laser beam (wavelength, intensity distribution, and polarization distribution), and that the assembled structures possess broadband spectra and exhibit a strong optical response to the irradiated laser beam through the optimization with the help of fluctuations.

Propagation of a vortex Airy beam in chiral medium

The analytical expression for the propagation of a vortex Airy beam through ABCD optical systems is derived. As an example, the propagation of the beam in chiral medium is discussed. It is shown that the vortex will destroy the center lobe of the Airy beam at a critical position which is different for the left circularly polarized (LCP) and the right circularly polarized (RCP) vortex Airy beam. The intensity distribution exhibits novel features due to the existence of the vortex. In addition, the intensity distributions of the LCP beam and the RCP beam are more sensitive to the chirality parameter in far-zone than that in near-zone. The transverse shift of the center lobe of a vortex Airy beam during propagation is affected by the chiral parameter.

Multiple-beam output of a surface-emitted terahertz-wave parametric oscillator by using a slab MgO:LiNbO_3 crystal

A MgO:LiNbO₃ slab configuration for the surface-emitted terahertz-wave parametric oscillator (TPO) is presented. The pump and the oscillating Stokes beams were totally reflected at the slab surface and propagated zigzaggedly in the slab MgO:LiNbO₃ crystal. Up to five terahertz beams were emitted perpendicularly to the surface of the crystal. The total output energy of the five THz-wave beams was 3.56 times as large as that obtained from the conventional surface-emitted TPO at the same experimental conditions. The intensity distributions of the THz wave beams were measured, and they were unsymmetrical in the horizontal direction while symmetrical in the vertical direction.

Beam Profile Evolution and Beam Quality Changes Inside a Diode-End-Pumped Laser Oscillator

Experimental observations of beam profile evolution and beam quality changes in an asymmetrical diode-end-pumped laser oscillator are presented. The beam intensity distribution and beam size show great differences between the two intra-cavity counter-propagating beams. Measurements also show that the beam quality changes when the beam passes through the gain medium. These phenomena are attributed to the thermally induced aberrations and soft aperture induced diffractions. The results present a novel clue of designing a high power laser oscillator with fundamental mode output.

Airyprime beams and their propagation characteristics

A type of Airyprime beam is introduced in this document. An analytical expression of Airyprime beams passing through a separable ABCD paraxial optical system is derived. The beam propagation factor of the Airyprime beam is proved to be 3.676. An analytical expression of the kurtosis parameter of an Airyprime beam passing through a separable ABCD paraxial optical system is also presented. The kurtosis parameter of the Airyprime beam passing through a separable ABCD paraxial optical system depends on the two ratios B/(Azrx) and B/(Azry). As a numerical example, the propagation characteristics of an Airyprime beam is demonstrated in free space. In the source plane, the Airyprime beam has nine lobes, one of which is the central dominant lobe. In the far field, the Airyprime beam becomes a dark-hollow beam with four uniform lobes. The evolvement of an Airyprime beam propagating in free space is well exhibited. Upon propagation, the intensity distribution of the Airyprime beam becomes flatter and the kurtosis parameter decreases from the maximum value 2.973 to a saturated value 1.302. The Airyprime beam is also compared with the second-order elegant Hermite–Gaussian beam. The novel propagation characteristics of Airyprime beams denote that they could have potential application prospects such as optical trapping.

A transverse emittance and acceptance measurement system in a low-energy beam transport line

A transverse beam emittance and acceptance measurement system has been developed to visualize the relationship between the injected beam emittance and the acceptance of a cyclotron. The system is composed of a steering magnet, two pairs of slits to limit the horizontal and vertical phase-space, a beam intensity detector just behind the slits for the emittance measurement, and a beam intensity detector in the cyclotron for the acceptance measurement. The emittance is obtained by scanning the slits and measuring the beam intensity distribution. The acceptance is obtained by measuring the distribution of relative beam transmission by injecting small emittance beams at various positions in a transverse phase-space using the slits. In the acceptance measurement, the beam from an ion source is deflected to the defined region by the slits using the steering magnet so that measurable acceptance area covers a region outside the injection beam emittance. Measurement tests were carried out under the condition of accelerating a beam of (16)O(6+) from 50.2 keV to 160 MeV. The emittance of the injected beam and the acceptance for accelerating and transporting the beam to the entrance of the extraction deflector were successfully measured. The relationship between the emittance and acceptance is visualized by displaying the results in the same phase-plane.

Propagation properties of hollow sinh-Gaussian beams through fractional Fourier transform optical systems

A hollow sinh-Gaussian beam (HsG) is an appropriate model to describe the dark-hollow beam. Based on Collins integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of a HsG beam passing through fractional Fourier transform (FRFT) optical systems with and without apertures have been studied in detail by some typical numerical examples. The results obtained using the approximate analytical formula are in good agreement with those obtained using numerical integral calculation. Further, the studies indicate that the normalized intensity distribution of the HsG beam in FRFT plane is closely related with not only the fractional order but also the beam order and the truncation parameter. The FRFT optical systems provide a convenient way for laser beam shaping. • We study the propagation of a HsG beam through an ideal FRFT optical system. • The properties of a HsG beam through an apertured FRFT system have also been studied. • The intensity of the HsG beam in FRFT plane is closely related some parameters. • The FRFT optical systems provide a convenient way for laser beam shaping.

Modifying the laser beam intensity distribution for obtaining improved strength characteristics of an optical trap

In this article we study modified optical beams used as optical tweezers for guiding biological micro-objects. We mean to achieve more efficient micromanipulation by using crescent intensity distribution. During laboratory experiments to test their theoretical projections we manufactured a diffractive optical element (DOE) to generate the proposed intensity distribution. Experimental estimations are provided for DOE energy efficiency. We conduct both theoretical and experimental studies of the crescent beam trapping strength. It transpires that in some cases crescent-shaped beams are more efficient than more commonly used Gaussian beams.