Transverse Intensity Patterns Research Articles

Proposal for the generation of an ion vortex beam and study of its electromagnetic fields

We propose a scheme for the generation of an ion vortex beam and we study the properties of its electromagnetic field on a plane transverse to its propagation direction. The ion vortex is created by the diffraction of an ionic beam by a light mask with a spiral-like transverse intensity pattern. The diffraction is a result of a short time optical dipole interaction between the light mask and the ion which results to a phase imprint on the ionic wave function. It is shown that as the order of the vortex states that are generated by the various diffraction gets higher the electromagnetic field components have reduced magnitudes. The properties of these fields are studied against the various parameters of the problem.

Structurally Invariant Higher-Order Ince-Gaussian Beams and Their Expansions into Hermite-Gaussian or Laguerre-Gaussian Beams

Paraxial beam modes, which propagate in space and focus without changing their transverse intensity pattern, are of great value for multiplexing transmitted data in optical communications, both in waveguides and in free space. The best-known paraxial modes are the Hermite-Gaussian and Laguerre-Gaussian beams. Here, we derive explicit analytical expressions for Ince-Gaussian (IG) beams for several first values of the indices p = 3, 4, 5, and 6. In total, we obtain expressions for the amplitudes of 24 IG beams. These formulae are written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Due to simultaneous representation of the IG modes via the LG and HG modes, it is easy to obtain the IG modes in the limiting cases wherein the ellipticity parameter is zero or approaches infinity. The explicit dependence of the obtained expressions for the IG modes on the ellipticity parameter makes it possible to change the intensity pattern at the beam cross-section by continuously varying the parameter values. For the first time, the intensity distributions of the IG beams are obtained for negative values of the ellipticity parameter. The obtained expressions could facilitate a theoretical analysis of properties of the IG modes and could find practical applications in the numerical simulation or generation of such beams with a liquid-crystal spatial light modulator.

Conical refraction with flat-topped vortex hollow beam through biaxial crystals

This paper presents a new theoretical method to determine conical refraction (CR) with a light beam by examining the flat-topped vortex hollow beam in a biaxial crystal. The analytical formula for the considered CR is derived in a closed form. Some graphical representations are plotted to show how the source beam parameters N and M, the control parameter ρ0 of CR between the cylinder radius R0 and the waist radius ω, and the propagation distance z, affect the transverse intensity pattern behind the biaxial crystal. Results show that the circularly polarized flat-topped vortex hollow beams entering the crystal will transform the classical double-ring pattern into a multi-ring one consisting of bright rings. The evolution properties of CR with vortex beams upon propagation is also discussed and compared with the reference beam. Through numerical simulations, we established a good agreement between the integrated expressions method and our analytical formula. The present study generalizes the cases of the circularly polarized Gaussian and the flat-topped Gaussian transformed by the CR in a biaxial crystal.

Propagation of Asymmetric Bessel Mode in Turbulent Atmosphere

Aiming at asymmetric Bessel mode, we investigate the propagation characteristics of vortex mode in atmospheric turbulence. The theoretical expressions of mode detection probability are derived for signal and crosstalk modes, based on which channel capacity is further analyzed. The detection probability distribution is mainly affected by mode wavelength and asymmetric factor. The increment of asymmetric factor can diversify the transverse mode intensity pattern, but cause the decline of signal probability and channel capacity. To improve channel capacity, longer wavelength and more transmitted modes are beneficial, while the adjustments of mode topological charge and Bessel cone angle have no effect. Besides, the influences of atmospheric turbulence conditions are discussed. The results are referential for exploring the use of asymmetric Bessel mode as signal source.

Azimuthally modulated axicon vortical beams for laser microprocessing

Non-diffracting beams have contributed greatly to recent developments in high power applications such as laser micromachining. Well known for their elongated focal region (also known as a focal line) are zeroth-order Bessel and Bessel vortical beams which allow achieving high aspect ratio modifications inside transparent materials. A superposition of several optical Bessel vortices of different topological charges allows generating high aspect ratio beams with complexly engineered transverse intensity patterns. Non-diffracting Bessel vortices commonly are created using a conical prism — an axicon. Therefore, they can be referred to as axicon beams. In this work, we have studied the formation of high power and energy axicon vortical beams both numerically and experimentally. We have inscribed sub-wavelength birefringent structures inside fused silica glass to create geometrical phase elements for the azimuthal modulation of the spatial spectra of a zeroth-order axicon (Bessel) beam which allows creating a high power superposition of several Bessel vortices. To prove the concept, we apply azimuthally modulated axicon vortical beams to create modifications inside fused silica glass samples.

Tricomi beams and nondiffracting sheet beams

We introduce a non-diffracting beam family as a new beam solution of the scalar Helmholtz equation in Cartesian coordinates whose complex amplitude is mainly described by the Tricomi functions and characterized by four parameters. Based on the proposed beam model, the on-axial, off-axial, and asymmetrical Bessel beams can be obtained as special cases through appropriate selection of the complex parameters. We show that both the intensity and phase distributions can be tailored in a controlled manner through modulation of the angular spectra in the frequency space, enabling the transverse intensity pattern to be varied from a concentric ring structure, through a concentric arc configuration, to a single sheet pattern with different orientations and central positions.

Controllable anomalous hollow beam and its propagation properties

The model of controllable anomalous hollow beam (CAHB) is proposed. The analytical expression of CAHB propagating in ABCD paraxial optical systems is derived. The light intensity distribution of CAHB at the initial position can be controlled by selecting the beam parameters, and it can be divided into different types. The propagation characteristics of CAHB in free space, such as the transverse intensity patterns, the on-axis light intensity and the evolution of beam width are analyzed in detail by means of mathematical analysis. Numerical simulations are also performed to show these propagation characteristics. We focus on the propagation properties of several typical CAHB with different central and transverse intensity distributions through parameter control.

Propagation characteristics of non-diffracting Lommel beams in a gradient-index medium

We investigate the propagation of the Lommel beams in a gradient-index medium. Based on the ABCD transfer matrix and Collins diffraction integral formula, the analytical expressions of the complex amplitude of the Lommel beams through the gradient-index medium are derived. The intensity distribution and the Poynting vector of the Lommel beams are studied analytically and numerically. The results show that the Lommel beam is focused at the singularities and the corresponding periodic beam profile is induced by the symmetrical refractive index pattern during the beam propagating in the gradient-index medium. The effects of the asymmetry factor and the topological charge on the propagation characteristics of the Lommel beams in the gradient-index medium are discussed in detail. Especially, the propagation trajectories of the Lommel beams become visible as the topological charge increases and the symmetry of the Lommel beam’s transverse intensity pattern can be controlled by varying the asymmetry factor. It is expected that the results obtained in this paper may be useful for potential applications of optical control and trapping.

Ring-broken optical vortices with an adjustable opening

A modified helical phase is presented in this paper. The generated vortex beams with the modified helical phases are characterized with ring-broken intensity distributions. The transverse intensity patterns of the generated vortex beams at a defined axial position and the focal plane are analyzed, respectively. The results demonstrate that the generated beam has an opening, whose size can be customized with a variable l′. The proposed vortex beams realized optical guiding of microparticles in the transverse planes of the beams. This kind of ring-broken beams will be promising for optical manipulation.

Shape-variable four-petal Gaussian vortex breathers in strongly nonlocal nonlinear media

In this paper, we mainly investigate the propagation properties of shape-variable four-petal Gaussian vortex breathers in strongly nonlocal nonlinear media. The analytical expression of the shape-variable four-petal Gaussian vortex breather is derived in Cartesian coordinate system by means of mathematical integral method. A series of evolution properties are described analytically and numerically, such as the transverse intensity pattern, the phase distribution, the variation of the second-order moment beam width, and the on-axis light intensity. It is found that the topological charge number and the beam order of the shape-variable four-petal Gaussian vortex breather play important roles in the propagation process, and their effects on the propagation properties of the shape-variable four-petal Gaussian vortex breather are discussed graphically.

Influence of pump-beam parameters and crystal optical properties on propagation of thermally affected Bessel–Gaussian beams generated by a solid-state laser

In diode-pumped solid-state laser system, the generation and propagation of Helmholtz–Gaussian beam families such as Bessel–Gaussian (BG) beam can dramatically suffer from the effects of heat load. In this study, based on the ABCD matrix for BG beams passing through a graded-index medium, expressions for the thermal lens focal length and the output beam are obtained. Furthermore, to evaluate the impact of the pump-beam parameters and crystal optical properties, the intensity distribution of the zeroth- and first-order BG beams against radial distance together with its corresponding transverse intensity pattern on X–Y plane under different pump powers, pump beam waists, absorption coefficients, and thermal conductivities are simulated and compared. The simulation results indicate that for powerful narrow pump beam, the thermal-induced effects are so dramatic that the intensity profiles are altered, as the discernment of BG beams is not easily feasible; however, taking into account the large pump waist, high thermal conductivity and small absorption coefficient can partly cause the laser output similar to non-thermal one despite high pumping power is received. Therefore, the precise selection of laser parameters can considerably reduce the effects of induced heat on the generation and propagation of BG beams. The obtained results are a valuable hint to experimenters for beam identification and beam quality monitoring.

Astigmatic transformation of the Bessel beam and the Gauss–Laguerre beam

In studies of the anisotropy may be useful the Bessel beams, which have a high sensitivity to the asymmetry of the wave front. Beams Gauss-Laguerre are capable of to maintain their structure in free space. Gauss-Laguerre modes have found their application in optical manipulation of micro-objects, quantum optics, optical communications. In this paper presents a numerical calculation and analysis of the passage of a Bessel beam of zero order and a Gauss-lager beam through polarization devices. Transverse intensity patterns are obtained for beam propagation after passing through wave plates with different types of polarization. This work provides detailed information on polarization transformations of light beams, which can be useful in acute focusing, with optical manipulation of micro-objects. The study of astigmatic transformations of Bessel beams can be useful in capturing and controlling microparticles.

Tightly focused field modulated by spiral phase with an off-axis singularity

We examine the influences of an off-axis singularity in spiral phase on the tightly focused field. Through vectorial diffraction theory, the tightly focused fields modulated by the off-axis singularity displacements and polarization states have been presented and analyzed. The results demonstrate that, the intensity patterns in the focal plane transform along the direction determined by the off-axis singularity displacement and handedness of spiral phase. The off-axis singularity induces the transverse intensity patterns rotate along the propagation, and the direction of rotation is corresponding to the handedness of spiral phase. The profiles and transformation degree of all intensity patterns are dependent on off-axis singularity displacement, polarization state and amplitude distribution of incident light beam. Collaborating with polarization and amplitude modulation, the off-axis singularity in spiral phase is helpful to construct various tightly focused fields potentially applied in these areas, such as optical imaging, manipulation or measurement.

Analysis of few-mode EDFAs with complex doping profiles by theoretical models based on vector modes

Tailoring erbium doping profile is one of the important methods to equalize modal gain of few-mode optical amplifiers. For accurate analysis of these amplifiers, the vector nature of pump and signal modes should be considered in numerical models. In the vector-mode-based models (VMM), the off-centered linearly polarized (LP) modes evolve their transverse intensity patterns (TIPs) during propagation, instead of being assumed to have constant TIPs as done in the LP-mode-based scalar models. The evolved TIPs change the spatial overlaps between pump and signal modes and hence would lead to a different amplifier performance relative to the one obtained by scalar models. Based on VMM, we analyze the gain characteristics of a two-LP-mode erbium-doped fiber amplifier (2LPEDFA) with a ring-doped core and a double-ring-doped 4LPEDFA, respectively. Further, results computed by scalar models are also presented for comparison, showing that the TIP evolutions in the 2LPEDFA have negligible impact upon the modal gain and optimal doping radii. While for the 4LPEDFA, differences in both modal gain and optimal doping radii have been demonstrated between the vector- and LP-mode-based methods. Our results show that vector models are preferable to implement high-precision design of few-mode EDFAs with complex erbium doping profiles.

Resonant excitation of transverse patterns in broad-area lasers by periodic temporal pump modulation

We demonstrate numerically that the temporal periodic modulation of the pump can excite regular transverse spatiotemporal intensity patterns in broad-area lasers. The Floquet stability analysis is used to characterize dynamics of modulated systems. Pattern formation occurs when the modulation frequency is approximately equal to the relaxation frequency or twice the value of this frequency. Instability of homogeneous oscillations leads to the formation of regular optical patterns, such as stripes and hexagons. The characteristic sizes of the observed patterns are in good agreement with predictions of the Floquet analysis.

Architecting new diffraction-resistant light structures and their possible applications in atom guidance.

In this work we extend the so called frozen wave method in order to obtain new diffraction resistant light structures that can be shaped on demand, with possible applications in atom guidance. The resulting beams and the corresponding optical dipole potentials exhibit a strong resistance to diffraction effects and their longitudinal and transverse intensity patterns can be chosen a priori. Besides the theoretical development, we also present the experimental confirmation of our approach; specifically, by generating three different beam profiles using a spatial light modulator that is addressed by a computer-generated hologram. In addition to its many potential applications in atom guiding, the method developed here can also lead to many new developments in optics and photonics in general.

Conical refraction healing after partially blocking the input beam

In conical refraction, when a focused Gaussian beam passes along one of the optic axes of a biaxial crystal, it is transformed into a pair of concentric bright rings at the focal plane. We demonstrate both theoretically and experimentally that this transformation is hardly affected by partially blocking the Gaussian input beam with an obstacle. We analyze the influence of the size of the obstruction both on the transverse intensity pattern of the beam and on its state of polarization, which is shown to be very robust.

Sharp focusing of linearly polarized asymmetric Bessel beam

We conduct the numerical and experimental study of sharp focusing of a linearly polarized asymmetric Bessel beam with topological charge n = 3 and a crescent-shaped transverse intensity pattern. Using the Debye integral, we show that in the focal plane of a high NA aplanatic lens (NA = 0.9 – 0.95) the intensity distribution is also crescent-shaped. Using the FDTD method it is shown that a binary zone plate with NA = 0.995 also forms a crescent-shaped focal spot that is rotated around the optical axis. An asymmetric Bessel beam was generated using a spatial light modulator (SLM) and focused using an immersion objective with NA = 1.25. A crescent-shaped intensity pattern formed in the focal plane was rotated by 90 degrees relative to the SLM-aided crescent.

Propagation of Ince–Gaussian beams in strongly nonlocal nonlinear media using paraxial group transformation

In this paper, the propagation of Ince–Gaussian beams in strongly nonlocal nonlinear media is studied by using paraxial group transformation. An analytical expression for the Ince–Gaussian beams propagating through optical ABCD system is introduced. Then, by considering the transfer matrix of the strongly nonlocal nonlinear media, the transverse intensity patterns of the Ince–Gaussian beams propagate in these media are simulated analytically.

Production of accelerating quad Airy beams and their optical characteristics.

Based on a geometric caustic argument and diffraction catastrophe theory, we generate a novel form of accelerating beams using a symmetric 3/2 phase-only pattern. Such beams can be called accelerating quad Airy beams (AQABs) because they look very much like four face-to-face combined Airy beams. Optical characteristics of AQABs are subsequently investigated. The research results show that the beams have axial-symmetrical and centrosymmetrical transverse intensity patterns and quasi-diffraction-free propagation features for their four main lobes while undergoing transverse shift along parabolic trajectories. Moreover, we also demonstrate that AQABs possess self-construction ability when local areas are blocked. The unique optical properties of these beams will make them useful tools for future scientific applications.