We theoretically and experimentally investigate the mutual collapse dynamics of two spatially separated optical beams in a Kerr medium. Depending on the initial power, beam separation, and the relative phase, we observe repulsion or attraction, which in the latter case reveals a sharp transition to a single collapsing beam. This transition to fusion of the beams is accompanied by an increase in the collapse distance, indicating the effect of the nonlinear coupling on the individual collapse dynamics. Our results shed light on the basic nonlinear interaction between self-focused beams and provide a mechanism to control the collapse dynamics of such beams.
We worked out a new group of collimated plasmon beams by the means of in-plane diffraction with symmetric phase modulation. As the phase type changes from 1.8 to 1.0, the beam undergoes an interesting evolution from focusing to a straight line. Upon this, an intuitive diagram was proposed to elucidate the beam nature and answer the question whether they are nondiffracting or linear focusing. Based on this diagram, we further achieved a highly designable scheme to modulate the beam intensity (e.g., 'lossless' plasmon). Our finding holds remarkable generality and flexibility in beam engineering …
A theoretical study of power loss from periphery of an ultrashort pulse laser beam and temporally resolved defocussing produced by laser induced plasma are performed using paraxial approximation. Our analysis incorporate consideration of spatial distribution of the laser beam irradiance and the results show that substantial power losses (10%-80%) occur from the beam periphery limiting length of a filament. It was also shown that generally accepted concept of self-focusing critical power is inconsistent with consideration of self-induced refraction of spatially distributed laser beam. A new cri…
In this work we study the natural focusing of Airy beams symmetric under reflection of the transverse coordinates. Following a recent proposal, their angular spectra depend on the absolute value of the third power of the transverse components of the wave vector. We show that these beams are related to Airy and Scorer special functions. The caustics have a morphology that does not correspond to the ones described by standard catastrophe optics. The structural stability of symmetric Airy beams is experimentally probed
Self-focusing of a cw laser beam in rubidium atomic vapor was studied. The beam power and beam spot size at entrance of a glass cell with the rubidium vapor were variable parameters. A steep grow of the threshold power of self-focusing for the small beam radii (< 30 μm) was observed. Our experimental data are in an agreement with the theoretical results published by Semak and Shneider in 2013. Additional experiments in resonance and transparent media are suggested in order to check and extend our measurements.
We show that an azimuthally-periodically-modulated bright ring "necklace" beam can self-trap in self-focusing Kerr media and can exhibit stable propagation for very large distances. These are the first bright (2+1) D beams to exhibit stable self-trapping in a system described by the cubic (2+1) D Nonlinear Schrodinger Equation (NLSE).
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanis…
Self-focusing of high-intensity beams with grid structures
CREOL, The College of Optics and Photonics at the University of Central Florida（中佛罗里达大学光学与光子学院）；University of Rochester（罗切斯特大学）；The Institute of Optics, University of Rochester（罗切斯特大学光学研究所）；University of Ottawa（渥太华大学）
We consider recently introduced self-focusing fields that carry orbital angular momentum (OAM) [Opt. Lett. $\textbf{46}$, 2384$-$2387 (2021)] and in particular, their propagation properties through a turbulent ocean. We show that this type of field is especially robust against turbulence induced degradation, when compared to a completely coherent beam. In moderately strong oceanic turbulence, the self-focusing OAM beam features over five orders of magnitude higher peak intensities at the receiver plane, an $\sim$80 $\%$ detection probability for the signal mode, as well as an energy transmissi…
We demonstrate that a planar and ultrathin binary lens can focus an azimuthally polarized beam with vortical phase (APV) to a subwavelength spot of transverse polarization. The results elaborates that, in the multi-layer medium, this focused spot, which is beyond the Rayleigh diffraction limitation, can be well maintained for several wavelengths after travelling through the dielectric interfaces, which is not attainable by using other vector beams (i.e., radially, linearly and circularly polarized beams) as the illuminating light. This compact optical system can be valuable in data writing and…
We study the interaction of focused radially-polarized light with metal nanospheres. By expanding the electromagnetic field in terms of multipoles, we gain insight on the excitation of localized surface plasmon-polariton resonances in the nanoparticle. We show that focused radially-polarized beams offer more opportunities than a focused plane wave or a Gaussian beam for tuning the near- and far-field system response. These results find applications in nano-optics, optical tweezers, and optical data storage.
By experimentally studying high-order harmonic beams generated in gases, we show how the spatial characteristics of these ultrashort XUV beams can be finely controlled under standard generation conditions. For the first time, we demonstrate that these XUV beams can be emitted as converging beams and get thereby focused after generation. We study this mirrorless focusing using a spatially chirped beam that acts as a spatially localized probe located inside the harmonic generation medium. We analyze the XUV beam evolution with an analytical model providing the beam characteristics and obtain ver…
In this paper, focal shift of a Guassian laser beam tightly focused through several planar dielectric interfaces is discussed. It is shown that the focal shift and focus point can be changed by variation of refractive index mismatch and this shift could be positive or negative, and it is proportional to refractive index mismatch between coverglass and immersion medium. It is shown also that for every immersion medium(coverglass), focal shift could be removed for a continuous range of depths by choosing a coverglass (immersion medium) with appropriate refractive index.
Remote focusing of light in a graded-index medium via mode interference is demonstrated using exact analytical solutions of the wave equation. Strong focusing of light occurs at extremely long distances and it revivals periodically with distance due to mode interference. High efficiency transfer of a strongly focused subwavelength spot through optical waveguide over large distances takes place with a period of revival. Super-oscillatory hot-spots with the sizes which are beyond the conventional Abbe diffraction limit can be observed at large distances from the source. This can provide the poss…
Although negative-refractive-index metamaterials have successfully achieved subwavelength focusing, image resolution is limited by the presence of losses. In this Letter, a metal transmission screen with subwavelength spaced slots is proposed that focuses the near-field beyond the diffraction limit and furthermore, is easily scaled from microwave frequencies to the optical regime. An analytical model based on the superposition of shifted beam patterns is developed that agrees very well with full-wave simulations and is corroborated by experimental results at microwave frequencies.
A nonlinear self-focusing material can amplify random small-amplitude phase modulations present in an optical beam, leading to the formation of amplitude singularities commonly referred to as optical caustics. By imposing polarization structuring on the beam, we demonstrate the suppression of amplitude singularities caused by nonlinear self-phase modulation. Our results are the first to indicate that polarization-structured beams can suppress nonlinear caustic formation in a saturable self-focusing medium and add to the growing understanding of catastrophic self-focusing effects in beams conta…
We experimentally demonstrate for the first time that a radially polarized field can be focussed to a spot size significantly smaller (0.16(1) lambda^2) than for linear polarization (0.26 lambda^2). The effect of the vector properties of light is shown by a comparison of the focal intensity distribution for radially and azimuthally polarized input fields. For strong focusing a radially polarized field leads to a longitudinal electric field component at the focus which is sharp and centered at the optical axis. The relative contribution of this component is enhanced by using an annular aperture…
Conventional light focusing, i. e. concentration of an extended optical field within a small area around a point, is a frequently used process in Optics. An important extension to conventional focusing is the generation of the annular focal field of an optical beam. We discuss a simple optical setup that achieves this kind of focusing employing a phase plate as unique optical component. We first establish the class of beams that being transmitted through the phase plate can be focused into an annular field with topological charge of arbitrary integer order q. Then, for each beam in this class …
Filamentation of linear polarized ultrashort laser pulses in non-axisymmetric optical schemes with preferential directions to the optical axis in dependence on the beam orientation was experimentally studied. Our experiments demonstrated strong influence of a laser beam orientation on self-focusing of the beam and plasma generation during filamentation. Maximum of linear plasma density generated by an astigmatic laser pulse was different in both meridional and sagittal foci and depended on the beam orientation. A difference of linear plasma density was observed in the case of superposition of …
Controlling the wavefront of an extreme ultraviolet (XUV) high-order harmonic beam during the generation process offers to focus the beam without resorting to any XUV optics. By characterizing the XUV intensity profile and wavefront, we quantitatively retrieve both the size and the position of the waist of each generated harmonics and show that optics-free focusing leads to focused XUV spot with micrometer size. We use this remarkable coherent effect to demonstrate efficient and adjustable spectral filtering of the XUV light, along with a strong rejection of the fundamental beam, without using…
We show that ballistic transport of optically excited atoms in an atomic vapor provides a nonlocal nonlinearity which stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing nonlinearity. Numerical experiments demonstrate stable propagation of lowest and higher order vortices over a hundred diffraction lengths, before dissipation leads to decay of these structures.
We report on an experimental comparison on critical intensities of nonlinear self-focusing in air with conventional focusing and spatiotemporal focusing schemes. Our results show that the conventional focusing with the focal lens completely filled with the incident beam allows for the strongest axial intensity confinement against the self-focusing effect. This is because that in the high-numerical-aperture condition, the focal spot will have a compact size which results in a high focal intensity. Meanwhile, the Rayleigh length of the focused beam will be substantially shortened which efficient…
We study nonlinear coupling of mutually incoherent beams associated with different Floquet-Bloch waves in a one-dimensional optically-induced photonic lattice. We demonstrate experimentally how such interactions lead to asymmetric mutual focusing and, for waves with opposite diffraction properties, to simultaneous focusing and defocusing as well as discreteness-induced beam localization and reshaping effects.
A 2-D near-field focusing design is proposed based on the circular slot array waveguide structures, synthesized using the array-factor theory, and demonstrated by full-wave simulations. The principle of beam-focusing is extended to the 2-D angularly discretized configuration using regular center-fed linear slots arranged in a circular pattern. By the mirror image arrangement of the slots, a linearly polarized focus in the near-field of the antenna, with negligible cross-polarization is achieved. Its beam-focusing properties are discussed in details and demonstrated by simulations.
The work is devoted to the self-action of laser beams propagating in the isotropic phase of a cholesteric liquid crystal near the transition temperature to the mesophase in a wide range of parameter values characterizing the nonlocality of the nonlinear optical response of the medium, defocusing in the medium, the power of incident laser radiation and diffraction in the liquid crystal. The origin of the primary singularities of both polarization components of radiation in a wide range of parameters of radiation and the medium is investigated for different values of the parameter characterizing…
The focusing properties of three aspheric lenses with numerical aperture (NA) between 0.53 and 0.68 were directly measured using an interferometrically referenced scanning knife-edge beam profiler with sub-micron resolution. The results obtained for two of the three lenses tested were in agreement with paraxial gaussian beam theory. It was also found that the highest NA aspheric lens which was designed for 830nm was not diffraction limited at 633nm. This process was automated using motorized translation stages and provides a direct method for testing the design specifications of high numerical…
We demonstrate that polarization modulation of an illumination beam can effectively control the spatial profile of the light transmitted through turbid media. Since the transmitted electric fields are completely mingled in turbid media, polarization states of an illumination beam can be effectively used to control the propagation of light through turbid media. Numerical simulations were performed which agree with experimental results obtained using a commercial in-plane switching liquid-crystal display for modulating the input polarization states.
Using a variational approach, we obtain the self-focusing critical power for a single and for any number of interacting Laguerre-Gauss beams propagating in a Kerr nonlinear optical medium. As is known, the critical power for freely propagating higher-order modes is always greater than that of the fundamental Gaussian mode. Here, we generalize that result for an arbitrary incoherent superposition of Laguerre-Gauss beams, adding interactions between them. This leads to a vast and rich spectrum of self-focusing phenomena, which is absent in the single-beam case. Specifically, we find that interac…
On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase compensation by LHM slab. Because of the negative refractive index of LHM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. It is shown that the phase difference caused by the Gouy phase shift in right-handed material (RHM) can be compensated by that caused by the inverse Gouy phase shift in LHM. If c…
We demonstrate that laser beam collapse in highly nonlinear media can be described, for a large number of experimental conditions, by the geometrical optics approximation within high accuracy. Taking into account this fact we succeed in constructing analytical solutions of the eikonal equation, which are exact on the beam axis and provide: i) a first-principles determination of the self-focusing position, thus replacing the widely used empirical Marburger formula, ii) a benchmark solution for numerical simulations, and iii) a tool for the experimental determination of the high-order nonlinear …
We present a novel family of paraxial optical beams having a confluent hypergeometric transverse profile, which we name hypergeometric Gauss modes of type-II (HyGG-II). These modes are eigenmodes of the photon orbital angular momentum and they have the lowest beam divergence at waist of HyGG-II among all known finite power families of paraxial modes. We propose to exploit this feature of HyGG-II modes for generating, after suitable focusing, a "light needle" having record properties in terms of size and aspect ratio, possibly useful for near-field optics applications.
When an ultrashort laser pulse is tightly focused to a size approaching its central wavelength, the properties of the focused spot diverge from the diffraction limited case. Here we report on this change in behavior of a tightly focused Petawatt class laser beam by an F/1 off-axis paraboloid (OAP). Considering the effects of residual aberration, the spatial profile of the near field and pointing error, we estimate the deviation in peak intensities of the focused spot from the ideal case. We verify that the estimated peak intensity values are within an acceptable error range of the measured val…
The possibility of focusing light to an ever tighter spot has important implications for many applications and fields of optics research, such as nano-optics and plasmonics, laser-scanning microscopy, optical data storage and many more. The size of lateral features of the field at the focus depends on several parameters, including the numerical aperture of the focusing system, but also the wavelength and polarization, phase and intensity distribution of the input beam. Here, we study the smallest achievable focal feature sizes of coherent superpositions of two co-propagating beams carrying opp…
Institute for Quantum Studies, Chapman University（查普曼大学量子研究所）；Nexus for Quantum Technologies, University of Ottawa（渥太华大学量子技术联盟）；German Aerospace Center (DLR), Institute of Quantum Technologies（德国航空航天中心（DLR）量子技术研究所）
Beam self-imaging in nonlinear graded-index multimode optical fibers is of interest for many applications, such as implementing a fast saturable absorber mechanism in fiber lasers via multimode interference. We obtain an exact solution for the nonlinear evolution of first and second order moments of a laser beam carried by a graded-index multimode fiber, predicting that the spatial self-imaging period does not vary with power. Whereas the amplitude of the oscillation of the beam width is power-dependent. We have experimentally studied the longitudinal evolution of beam self-imaging by means of…
We propose to combine multiple laser beams into a single diffraction-limited beam by the beam self-focusing (collapse) in the Kerr medium. The beams with the total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with the Kerr nonlinearity. Random fluctuations during propagation eventually trigger strong self-focusing event and produce diffraction-limited beam carrying the critical power.
Focusing petawatt-level laser beams to a variety of spot sizes for different applications is expensive in cost, labor and space. In this paper, we propose a plasma lens to flexibly resize the laser beam by utilizing the laser self-focusing effect. Using a fixed conventional focusing system to focus the laser a short distance in front of the plasma, we can adjust the effective laser beam waist within a certain range, as if a variety of focusing systems were used with the plasma lens acting as an adjustable eyepiece in a telescope. Such a setup is a powerful tool for laser wakefield accelerator …
We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z)^{1/2}$ scaling law with the well-known leading order modification of loglog type $\propto (\ln|\ln(z_c-z)|)^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\sim {10^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive a new equation for the adiabatically slow parameter which d…
We theoretically investigate the influence of a longitudinal laser polarization component from beam focusing on spin dynamics in Kapitza-Dirac scattering by solving the relativistic Dirac equation with time-dependent perturbation theory. The transverse spacial dependence of the longitudinal beam polarization component is accounted for, by approximating a Gaussian beam with plane-wave components. We find that corrections from a longitudinal laser beam polarization component approximately scale with the second power of the diffraction angle $ε$, from which we conclude that a related influence fr…
We simulate the focusing of a partially-coherent X-ray beam emitted by an undulator in a fourth-generation storage ring performing coherent mode decomposition and wave optics propagation. The focus position is shifted, and its size is enlarged when an entrance slit crops the beam. This is the usual case when a slit is used to select the coherent fraction. The pairing of two focusing elements (mirrors, lenses or transfocators) to ensure a fixed focal position is also analyzed. Our results show that the image of a partially coherent source, such an undulator in a low-emittance storage ring, is a…
Nonlinear losses accompanying Kerr self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrodinger equation which are stable against radial collapse. These are featured by linear conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as strong attractor for the self-focusing dynamics in Kerr media.
