Optical analysis of time-averaged multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens

Current methods for generating Bessel beams are limited to fixed beam sizes or, in the case of conventional adaptive optics, relatively long switching times between beam shapes. We analyze the multiscale Bessel beams created using an alternative rapidly switchable device: a tunable acoustic gradient index (TAG) lens. The shape of the beams and their nondiffracting, self-healing characteristics are studied experimentally and explained theoretically using both geometric and Fourier optics. By adjusting the electrical driving signal, we can tune the ring spacings, the size of the central spot, and the working distance of the lens. The results presented here will enable researchers to employ dynamic Bessel beams generated by TAG lenses.     

Optical parametric oscillator pumped by a Bessel beam

We demonstrate operation of a KTP optical parametric oscillator (OPO) pumped by a Bessel beam for the first time to our knowledge. It is shown that the output of the OPO has a transverse profile, which is consistent with noncollinear phase-matching relations defined by a conical pump. The central spot and ring related to the pair of signal and idler beams were generated in the OPO. By adjusting the OPO cavity mirrors, we easily selected the lowest-order mode as well as the higher-order transverse modes in the central spot. Bessel beam pumping was shown to be useful, providing tubular beam coupling into OPO cavity modes. The OPO threshold pump energy was ~100 muJ in a 6-ns pulse.     

Range-finding by triangulation with nondiffracting beams

Nondiffracting beams are useful for alignment applications because the size of the beam does not change as the beam propagates. In this research we report a technique that allows for distance measurements with nondiffracting beams. With our approach a diffractive optical element is designed that generates two off-axis, tilted, nondiffracting Bessel function beams. These beams intersect at a desired distance from the input plane, producing interference. We generate these Bessel function arrays with a programmable spatial light modulator allowing external control over the intersection distance.     

Fully vectorial highly nonparaxial beam close to the waist

I use the angular spectrum representation to compute exactly the Gaussian beam close to the waist (w(0)) in the case of a highly nonparaxial field (w(0)相似文献   

Reflection and transmission of strongly focused light beams at a dielectric interface

The reflection and transmission of tightly focused azimuthally, radially and linearly polarized electromagnetic wave beams with subwavelength spot size and wavefront curvature at a dielectric interface are investigated. For a given wavefront radius, the existence of the optimal radius of beam spot corresponding to a minimal reflectance and maximal transmittance is shown. Significant lateral shift in the transmitted intensity peak is revealed for strongly focused azimuthally and radially polarized beams that are normally incident to an interface. The reflection and transmission of transverse-electric- and transverse-magnetic- polarized extremely narrow wave beams which are obliquely incident on the dielectric interface is analysed. Disappearance of the Brewster angle and total internal reflection effects for the strongly focused beams are predicted. The change in beam profile after reflection and transmission for different polarizations, incident beam spots and incidence angles are analysed.     

Role of evanescent waves in power calculations for counterpropagating beams

A general expression is obtained for the time-average power passing through a plane transverse to the direction of propagation for two counterpropagating electromagnetic beams. Each beam is represented by its plane-wave spectrum, which contains both propagating and evanescent plane waves. The expression clearly shows that, under certain conditions, the evanescent plane waves contribute to the time-average power passing through the plane. This is in contrast to the case of a single electromagnetic beam, in which only the propagating plane waves contribute to the time-average power passing through the plane. The utility of the expression is demonstrated with a practical example: a line current placed over a dielectric slab. Here the counterpropagating beams are the incident and reflected fields in the region between the current and the slab. The expression is applied to a plane in this region, and it is used to determine the time-average power associated with the evanescent waves passing through this plane. This power is then shown to be equal to the time-average power carried by the guided modes of the slab.     

Experimental study of holographic generation of fractional Bessel beams

We demonstrate the experimental generation of a fractional Bessel beam by holographic means. Such fractional modes of Bessel beams possess an intrinsic opening gap across concentric intensity rings on propagation. We also show that the opening gaps within the fractional modes are diffraction free for a working distance while a fractional helical wave front is maintained.     

Evanescent and propagating fields of a strongly focused beam

Evanescent- and propagating-field distributions from a strongly-focused-wave beam with subwavelength waist w(a) < lambda as a function of polar angle and distance are investigated. Exact amplitudes and intensities of evanescent E(ev) and propagating E(p) fields, including interference terms, are presented both in near- and far-field regions. It is shown that the amplitude of E(ev) decays as exp(-r/w(a)) in the near-field region and that evanescent waves do not contribute to the far field in the forward direction as they do in the transverse directions theta = pi/2, even though the oscillating evanescent field of the same strength but opposite in sign to the propagating field exists in the transverse plane.     

基于方环型频率选择表面的小型化设计

 为解决频率选择表面（frequency selective surface, FSS）在工程应用中的尺寸限制问题,提出了一种新型小型化FSS. 新结构通过增大方环谐振单元的等效电容和等效电感实现频率选择表面的小型化,与前人提出的小型化FSS比较,该新型FSS单元的尺寸更小,仅为0.079λ₀×0.079λ₀（λ₀为阻带中心频率点对应的波长）.另外,新结构的高度对称性确保了其性能的高稳定性,仿真和实测结果表明：新结构对不同角度和不同模式的入射波保持了十分稳定的传输特性．     

Propagation of Bessel beams from a dielectric to a conducting medium

Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of ground penetrating radar systems has been considered. Therefore, an analysis of the propagation of Bessel beams in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect dielectric and impinging on a conducting medium, i.e., the propagation of a Bessel beam generated by refracted inhomogeneous waves. The remarkable and unexpected result is that the incident Bessel beam does not change its shape even when propagating in the conducting medium.     

Conversion of the high-mode solitons in strongly nonlocal nonlinear media

The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder–Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince–Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite–Gaussian beams and Laguerre–Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG soliton and the corresponding LG soliton is remarkable from the Poynting vector and phase plots at their profiles along the propagating axis.     

Propagation of high-order Bessel–Gaussian beams through a hard-aperture misaligned optical system

In this paper, we consider the propagation of high-order Bessel–Gaussian beams (HBGBs) passing through a hard-aperture misaligned optical system. By expanding the hard-aperture function into a finite sum of complex Gaussian functions, a general propagating formula of HBGBs is derived in terms of the generalized diffraction integrals. Based on the derived formula, the diffraction properties of HBGBs propagating through a simple misaligned lens system are numerically illustrated. This method provides a convenient tool for studying the propagation and transformation properties of a high-order Bessel–Gaussian beam through an apertured misaligned optical system.     

Beam splitting of low-contrast binary gratings under second Bragg angle incidence

Beam splitting of low-contrast rectangular gratings under second Bragg angle incidence is studied. The grating period is between lambda and 2lambda. The diffraction behaviors of the three transmitted propagating orders are illustrated by analyzing the first three propagating grating modes. From a simplified modal approach, the design conditions of gratings as a high-efficiency element with most of its energy concentrated in the -2nd transmitted order (~90%) and of gratings as a 1 x 2 beam splitter with a total efficiency over 90% are derived. The grating parameters for achieving exactly the splitting pattern by use of rigorous coupled-wave analysis verified the design method. A 1 x 3 beam splitter is also demonstrated. Moreover, the polarization-dependent diffraction behaviors are investigated, which suggest the possibility of designing polarization-selective elements under such a configuration. The proposed concept of using the second Bragg angle should be helpful for developing new grating-based devices.     

Astigmatic bessel laser beams

Abstract

The oblique incidence of a He-Ne laser beam onto a phase-only diffractive optical element (DOE) that simultaneously produces several unimode different-order Bessel beams propagating at various angles with respect to the optical axis is studied theoretically and experimentally. It is shown that, under obliquely incident illumination of a DOE that forms Bessel beams, the resulting astigmatic diffraction pattern can be used to unambiguously identify the direction of the Bessel beam's phase rotation and the order of the Bessel mode.     

Partial-wave expansions of angular spectra of plane waves

Focused electromagnetic beams are frequently modeled by either an angular spectrum of plane waves or a partial-wave sum of spherical multipole waves. The connection between these two beam models is explored here. The partial-wave expansion of an angular spectrum containing evanescent components is found to possess only odd partial waves. On the other hand, the partial-wave expansion of an alternate angular spectrum constructed so as to be free of evanescent components contains all partial waves but describes a propagating beam with a small amount of standing-wave component mixed in. A procedure is described for minimizing the standing-wave component so as to more accurately model a purely forward propagating experimental beam.     

Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence

The closed-form expression for the mean-squared beam width of partially coherent Hermite-Gaussian (H-G) beams propagating through atmospheric turbulence is derived. The influence of turbulence on the spreading of partially coherent H-G beams is studied quantitatively by examining the mean-squared beam width. It is found that the smaller the coherence length sigma(0) of the source is, and the larger the beam order m and the wavelength lambda are, the less partially coherent H-G beams are affected by the turbulence, although the beams with smaller sigma(0), larger m, and larger lambda have greater spreading in free space. In addition, it is shown that two partially coherent H-G beams may generate the same angular spread and that there exist equivalent partially coherent H-G beams that may have the same directionality as a fully coherent Gaussian beam in free space and also in turbulence. The results are illustrated by examples, and a comparison with previous work is also made.     

Cross-phase modulation and population redistribution in a periodic tripod medium

The cross-Kerr effect is studied for two weak beams, probe and trigger, propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam in a regime of electromagnetically induced transparency. The nonlinear phase shifts for both transmitted and reflected probe beams induced by the trigger's presence are found to depend on the probe detuning, the control beam's intensity, the relaxation rates and, in particular, on the redistribution of the population among the atomic levels. Such a quantitative analysis indicates that the transmitted and reflected probe beam components and their respective phase shifts can be easily controlled and optimized.     

Bessel pulse beams and focus wave modes

Free-space propagation of ultrashort pulses is investigated. Space-time couplings are reduced for a particular form of beams that is termed a pulse beam, or a type 3 pulsed beam. General conditions for the formation of pulse beams in the paraxial approximation are presented. The free-space propagation of spatially localized ultrashort laser pulses is investigated. This treatment is based on a particular pulsed form of the well-known Bessel beam, which is termed a Bessel pulse beam. The connections with focus wave modes and X waves are discussed.     

Simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam

A simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam has been deduced by use of the vector interference theory. This analytical expression can easily be used to calculate accurately the propagation field distribution of azimuthally polarized beams throughout the whole space behind an axicon with any size base angle, not just restricted inside the geometric focal region as does the Fresnel diffraction integral. The numerical results show that the pattern of the beam produced by the azimuthally polarized Gaussian beam that passes through an axicon is a multiring, almost-equal-intensity, and propagation-invariant interference beam in the geometric focal region. The number of bright rings increases with the propagation distance, reaching its maximum at half of the geometric focal length and then decreasing. The intensity of bright rings gradually decreases with the propagation distance in the geometric focal region. However, in the far-field (noninterference) region, only one single-ring pattern is produced and the dark spot size expands rapidly with propagation distance.