Gaussian Beam In Free Space Research Articles

Evolution of conically diffracted Gaussian beams in free space

We present results of our observations on the free space evolution of conically diffracted beams from both single and cascade systems using various combinations of four biaxial crystals of the monoclinic double tungstate family [KGd(WO4)2]. Longitudinal shifts and radii of the Hamilton-Lloyd pair of rings were measured. In each case, the symmetric - forward and backward - evolution of the beam in free space from its focal image plane was monitored and quantified. Theoretical ring plane patterns based on a recently presented theoretical model are also compared to experimental patterns and found to be in good agreement.

ORBITAL ANGULAR MOMENTUM DENSITY OF A HOLLOW VORTEX GAUSSIAN BEAM

Here the hollow vortex Gaussian beam is described by the exact solution of the Maxwell equations. By means of the method of the vectorial angular spectrum, analytical expressions of the electromagnetic fields of a hollow vortex Gaussian beam propagating in free space are derived. By using the electromagnetic fields of a hollow vortex Gaussian beam beyond the paraxial approximation, one can calculate the orbital angular momentum density distribution of a hollow vortex Gaussian beam in free space. The overall transverse components of the orbital angular momentum of a hollow vortex Gaussian beam are equal to zero. Therefore, the influences of the topological charge, beam order, Gaussian waist size, and linearly polarized angle on the distribution of longitudinal component of the orbital angular momentum density of a hollow vortex Gaussian beam are numerically demonstrated in the reference plane. The outcome is useful to optical trapping, optical guiding, and optical manipulation using the hollow vortex Gaussian beams.

Hollow vortex Gaussian beams

A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular momentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respectively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter γ, and transfer matrix elements A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in optical micromanipulation.

ORBITAL ANGULAR MOMENTUM DENSITY OF AN ELEGANT LAGUERRE-GAUSSIAN BEAM

Based on the method of the vectorial angular spectrum, an analytical expression of the electric fleld of an elegant Laguerre- Gaussian beam in free space is derived beyond the paraxial approximation, and the corresponding magnetic fleld is obtained by taking the curl of the electric fleld. By using the expressions for the electromagnetic flelds, the expression of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is derived, which is applicable to both the near and far flelds. The efiects of the three beam parameters on the distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam are studied. The distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is also compared with that of the standard Laguerre-Gaussian beam. The result shows that the distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is more simple and centralized than that of the standard Laguerre-Gaussian beam.

On the free-space Gaussian beam coupling to droplet optical resonators

In this paper, light coupling into droplet optical resonators by means of a free-space Gaussian beam (GB) is investigated through numerical simulations and experiments. This method is introduced as an alternative to previously reported methods based on coupling through tapered fibers or prisms. Though applicable to solid-state optical resonators, this method is investigated here in the context of optofluidics for preserving the integrity of the droplet shape and for facilitating the steps of alignment and light coupling. The glycerol droplet under study is supported by a super-hydrophobic surface, which consists of Teflon-coated nanostructured silicon, to provide the advantage of keeping the droplet at a specific location, while maintaining a nearly spherical shape. The effectiveness of this method is tested with millimeter-sized droplets through measurements of their spectral responses. Quality factors Q in excess of 6 × 10(3) have been recorded. An analytical model for the external quality factor associated with this coupling technique has been derived, and the effect of the coupling parameters is demonstrated, allowing discussion about the scaling effects.

An analysis on radius of curvature aspects of hyperbolic and sinusoidal Gaussian beams

The effective radius of curvature of hyperbolic and sinusoidal Gaussian beams in free space and turbulent atmosphere is studied analytically and numerically. It is shown that the radius of curvature rises with growing source size, and changes slowly with wavelength. In general, given the same source and propagation settings, the beams can be listed in descending order of radius of curvature magnitudes as sinh Gaussian, cosh Gaussian, sine Gaussian, pure Gaussian and cos Gaussian beams. However, the radius of curvature and the difference of the radius of curvature between the different beams reduce with growing strength of turbulence because the beam’s spatial phase distribution is destroyed by turbulence.

INVESTIGATION ON RADIATION FROM A VLASOV MODE CONVERTER FOR W-BAND WHISPERING-GALLERY MODE GYROTRON

The principle of Vlasov mode converter for whispering-gallery mode gyrotron was studied in detail by using a geometric optics model.The radiation field passing through the mode converter was analyzed by using the equivalent image source model and the vector diffraction theory.After considering some particular parameters of W-band whispering-gallery mode gyrotron,the field distribution of radiated beam passing throngh Vlasov mode converter was discussed by numerical calculation.The results indicate that the high-order whispering-gallery mode inside the gyrotron is converted into Gaussian beams in free space by Vlasov mode converter,and the Gaussian distribution in the far zone is superior to that in the near zone.

Parametric characteristics for a broadband Gaussian beam in free space

Based on the theory of the second-order intensity moment and the method of Fourier transformation, some parameters for a broadband Gaussian beam in free space are studied analytically and numerically. It is shown that the beam width and the divergence angle for a broadband Gaussian beam in free space are both larger than those for a monochromatic Gaussian beam. The broader the bandwidth of a light beam, the larger the beam width and the divergence angle of the light beam. The beam propagation factor for a broadband Gaussian beam in free space is larger than that for a monochromatic Gaussian beam and increases slowly with bandwidth. The kurtosis parameter for a broadband Gaussian beam in free space increases with propagation distance and bandwidth. The kurtosis parameter for a broadband Gaussian beam with much broader bandwidth increases more remarkably with propagation distance.

Consistency of the directionality of partially coherent beams in turbulence expressed in terms of the angular spread and the far-field average intensity

Under the quadratic approximation of the Rytov's phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.

Enhancing X-Ray Generation by Electron-Beam–Laser Interaction in an Optical Bragg Structure

We demonstrate that x-ray radiation emitted by relativistic electrons scattered by a counter-propagating laser pulse guided by an adequate Bragg structure surpasses by about 2 orders of magnitude the energy generated by a conventional free-space Gaussian-beam configuration, given the same e beam and injected laser power in both configurations.

Metal slit array Fresnel lens for wavelength-scale optical coupling to nanophotonic waveguides

We propose a novel metal slit array Fresnel lens for wavelength-scale optical coupling into a nanophotonic waveguide. Using the plasmonic waveguide structure in Fresnel lens form, a much wider beam acceptance angle and wavelength-scale working distance of the lens was realized compared to a conventional dielectric Fresnel lens. By applying the plasmon waveguide dispersion relation to a phased antenna array model, we also develop and analyze design rules and parameters for the suggested metal slit Fresnel lens. Numerical assessment of the suggested structure shows excellent coupling efficiency (up to 59%) of the 10 mum free-space Gaussian beam to the 0.36 mum Si waveguide within a working distance of a few mum.

An investigation of the lowest-order transverse-electric (TE_1) mode of the parallel-plate waveguide for THz pulse propagation

We experimentally and theoretically investigate the lowest-order transverse-electric (TE1) mode of the parallel-plate waveguide (PPWG) for the propagation of broadband THz pulses. We demonstrate undistorted THz pulse propagation via the single TE1 mode, solving the group-velocity-dispersion and spectral-filtering problems caused by the mode's low-frequency cutoff. We observe a remarkable counterintuitive property of the TE1 mode: its attenuation decreases with increasing frequency for all frequencies above cutoff. This phenomenon has not been observed with any other THz waveguide to date, and it can enable extremely low-loss propagation. We present a physical interpretation of this frequency-dependent behavior using a simple plane-wave description of the TE1 mode propagation. We also find that it is possible to achieve almost 100% coupling to the TE1 mode from a focused free-space Gaussian beam. In addition, using the above plane-wave analysis, we show how to mitigate the diffraction losses inherent to long path-length PPWGs via the use of transverse-concave plates.

Directionality of general beams

The directionality of general beams propagating in free space and in atmospheric turbulence is studied. Based on the partial-coherence theory, the analytical expressions for the mean-squared width and the angular spread of general beams are derived by using the integral transform technique. It is shown that the mean-squared width and the angular spread depend not only on the weighting factors of all basis modes but also on the weighting factors of the corresponding mode coherence coefficients of the ith and the (i+2)th if the Hermite-Gaussian modes are adopted. It is found that under a certain condition there exist the equivalent general beams which may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The result holds true, irrespective of the model of turbulence used.

Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the angular spread θ sp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition of the intensity. However, the θ sp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition of the cross-spectral density function. For the superposition of the cross-spectral density function, θ sp of GSM array beams with smaller coherence length σ 0, smaller waist width w 0, smaller beam number N, and larger separation distance x d are less affected by turbulence than of those with larger σ 0,w 0,N, and smaller x d ; while, for the superposition of the intensity, the effect of turbulence on θ sp is independent of N and x d . In addition, the angular spread is nearly the same for the two types of superposition when σ 0 or w 0 is small enough, or x d is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence.

Calculation of Radiation from a Helically Cut Waveguide for a Gyrotron Mode Converter in the Quasi-Optical Approximation

We present results of calculations of the radiation from a helically cut waveguide launcher, a so-called Vlasov launcher, which is commonly used either internal or external to a gyrotron for purposes of mode conversion. A gyrotron internal mode converter consists of such a launcher that radiates the waveguide mode as a nearly Gaussian beam in free space followed by a set of mirrors to focus and direct the radiation. The radiation from the launcher is first calculated using a geometric optics representation of the waveguide mode. Then the radiation is calculated in the quasi-optical limit, including diffraction. These analytic results are compared to a rigorous calculation using the computer code SURF3D, which uses an electric field integral equation (EFIE) approach. Good agreement is obtained between the quasi-optical theory and the SURF3D calculation. The present results provide new insights into the accuracy of the quasi-optical theory and may be useful for the design and improvement of Vlasov-type mode converters.

The far-field directionality of partially coherent flat-topped beams propagating through atmospheric turbulence

The far-field directionality of partially coherent flat-topped beams propagating through atmospheric turbulence is studied. The closed-form expressions for the mean squared beam width and angular spread of partially coherent flat-topped beams propagating through atmospheric turbulence are derived. It is shown that two partially coherent flat-topped beams may generate the same angular spread, and there exist equivalent partially coherent flat-topped beams which may have the same far-field directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The far-field directionality of Gaussian Schell-model (GSM) beams in atmospheric turbulence is treated as a special case of partially coherent flat-topped beams. The theoretical results are illustrated by numerical examples and interpreted physically.

Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence

The propagation of partially coherent Hermite-cosh-Gaussian (H-ChG)beams through atmospheric turbulence is studied in detail. The analytical expression for the angular spread of partially coherent H-ChG beams in turbulence is derived. It is shown that the angular spread of partially coherent H-ChG beams with smaller spatial correlation length sigma0, smaller waist width w0, smaller beam parameter Omega0, and larger beam orders m, n is less affected by turbulence than that of partially coherent H-ChG beams with larger sigma0, w0, Omega0, and smaller m, n. Under a certain condition partially coherent H-ChG beams may generate the same angular spread as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The angular spread of partially coherent Hermite-Gaussian (H-G), cosh-Gaussian (ChG), Gaussian Schell-model (GSM) beams, and fully coherent H-ChG, H-G, ChG, Gaussian beams is studied and treated as special cases of partially coherent H-ChG beams. The results are interpreted physically.

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.

Divergence of geometrical optics series at the boundary of its applicability: An analytical example in elementary functions (2D Gaussian beam in free space)

Abstract An analytical example in elementary functions is presented (2D Gaussian beam diffraction in free space), which demonstrates the divergence of the geometrical optics (GO) series when the conditions for its applicability are violated. This example shows that accounting for higher terms in GO power series leads to divergence and therefore becomes completely useless beyond the boundaries of GO applicability.

Vectorial nonparaxial flattened gaussian beams and their beam quality in terms of the power in the bucket

The closed-form propagation equations of vectorial nonparaxial flattened Gaussian beams in free space are derived and some special cases are discussed. The power in the bucket (PIB) is extended to the nonparaxial regime, where the intensity is replaced by the z component of the time-averaged Poynting vector, and used to characterize beam quality of nonparaxial beams in the far field. Numerical calculation results show the dependence of the PIB of vectorial nonparaxial FGBs on the waist-width to wavelength ratio w 0/ λ and beam order N.