Superposition Of Beams Research Articles

Deterministic Subwavelength Control of Light Confinement in Nanostructures

We propose a novel deterministic protocol, based on continuous light flows, that enables us to control the concentration of light in generic plasmonic nanostructures. Based on an exact inversion of the response tensor of the nanosystem, the so-called deterministic optical inversion protocol provides a physical solution for the incident field leading to a desired near-field pattern, expressed in the form of a coherent superposition of high-order beams. We demonstrate the high degree of control achieved on complex plasmonic architectures and quantify its efficiency and accuracy.

Diffraction–attenuation resistant beams: their higher-order versions and finite-aperture generations

Recently, a method for obtaining diffraction-attenuation resistant beams in absorbing media has been developed in terms of suitable superposition of ideal zero-order Bessel beams. In this work, we show that such beams keep their resistance to diffraction and absorption even when generated by finite apertures. Moreover, we shall extend the original method to allow a higher control over the transverse intensity profile of the beams. Although the method is developed for scalar fields, it can be applied to paraxial vector wave fields, as well. These new beams have many potential applications, such as in free-space optics, medical apparatus, remote sensing, and optical tweezers.

Intensity clamping during dual-beam interference

One has prospected to overcome the intensity clamping phenomenon during femtosecond laser filamentation by superimposing two beams. This experimental scheme is thus studied in our work. We have realized the interference of two ultrashort laser beams and one of them creates a filament in air. The formation of a dynamic plasma grating induced by the interference pattern is observed. However, qualitative analysis of the experimental results indicates that intensity clamping still governs the intensity evolution during the dual-beam interaction. The expectation of greatly increasing laser intensity by dual beams superposition might not be realistic.

Axion-like-particle search with high-intensity lasers

We study ALP-photon-conversion within strong inhomogeneous electromagnetic fields as provided by contemporary high-intensity laser systems. We observe that probe photons traversing the focal spot of a superposition of Gaussian beams of a single high-intensity laser at fundamental and frequency-doubled mode can experience a frequency shift due to their intermittent propagation as axion-like-particles. This process is strongly peaked for resonant masses on the order of the involved laser frequencies. Purely laser-based experiments in optical setups are sensitive to ALPs in the $\mathrm{eV}$ mass range and can thus complement ALP searches at dipole magnets.

Tunable surface texturing by polarization-controlled three-beam interference

For the fabrication of periodic microstructures, a high-precision and highly efficient polarization-controlled three-beam interference technology (PoTBI) has been developed. With the theory of superposition of multiple laser beams, simulations on the influence of polarization upon the intensity distribution in the overlapped area have been carried out. By controlling the polarization of the interfering beams, various intensity patterns can be obtained. An optical setup for PoTBI has been realized and used to generate microstructures in polyimide foil. Micro cavities, micro bumps, eye-like cavities and rectangular columns of hexagonal symmetry and one-dimensional lines are produced. Compared with other multi-beam interference technologies, different surface textures of hexagonal symmetry with the same periodicity can be obtained only by changing the polarization status of the interfering beams without changing the geometrical interference setup. Thus, PoTBI provides a simply tunable texturing technology with a wide range of applications in surface structuring.

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by a “fork” hologram from an incident circular Laguerre–Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric–Gaussian beams. The diffracted beam structure is determined by combination of the “proper” topological charge m of the incident vortex beam and the topological charge l of the singularity “imparted” by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.

Atomic dipole traps with Amplified Spontaneous Emission: A proposal

We propose what we believe to be a novel type of optical source for ultra-cold atomic Far Off-Resonance optical-dipole Traps. The source is based on an Erbium Amplified Spontaneous Emission (ASE) source that seeds a high power Erbium Doped Fiber Amplifier. The main interest of this source is its very short coherence length, thus allowing an incoherent superposition of several trapping beams without any optical interference. The behavior of the superimposed beams is then a scalar sum greatly simplifying complex configurations. As an illustration, we report an estimation of the intensity noise of this source and an estimation of the additional atomic heating rate for an evaporative cooling experiment application. They are both found to be suitable for cold atoms experiments.

Sci—Thur PM: YIS — 04: Aperture Superposition Algorithm for Photon Dose Calculations of Finite Size Cobalt‐60 Radiation Source for Tomotherapy Dose Deliveries

The finite size pencil beam (FSPB) superposition method is commonly used to calculate dose for intensity modulated beams in IMRT. The FSPB model assumes that broad beam dose from a radiation originating from a point source can be calculated by a superposition of dose from pencil beams. For finite size sources, such as a Cobalt‐60 (Co‐60) source of 2 cm diameter, this method is no longer valid. In this paper we propose an aperture superposition (AS) dose calculation method that can be used for dose calculations of intensity modulated beams from finite size radiation sources. The model is applied to fan beams, as encountered in tomotherapy, and results are compared to the FSPB model and the film measurements. The comparisons between the AS model and film measurements show agreement to 1.5% in the high dose regions and 3.7% in the low dose regions. On the other hand, film measurement comparisons to the FSPB model show that the FSPB model underestimates the dose by up to 7% for small field sizes such as 2×2cm2 and 20% for larger field sizes such as 20×2 cm2. In conclusion, the AS model provides a better accuracy than the FSPB model when calculating dose for fan beams from large radiation sources. Research is underway to extend the application of this model to broad IMRT beams obtained from non‐binary multi‐leaf collimators. The implementation of this model to the current treatment planning systems can be useful for treatment planning of Co‐60 based IMRT and tomotherapy.

Nondiffracting beams for vortex tomography

We propose a reconstruction of vortex beams based on implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the angular probability distribution at different positions allows for the reconstruction of the Wigner function.

Coherent beam superposition of ten diode lasers with a Dammann grating

We demonstrate the use of a binary diffractive optical element in a very simple setup to convert the multilobed beam from a low fill factor array of coherent laser diodes into a quasi-Gaussian beam. The phase profile of the grating is determined with a phase retrieval algorithm. Experimentally, the conversion efficiency reaches more than 44%. We also establish that this setup can be used to make an effective measurement of the coherency of the laser array.

A new form of Gaussian beam function as the base function for generic wave field analysis.

Wave propagations are best described by three major approaches: the spherical wave approach represented by Rayleigh integral, the planar wave approach represented by spatial Fourier analysis, and the Gaussian beam approach. Spherical and planar wave approaches, both in form of double integrals, are analytically inconvenient and computationally expensive. In contrast, the Gaussian beam approach, with huge advantages in analytical operability and computational efficiency, has been quietly but firmly winning popularity. Dr. Breazeale’s article: A diffraction beam field expressed as the superposition of Gaussian beams, co-authored with Wen, is not only a most representative work for Gaussian beam approach but also a most cited academic work in sound field analysis and computation. As a memory of Dr. Breazeale’s pioneer role in the raise of Gaussian beam method, this article presents a new enhancement to the existing Gaussian beam method. A modified form of Gaussian beam function introduced as the base function set for wave field analysis greatly reduces the error rooted from the parabolic approximation, the number of Gaussian beams needed, and the run-time computation burden. The process for calculating the beam coefficients and beam parameters is also greatly simplified.

Taylor expansion and discretization errors in Gaussian beam superposition

The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error estimates related to the discretization of the superposition integral and the Taylor expansion of the phase and amplitude off the center of the beam. We show that in the case of odd order beams, the error is smaller than a simple analysis would indicate because of error cancellation effects between the beams. Since the cancellation happens only when odd order beams are used, there is no remarkable gain in using even order beams. Moreover, applying the error estimate to the problem with constant speed of propagation, we show that in this case the local beam width is not a good indicator of accuracy, and there is no direct relation between the error and the beam width. We present numerical examples to verify the error estimates.

Normalization of optical Weber waves and Weber-Gauss beams

The normalization of energy divergent Weber waves and finite energy Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used to derive the integral relations between circular, elliptic, and parabolic waves and to present the Bessel and Mathieu wave decomposition of the Weber waves. The efficiency to approximate a Weber-Gauss beam as a finite superposition of Bessel-Gauss beams is also given.

Recovery of High Frequency Wave Fields for the Acoustic Wave Equation

Computation of high frequency solutions to wave equations is important in many applications and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to PDEs. An alternative way to compute Gaussian beam components such as phase, amplitude, and Hessian of the phase is to capture them in phase space by solving Liouville-type equations on uniform grids. Following [H. Liu and J. Ralston, Multiscale Model. Simul., to appear] we present a systematic construction of asymptotic high frequency wave fields from computations in phase space for acoustic wave equations; the superposition of phase space based Gaussian beams over two moving domains is shown to be necessary. Moreover, we prove that the kth order Gaussian beam superposition converges to the original wave field in the energy norm at the rate of $\epsilon^{\frac{k}{2}+\frac{1-n}{4}}$ in dimension n.

Recovery of High Frequency Wave Fields from Phase Space–Based Measurements

Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool for generating more general high frequency solutions to PDEs. An alternative way to compute Gaussian beam components such as phase, amplitude, and Hessian of the phase is to capture them in phase space by solving Liouville-type equations on uniform grids. In this work we review and extend recent constructions of asymptotic high frequency wave fields from computations in phase space. We give a new level set method of computing the Hessian and higher derivatives of the phase. Moreover, we prove that the kth order phase space–based Gaussian beam superposition converges to the original wave field in $L^2$ at the rate of $\epsilon^{\frac{k}{2}-\frac{n}{4}}$ in dimension n.

基于倾斜多高斯光束叠加的均匀化照明整形方法

基于倾斜多高斯光束叠加的均匀化照明整形方法

Superposition of helical beams by using a Michelson interferometer

Orbital angular momentum (OAM) of a helical beam is of great interests in the high density optical communication due to its infinite number of eigen-states. In this paper, an experimental setup is realized to the information encoding and decoding on the OAM eigen-states. A hologram designed by the iterative method is used to generate the helical beams, and a Michelson interferometer with two Porro prisms is used for the superposition of two helical beams. The experimental results of the collinear superposition of helical beams and their OAM eigen-states detection are presented.

Generating superpositions of higher–order Bessel beams

We report the first experimental generation of the superposition of higher-order Bessel beams, by means of a spatial light modulator (SLM) and a ring slit aperture. We present illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two or more higher-order Bessel beams. The experimentally produced fields are in good agreement with those calculated theoretically. The significance of these fields is that even though one is able to generate fields which carry zero orbital angular momentum, a rotation in the field's intensity profile as it propagates is observed.

Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams

The analytical expression for the beam propagation factor ( M 2-factor) of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the M 2-factor of GSM array beams depends on the beam number, the relative beam separation distance, the beam coherence parameter, the type of beam superposition, and the strength of turbulence. The turbulence results in an increase of the M 2-factor. However, for the superposition of the intensity the M 2-factor is less sensitive to turbulence than that for the superposition of the cross-spectral density function. The M 2-factor of GSM array beams is larger than that of the corresponding Gaussian array beams. However, the M 2-factor of GSM array beams is less affected by turbulence than that of the corresponding Gaussian array beams. For the superposition of the cross-spectral density function a minimum of the M 2-factor of GSM array beams may appear in turbulence, which is even smaller than that of the corresponding single GSM beams.

Turbulence distance of radial Gaussian Schell-model array beams

The effect of turbulence on the spreading of radial Gaussian Schell-model (GSM) array beams is studied quantitatively by examining the mean-squared beam width. The analytical expression for the turbulence distance z T of radial GSM array beams is derived by using the integral transform technique, which indicates within what ranges radial GSM array beams will be less affected by turbulence. It is shown that the effect of turbulence on the spreading of radial GSM array beams can be reduced by choosing the suitable array beam parameters and the type of the beam superposition. In addition, a comparison with the previous work is also made.