Incoherent Beams Research Articles

Calculating optical forces using the boundary integral method

In this paper, we show that the boundary integral method is highly efficient for the calculation of optical forces on small dielectric and metallic objects. The boundary integral formulation for the Maxwell equations is stated, and an implementation of the equations is described, tested and used to derive new bistability results for two dielectric spheres in counterpropagating incoherent laser beams.

Solitons in complex optical lattices

We present an overview of our recent results in the area of soliton excitation and control in optical lattices induced by different types of nondiffracting beams featuring unique symmetries. Optical lattices offer the possibility to engineer and to control the diffraction of light beams in media with transversally modulated optical properties, to manage the corresponding reflection and transmission bands, and to form specially designed defects. Consequently, they afford the existence of a rich variety of new families of nonlinear stationary waves and solitons, lead to new rich dynamical phenomena, and offer novel conceptual opportunities for all-optical shaping, switching and routing of optical signals encoded in soliton formats. In this overview, we consider different types of solitons, including fundamental, multipole, and vortex solitons in reconfigurable lattices optically induced by nondiffracting radially symmetric and azimuthally modulated single Bessel beams, soliton control in networks, couplers, and switches induced by several mutually coherent or incoherent Bessel beams, we address soliton properties in three-dimensional Bessel lattices, as well as in lattices produced by Mathieu and parabolic optical beams.

Dark incoherent soliton splitting in biased photorefractive–photovoltaic crystals

Using the coherent density approach, we study the dark incoherent soliton splitting in biased photorefractive–photovoltaic crystals. We show that when the full width half maximum (FWHM) of the optical beam’s intensity is increased, the odd incoherent dark beam splits into an odd-number sequence of multiple dark stripes, whereas the even incoherent dark beam splits into an even-number sequence of multiple dark stripes. We find that when more incoherent solitons are generated, the separations between adjacent dark stripes become smaller and the stripes far away from the center become less visible and that for a given physical system and for a given splitting, the separations between adjacent dark stripes decrease with an increase in the intensity FWHM of the optical beam. On the other hand, the dark incoherent soliton splitting in biased photorefractive–photovoltaic crystals is the dark incoherent screening soliton splitting when the bulk photovoltaic effect is neglectable and the dark incoherent closed- and open-circuit photovoltaic soliton splitting when the external bias field is absent.

Novel All-Optical Switch Using Nonlinear Mach-Zehnder Interferometer

Using a nonlinear Mach-Zehnder interferometer, a novel all-optical switch that can mimic NOT/XOR, AND, and NAND gates is proposed. The proposed switch is novel in the sense that it functions with mutually incoherent input beams of the same wavelength and polarization, and the NOT/XOR and NAND gates constructed using it give “pure” output (i.e., output contains only one of the all-input beams and not a mixture of the input beams). Purity of output is an important feature as it is essential for cascadability. The operating power levels of the proposed switch could be adjusted by adjusting the length of the Mach-Zehnder interferometer that makes the proposed switch easily implementable in a circuit. Moreover, a cascadable NAND gate allows for Boolean completeness.

Coherent Forward Stimulated-Brillouin Scattering of a Spatially Incoherent Laser Beam in a Plasma and Its Effect on Beam Spray

A statistical model for forward stimulated-Brillouin scattering is developed for a spatially incoherent, monochromatic, laser beam propagating in a plasma. The threshold above which the laser beam spatial incoherence cannot prevent the coherent growth of forward stimulated-Brillouin scattering is computed. It is found to be well below the threshold for self-focusing. Three-dimensional simulations confirm its existence and reveal the onset of beam spray above it. From these results, we propose a new figure of merit for the control of propagation through a plasma of a spatially incoherent laser beam.

Dynamical tunneling of counterpropagating beams mediated by an optical photonic lattice

In a numerical study, we demonstrate the dynamical tunneling (DT) of two counterpropagating (CP) mutually incoherent beams in a two-dimensional photonic lattice, recorded in a photorefractive (PR) crystal. The beams are launched head-on from the opposite faces of a PR crystal in which an optically induced two-dimensional photonic lattice is established. The DT is caused by the spontaneous symmetry breaking of CP beams, which is induced by the nonlinear interaction between the beams and is mediated by the lattice. To observe DT we found no need to introduce a specific external tilt potential, as is done in the conventional Zener tunneling; the tilting is provided by the repulsive interaction between the beams, which causes ejection of one beam from the launching region of the other. As the beams propagate, they move laterally in real time, causing the leakage of radiation from the first Brillouin zone to the second and higher zones. In the process the beams also tunnel from the first photonic band zone to the higher zones, which by definition is the DT.

Mode competition in steady-state optical waveguide amplifiers

A theory of monochromatic light propagation in a fiber amplifier is developed. It is shown that competition between coherent gain-guided modes is qualitatively different from interaction between incoherent beams. Spatial beating between modes limits the gain of the mode with lower input power even if the corresponding modal gain coefficient is higher. Depending on the input beam parameters, the amplifier output can be dominated by either a single guided mode or their combination. The theory is illustrated by analyzing the gain behavior of a single planar waveguide and arrays of two and three narrow planar waveguides.

Coherent and incoherent combining of fiber array with hexagonal ring distribution

Beam combining of fiber array with hexagonal ring distribution has been studied in detail. The theoretical analysis and numerical calculation results are given to illustrate the propagation properties of the resulting beam through free space. A comparison between the coherent and the incoherent case shows that high peak irradiance and good beam quality for coherent combining can be obtained in the far field. The effects of phase errors and beam quality M 2 factor are also studied. Results indicate that the element numbers should be increased to achieve high power and the space between adjacent elements should be reduced to maintain a good beam quality. This is basically the same for both coherent and incoherent beam combining.

Incoherent Beam Combining of Continuous-Wave and Pulsed Yb-Doped Fiber Amplifiers

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We review the technique of incoherent beam combining and show experimentally the combination of four continuous wave fiber amplifiers to an average power of 2 kW and four pulsed 2 ns fiber amplifiers to an average power of 187 W (pulse energy 3.7 mJ) using binary dielectric gratings. The scaling potential and limitations are discussed in detail. </para>

Dynamics of Incoherent Photovoltaic Spatial Solitons

Propagation properties of bright and dark incoherent beams are numerically studied in photovoltaic-photorefractive crystal by using coherent density approach for the first time. Numerical simulations not only exhibit that bright incoherent photovoltaic quasi-soliton, grey-like incoherent photovoltaic soliton, incoherent soliton doublet and triplet can be established under proper conditions, but also display that the spatial coherence properties of these incoherent beams can be significantly affected during propagation by the photovoltaic field.

Automated collimation testing in Lau interferometry using phase shifting technique

We demonstrate an automated procedure for detection of collimation position of an incoherent beam in Lau interferometry using phase shifting technique. The experimental arrangement consists of a Lau-based interferometer in which light from a source grating illuminates a set of two coarse gratings separated by self-imaging distance. Phase shifting procedure is incorporated by translating the detector grating, corresponding to different positions of the collimating lens. The phase map is plotted corresponding to each position. The slope of the phase map is indicative of the collimation position of the optical beam. The technique is fully automatic and provides good accuracy and high precision.

Incoherent Combining and Atmospheric Propagation of High-Power Fiber Lasers for Directed-Energy Applications

High-power fiber lasers can be incoherently combined to form the basis of a directed high-energy laser system which is highly efficient, compact, robust, low-maintenance and has a long operating lifetime. This approach has a number of advantages over other beam combining methods. We present results of the first field demonstration of incoherent beam combining using kilowatt-class, single-mode fiber lasers. The experiment combined four fiber lasers using a beam director consisting of individually controlled steering mirrors. Propagation efficiencies of ~90%, at a range of 1.2 km, with transmitted continious-wave power levels of 3 kW were demonstrated in moderate atmospheric turbulence. We analyze the propagation of combined single-mode and multimode beams in atmospheric turbulence and find good agreement between theory, simulations and experiments.

Comparative study on the propagation performance of coherently combined and incoherently combined beams

Taking phase error, turbulent atmosphere, jitter, vacancy factor and tilt error into consideration, we propose a general propagation formula for both coherent and incoherent combined beams with different kinds of aberrations. Comparative study on the propagation performance of coherent and incoherent combined beams is presented. Beam propagation factor (BPF) defined as laser output power in a specified far-field bucket divided by the total output power radiating from the effective near-field exit aperture of the laser beam is introduced as the beam quality factor to give a quantitative study. It is revealed that the coherent combined beam has great advantage when propagating in free-space compared with the incoherent combined beams. However, the coherent combined beam is more sensitive to the environmental aberrations, and the beam quality degrades faster with an increase in the aberrations’ intensity. Scintillation index as the high moments of the combined intensity field is also studied. It is revealed that both coherent and incoherent combined beams exhibit less scintillations compared with a single-aperture beam, and the incoherent combined beam demonstrates better scintillations reducing the performance. Our methodology offers an all-round performance evaluation on the two kinds of laser systems.

Longitudinal optical binding of several spherical particles studied by the coupled dipole method

We employed a coupled dipole method (CDM) to study theoretically the interaction among several spherical particles placed into two counter-propagating mutually incoherent Bessel beams. This interaction is mediated by the light scattering among the particles. It has already been demonstrated that, if the intensity of the incident beam is sufficiently high, the scattered light is strong enough to self-arrange the objects in the space. Namely, the counter-propagating and incoherent Bessel beams are extremely useful to be employed because the interaction among the particles via the scattered light is not superimposed by other optical forces coming from the radiation pressure of each beam and axial gradients of the beam intensities. Therefore so-called optical binding between the particles is enhanced and leads to several stable configurations of the particles. We studied these stable configurations using the CDM for various properties of the beams and particles and we also compared these theoretical results with the experimental observations.

Cooperative interaction in azopolymers upon irradiation

We present two optical experiments which permits to evaluate individual and collective behaviours of molecules leading to a well-organized pattern in a randomly activated molecular assembly; in a first experiment a white light and a laser beam are sent together; in a second experiment a low-power coherent beam carrying polarization and wavelength information is used to organize a surface relief grating on a photochromic polymer thin film which is photo-activated by a powerful incoherent beam; we show that collective movements originate at the molecular level.

Mutual injection locking and coherent combining of three individual fiber lasers

Mutual injection locking and coherent combining of three individual erbium-doped fiber lasers are reported. Theoretical model of the three fiber lasers under mutual injection is also analyzed. Under free running state, the far field beam profile is a simple intensity superposition as three incoherent beams. Under mutual injection locking, interference lobes with high contrast ratio are obtained in the far field of three fiber lasers, which shows that the three fiber lasers have good interference characteristic under mutual injection. The experimental results are in good agreement with the theoretical results. According to this method, we can also realize coherent beam combining in more fiber lasers.

Mutual-focusing of two co-propagating beams and formation of trapped spatial breather pair in saturable nonlinear media

In this paper, using parabolic equation approach, coupled propagation of two coaxially co-propagating and mutually incoherent bright cylindrical beams in saturable nonlinear medium has been investigated. Considering the coupling coefficient equal to unity ( κ=1), a detailed account of formation of spatial soliton pair (i.e. both beams are stationary trapped) and spatial breather pair (i.e. width of each beam oscillates with the propagation distance) has been provided and existence of spatially trapped breather pair (i.e. average width of each breather of the pair does not change with the propagation distance) has been shown. Conditions of formation of trapped spatial breather pair and their existence line has also been revealed for arbitrary beam width ratio of the beams. It is revealed that spatial soliton pairs are just a special case of trapped breather pair. The regions (conditions) of mutual-focusing and mutual-defocusing of spatial soliton pair/breather pair have also been identified. Lastly, the law of trapped breather pair formation is proposed.

Neither Kerr Nor Thermal Nonlinear Response of Dye Doped Liquid Crystal Characterized by the Z-Scan Technique

In the experimental characterization of the nonlinear optical properties of dye-doped liquid crystals by the Z-scan technique with CW lasers it is rather common to assign it a Kerr or thermal nonlinear response. In this work, we demonstrate that neither of them correctly describes all features of the Z-scan obtained in planar samples of methyl red doped 5CB liquid crystal using He-Ne CW illumination, where a strong nonlinear optical response is observed. The Z-scan curves depend strongly on the input polarization of the beam obtaining negative and positive nonlinear response for polarizations parallel and orthogonal to the director vector. We discuss and compare the effect of an additional incoherent linearly-polarized beam and plain heating source on Z-scan experiments. A theoretical model, valid for small and large phase modulation, is proposed based on the assumption that the sample can be considered as a thin lens with a photoinduced focal length dependent on the Gaussian beam radius ω m (where m is an integer), obtaining good agreement with the experimental curves for m = 3, which is neither a Kerr nor thermal nonlinearity.

Self-deflection of partially spatially incoherent beams and solitons in photovoltaic photorefractive crystals

By considering the effect of background light and diffusion, the self-deflection process of partially spatially incoherent (PSIC) beams and photovoltaic (PV) solitons in open-circuit PV photorefractive crystals has been investigated by employing numerical method and the perturbation technique, respectively. The results from the two approaches are in good agreement: the center of PSIC PV solitons moves on a parabolic trajectory, which is similar to those of coherent solitons. In addition, we also discuss that the dependence of self-deflection effect on the coherent parameter θ 0 and find it is slight relative to θ 0 for quasi-soliton but decreases monotonously with θ 0 for PSIC beam.

An experimental study of the interactions of self-trapped white light beams in a photopolymer

Interactions of two parallel-propagating and mutually incoherent white light beams were examined in a photopolymerizable organosiloxane. The beams fused when separated by a distance corresponding to the width of each beam but at separation distances⪢beam width, formed two self-trapped beams that repelled each other. At separation distances&amp;lt;beam width, they suffered filamentation but ultimately fused into a single self-trapped beam.