Propagation of twisted gaussian Schell-model beams through a misaligned first-order optical system

Abstract

The propagation of twisted Gaussian Schell-model (TGSM) beams passing through a misaligned first-order optical system is studied. The explicit expressions for the cross-spectral density function and Wigner distribution function of the output beam are derived. As a result, generalized partially coherent beams called the decentred twisted Gaussian Schell-model (DTGSM) beams are introduced and their properties are discussed.     

Beam propagation factor of decentred gaussian and cosine—gaussian beams

Abstract

On the basis of the second moment method, the beam propagation factor (M ²?factor) of decentred Gaussian beam has been derived, and analysed physically. Then, the result is extended to novel sinusoidal-Gaussian beams, one type of which is the cosine—Gaussian beam, which can be regarded as a superposition of two decentred Gaussian beams.     

Generation of partially coherent laser beam directly from spatial-temporal phase modulated optical resonators

Abstract

The generation of a partially coherent laser beam directly from a spatial-temporal phase modulated optical resonator is investigated both experimentally and theoretically. The laser material used in the experiment is Nd:YAG rod pumped by Krypton lamps working in continuous wave mode. The phase modulation is fulfilled by an intra-cavity LiNbO₃ electro-optic crystal driven by high voltage. The experimental results show that intracavity phase modulation is an effective way to generate partially coherent laser beams. The theoretical analysis and numerical simulation shows that the output beam can be characterized by Gaussian Schell-model (GSM) beams. The two-slit interference experiment confirms that the output beam is partially coherent.     

Multi-Gaussian Beam Modeling for Multilayered Anisotropic Media,I: Modeling Foundations

A model is developed for the propagation and reflection/transmission of Gaussian beams in multilayered media where the layer materials can be general anisotropic, homogeneous elastic solids and the layer interfaces can be curved surfaces. It is shown that the Gaussian beams can be simply described in a set of slowness coordinates and that the complications arising from the multiple layers can be efficiently addressed through the use of an ABCD matrix approach. A multi-Gaussian beam model for an ultrasonic piston transducer radiating into very complex media is then developed by superimposing a small number of these propagating Gaussian beams.     

Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT

A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.     

The beamwidth of bessel-modulated gaussian beams

Abstract

Based on the second-order irradiance moment definition, a closed-form expression for the beam width of Bessel-modulated Gaussian beams (QBG beams) is derived, from which the expressions for the waist width, its position, and beam propagation factor (M ² factor) of QBG beams with complex parameter μ are obtained. The dependence of the beam width and waist position on the parameter μ is analysed and illustrated with numerical examples.     

Twisted Gaussian Schell-model Beams: A Superposition Model

Abstract

We present a simple model in which a twisted Gaussian Schell-model beam is produced by an incoherent superposition of ordinary Gaussian beams. The meaning and some direct consequences of the model are given.     

Propagation properties of cylindrical sinc Gaussian beam

Abstract

We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.     

Transformation of a Gaussian Beam into a Uniform Beam by a Lenslike Medium with Gain or Loss

Abstract

The propagation of Gaussian beams through lenslike media with gain or loss is analysed in order to discuss the transformation of these beams into uniform beams. The results obtained are applied to a lenslike medium with gain increasing along the radial direction.     

Influence of laser array performance on spectrally combined beam

Abstract

Incoherent spectral beam combining (SBC) of multiple laser beams is accomplished along the emitters’ arraying direction. Considering that the output beams from a laser array (LA) usually have deflection angles, positional displacements and divergence angles even after being collimated, a propagation model of SBC systems based on multilayer dielectric gratings has been built up. On the basis, properties of the spectrally combined beam affected by parameters of the LA have been discussed in detail. Simulation results show that with the increase in the deflection angle, both the power and the beam quality of the combined beam degrade dramatically. The positional displacement has little impact on the intensity distribution and the beam quality of combined beam but change the wavelength composition of the combined beam. The divergence angle strongly affects the intensity distribution and the beam quality of the combined beam. Additionally, the effect of the deflection angle on the output beam quality is more obvious and may shift the beam spot when comparing with that of the divergence angle.     

The Intensity Distribution of a Gaussian Schell-model Beam Focused by an Aperture Lens

Abstract

Starting from the generalized Huygens-Fresnel diffraction integral, we study the intensity distribution of a Gaussian Schell-model (GSM) beam diffracted at an aperture lens. A great number of numerical calculations have been performed to illustrate the focused field characteristics. Isophote diagrams are given for systems of different Fresnel numbers, which focus GSM beams, and the related analysis is presented.     

The M 2 factor of hermite-cosh-gaussian beams

Abstract

Based on the second-order moments method, the closed-form expression for the M ²-factor of Hermite-cosh-Gaussian beams is derived, which depends on the beam order n and decentred parameter a. The result shows a more general characteristic, because cosh-Gaussian, Hermite-Gaussian and fundamental Gaussian beams can be regarded as the special cases of Hermite-cosh-Gaussian beams.     

Nonparaxial analyses of cylindrical vector beams with arbitrary polarization order in the far field

Abstract

Based on the vector angular spectrum representation and the method of stationary phase, the analytical expressions for the electromagnetic fields of the cylindrical vector Laguerre–Gaussian beams with arbitrary polarization order are derived in the far field. The radially, anti-vortex and linearly polarized beams can be viewed as the special cases of our general result. The analyses indicate that the beam evolution properties and nonparaxiality are closely related to the radial mode number, the polarization order number and the ratio of the waist width to the wavelength. The high polarization order cylindrical vector beams compared with the radially polarized beams are more influenced by the nonparaxiality. This research provides a convenient approach to manipulate the cylindrical vector Laguerre–Gaussian beams by choosing the special state of polarization.     

Propagation and far-field beam quality of M × N Hermite–Gaussian beams propagating through atmospheric turbulence

The analytical propagation equation of M×N Hermite–Gaussian (H–G) beams, which are combined incoherently and propagate through atmospheric turbulence, is derived, which enables us to study their propagation properties and far-field beam quality. The propagation of M×N Gaussian beams through atmospheric turbulence and M×N H–G beams in free space are treated as special cases of our general result. The power in the bucket (PIB), β-parameter and Strehl ratio are chosen as the parameters characterizing the beam quality in the far field. The dependence of PIB, β-parameter and Strehl ratio of M×N H–G beams through atmospheric turbulence on the refraction index structure constant C _n ², beam numbers M, N, mode indices m, n and separate distances x_d , y_d is illustrated numerically and interpreted physically. It is found that M×N H–G beams are less sensitive to the effects of turbulence than M×N Gaussian beams.     

A comparative study of standard and elegant Hermite–Gaussian beams propagating through turbulent atmosphere

Based on the extended Huygens–Fresnel principle and the definition of the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the root-mean-square (rms) beam width and far-field divergence angle, curvature radius and M ²-factor of standard Hermite–Gaussian (SHG) and elegant Hermite–Gaussian (EHG) beams passing through turbulent atmosphere are derived and compared. It is shown that in turbulent atmosphere the far-field divergence angle of SHG and EHG beams is equal under the same conditions, but the rms beam width, curvature radius and the M ²-factor of SHG and EHG beams are different except for beam orders m?=?0 and m?=?1. The relative rms beam width, relative curvature radius and relative M ²-factor of SHG beams are less than those of EHG beams. Therefore, the conclusion that SHG beams are less influenced by turbulence than EHG beams can be drawn if we examine one of the above three relative beam parameters.     

Development of a cryogenic gas target for intense RI beam production at CRIB

Nuclear reactions of astrophysical interest, especially those under high-temperature and high-density conditions, require high-intensity low-energy radioactive ion beams, because the cross-sections are very small for the direct method study. Production of high-intensity radioactive ion beams is, therefore, one of the key developments for RI beam facilities.We report the development of a new cryogenic RI beam production gas target, along with its characteristics and performance. Some of its advantages are the increased stability against high-current primary beams and the increased thickness due to the cooling by liquid nitrogen.The target is being tested with heavy-ion beams. Measures by energy loss of the beam indicate that a thickness of about 2.4 mg/cm² of H₂ gas has been attained and a secondary beam of ⁷Be⁴⁺ at 4.0 MeV/u of more than 2×10⁸ pps was produced.     

Cross-spectral Density of Partially Coherent Gaussian Beams for Arbitrary Space Distances

Abstract

A formula for partially coherent Gaussian beams is presented, for which both of the arguments of the cross-spectral density are arbitrary points. Numerical discussions show ‘internal’ diffraction inside the beam.     

Validity of the cylindrical localized approximation for arbitrary shaped beams in generalized Lorenz-Mie theory for circular cylinders

Abstract

A so-called cylindrical localized approximation, allowing one to speed up the evaluation of beam shape distributions in generalized Lorenz-Mie theory for circular infinitely long cylinders, has been previously introduced and, in the case of Gaussian beams, rigorously justified. In this paper, we examine and demonstrate the validity of this approximation for arbitrary shaped beams.     

Electromagnetic Beam Fields

An electromagnetic beam is defined using mathematical properties of the associated angular spectrum of plane waves. It is found that the usual paraxial theory for the Hermite Gaussian or Laguerre Gaussian beams, produced by some lasers, can be replaced by a more general theory which is precise according to Maxwell's equations. In this theory the beams exhibit an amplitude distribution over any plane normal to the direction of propagation which can be described using prolate spheroidal wave functions. As the degree of collimation is increased, these beams asymptotically take on the familiar Gaussian amplitude cross section. However, as the divergence from focus is increased, these beams asymptotically approach modified dipole fields. It is found that two, mutually exclusive, classes of beam fields exist. For each beam in one class there is always a complementary beam in the other class. As the degree of collimation is increased, complementary beams become almost identical. Complementary beams contain electromagnetic components which are related to one another in the same manner as between the fields of similar electric and magnetic multipoles.     

Practical Bessel beam pumping of periodically poled optical parametric oscillators

Abstract

The pumping of periodically poled optical parametric oscillators (OPOs) by practically realizable Bessel beams is analysed. The effect of the deviation of practical Bessel beams from the ideal form is assessed, the influence of the particular structure of periodically poled materials is discussed, and the concept of phase-matching aperture is introduced. In a typical situation, the efficiency of a periodically poled lithium niobate OPO pumped by a practical Bessel beam has been measured; no efficiency advantage was found in comparison to the corresponding Gaussian beam pumped system or to that predicted by the standard Brosnan-Byer model.