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This paper uses a numerical simulation method to evaluate the propagation performance of the partially coherent flat-topped vortex hollow (FTVH) beam and the Gaussian Schell-model (GSM) beam through atmospheric turbulence along slant links. The atmospheric turbulence is simulated by random phase screens, and the performance of the beam models is evaluated by using scintillation index and signal-to-noise (SNR) on the receiver plane with various simulation conditions and parameters. This paper has shown that there is an optimal coherence length for both the partially coherent FTVH beam and the GSM beam. In different parameter settings, the partially coherent FTVH beam has the best propagation performance at N = 1 M = 1. Compared to the GSM beam, the partially coherent FTVH beam obtains an obvious improvement in SNR. The results show that the partially coherent FTVH beam is able to improve the communication efficiency of an FSOC system. [ABSTRACT FROM AUTHOR]

Optical weak measurements are a powerful tool for measuring small shifts of optical paths. When applied to the measurement of the Goos-Hänchen shift, in particular, a special step must be added to its protocol: the removal of the relative Goos-Hänchen phase, since its presence generates a destructive influence on the measurement. There is, however, a lack of description in the literature of the precise effect of the Goos-Hänchen phase on weak measurements. In this paper we address this issue, developing an analytic study for a Gaussian beam transmitted through a dielectric structure. We obtain analytic expressions for weak measurements as a function of the relative Goos-Hänchen phase and show how to remove it without the aid of waveplates. [ABSTRACT FROM AUTHOR]

Analytical expressions for the on-axis normalized transmittance and total transmittance z-scan of thick nonlocal nonlinear media illuminated by a Gaussian beam are obtained in this paper. The corresponding thin media transmittance expressions and the distributed lens method are used together with the assumption that the nonlocal media exhibits weak nonlinear absorption and refraction in order to obtain the formulas. The obtained expressions enable the consideration of different degrees of nonlocality and the reproduction of the results reported for local media. [ABSTRACT FROM AUTHOR]

In the present paper, we elaborate analytical field expressions of diffracted Hermite-Cosh-Gaussian (HChG) beams through an Airy Transform Optical System (ATOS). It is demonstrated that the resulting beams consist of a superposition of modes whose amplitudes are expressed as Airy function and derivative Airy function multiply polynomials. It is shown through numerical calculations that the outgoing fields possess the Airy-like profile with a central peak less powerful than the outer lobes. Furthermore, a complex structure of oscillations is observed for the third-order HChG beam. The effects of the beam order, the decentred parameter the ATOS parameters on the generated fields are illustrated in detail with numerical examples. This investigation constitutes a generalization of the previous studies dealing with the conversion of the fundamental Gaussian and cosh-Gaussian beams by an ATOS. [ABSTRACT FROM AUTHOR]

The Taiji programme is a Chinese space-based laser interferometer gravitational wave detection mission and the differential wavefront sensing (DWS) technique is introduced to reduce the effect of the laser pointing noise. As the distance between two adjacent satellites is about 3 × 10 6 km , the wavefront of the receiving beam is a flat top beam. In this paper, we construct an analytical model of the DWS signal under the circumstances of Gaussian beam-flat top beam interference and study the linearity performance. The position offset of the beams is found to greatly affect the linearity range. A numerical method is used to simulate the linearity range of the DWS signal under various operating conditions. The linearity range decrease with the increase of the offset angle of the Gaussian beam and the offset length of the flat top beam. The offset range of the beams based on the requirement of the Taiji is given at last. [ABSTRACT FROM AUTHOR]

For a long time, it was believed there was no reason to include the geometrical phase in studying the propagation of gaussian optical beams through dielectric blocks. This can be justified by the fact that the first-order term in the Taylor expansion of this phase is responsible for the lateral shift of the optical beam which is also predicted by ray optics. From this point of view, the geometrical phase can be seen as a purely auxiliary concept. In this paper, we show how the second-order term in the Taylor expansion accounts for the symmetry breaking of the transversal spatial distribution and acts as an axial spreading modifier. These new effects clearly show the importance of the geometrical phase in describing the correct behavior of light. To test our theoretical predictions, we briefly discuss a possible experimental implementation. [ABSTRACT FROM AUTHOR]

A micro-channel plate detector with wedge and strip anode can be used for visible and ultraviolet light imaging. In this paper, the imager electronics are designed in order to process specific output charge characteristics. The original signal output from the detector is shaped into a Gaussian pulse signal, and a digital Constant Fraction Discriminator is used to judge the arrival time of the pulse. The resolution of the electronic output image is 1024 × 1024, and the position decoding accuracy is 1 pixel. The experimental imaging resolving power of the detector is as high as 70 µm. [ABSTRACT FROM AUTHOR]

When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Hänchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay. [ABSTRACT FROM AUTHOR]

A new kind of light beam named the elliptical Hermite-cosine-Gaussian beam (EHCosGB) is introduced in this paper by using a tensor method. An analytical propagation expression for an EHCosGB passing through an axially nonsymmetrical optical system is derived by using vector integration. By virtue of numerical simulations, the propagation properties of EHCosGBs through a free space and a focusing system are illustrated, respectively. The results indicate that an EHCosGB on the input plane can be regarded as the elliptical Hermite-Gaussian beam (EHGB) modulated by the cosine curves with certain oscillating frequency. Some of the neighboring lobes are combined and TEM-type Hermite-cosh-Gaussian beams are formed during the propagation. [ABSTRACT FROM AUTHOR]

Reshaping of a Gaussian laser beam into a uniform or other intensity distribution is required for various applications. The laser beam shaping system with a radial birefringent filter is presented in this paper. With such a system the Gaussian beams can be transformed into uniform or annular beams. The theory and simulation of the proposed systems are described in detail. The primary advantage of such a system is that the out beam profile can be tunable with the rotation of the radial birefringent element. [ABSTRACT FROM AUTHOR]

Non-diffracting vortex beams are perspective information carriers for free space communications enabling an effective encoding, transfer and decoding of information. Adopting coaxial vortex superpositions, additional degrees of freedom of light are available to increase the density of the carried information. In this paper we present a novel decoding scheme motivated by a quantum state estimation technique capable of extracting full information encoded into an array of Bessel–Gauss beams. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for calculating the scattered field when a vertically polarized Gaussian beam is incident on a flat or slightly rough conducting surface at a grazing angle and the refractive index of the propagation medium has a profile which is not constant. The method is a solution to the parabolic approximation of the full wave equation. The results presented are taken for a linear and log-linear refractive index profile. [ABSTRACT FROM AUTHOR]

In this paper, the effects of nonzero inner scales and finite outer scales are investigated, in the context of Gaussian beam propagation along a slant path under general turbulence conditions. Theoretical expressions for the cut-off spatial frequencies are derived with an approach method, and thereby a modified scintillation model is developed to incorporate inner scale and outer scale parameters in the analysis. Then, inner and outer scale effects on the downlink are analysed with respect to the zenith angle, the altitude of the transmitter, the initial beam radius, as well as the turbulence strength. Numerical results indicate that the effects of a finite outer scale mainly influence transmission that occurs at large zenith angles or high altitudes, while the inner scale effects are more prevalent. This study may be helpful to improve the accuracy of calculation of slant-path scintillation index, and thus benefit the characterization and optimization of space/air-ground laser communication systems. [ABSTRACT FROM PUBLISHER]

In this paper a semi-classical model of the nonlinear operation of a laser is extended to describe a laser with a Gaussian mirror. Modified nonlinear self-consistent equations including transverse and longitudinal field dependence, gain saturation, spatial hole burning and nonlinear dispersion effects are derived. With the help of an energy theorem an approximate solution for steady-state single mode operation is presented, which relates the small signal gain to the output power and the laser system characteristic parameters. The laser output power characteristics are presented for various cavity configurations, especially, revealing an influence of the Gaussian mirror parameter on the power efficiency of the laser. [ABSTRACT FROM AUTHOR]

A novel optical-trap method for improving the trapping capability using a radially polarized narrow-width annular beam (NWAB) has been proposed. In this paper, we theoretically study the tight focusing properties of a radially polarized NWAB, formed by subtly blocking the central portion of a radially polarized Bessel–Gaussian beam (the original doughnut beam), through a high-numerical aperture objective. It is shown that a sub-wavelength focal spot () with a quite long depth of focus (about) can be formed in the vicinity of the focus. Furthermore, the optical trapping forces acting on a metallic Rayleigh particle are calculated for the case where a radially polarized annular beam is applied. Numerical results show that the radially polarized NWAB can largely enhance the transverse trap stiffness and broaden the longitudinal trap range compared with the usage of the original doughnut beam. The influence of the annular factorδon the focusing properties and the trap stiffness is investigated in detail. [ABSTRACT FROM AUTHOR]

Theoretical study of propagation behaviour of partially coherent divergent Gaussian beams through oceanic turbulence has been performed. Based on the previously developed knowledge of propagation of a partially coherent beam in atmosphere, the spatial power spectrum of the refractive index of ocean water, extended Huygens–Fresnel principle and the unified theory of coherence and polarization, analytical formulas for cross-spectral density matrix elements are derived. The analytical formulas for intensity distribution, beam width and spectral degree of coherence are determined by using cross-spectral density matrix elements. Then, the effects of some source factors and turbulent ocean parameters on statistical properties of divergent Gaussian beam propagating through turbulent water are analysed. It is found that beam’s statistical propagation behaviour is affected by both environmental and source parameters variations. [ABSTRACT FROM AUTHOR]

The multidomain integral equation method is used to calculate fluxes of radiation from various on- and off-axis point sources passing through two different homogeneous isotropic media and striking a surface of a circular disc perpendicular to the optical axes of these sources. This method is dedicated to radiation passing through attenuating or nonattenuating media with a Fresnel interface and is applicable for arbitrary radiation patterns of point sources. The paper presents, firstly, the generalized multidomain integral equation method, expressed by double iterated integrals, for calculating radiant fluxes from arbitrary emitting point sources. This generalized method is simplified then to the form of multidomain single integral equation method applicable for rotationally symmetrical radiation patterns with optical axes perpendicular to the disc. Next, the simplified method is used for computer simulation of radiant fluxes incident on the disc from small Lambertian and Gaussian sources represented by point source models. All numerical results obtained from this simulation have shown high accuracy and efficiency of the presented method. Selected results are illustrated graphically and validated by Optical Software for Layout and Optimization (OSLO) from Lambda Research Corporation. Potential applications of the presented method include optical sensing and metrology, optical coupling, immersion microscopes, light-extraction problems and creative lighting design. [ABSTRACT FROM AUTHOR]

In this paper, the response of a fiber ring cavity to chirped Gaussian pulsed laser injection is investigated theoretically, and the expression of the field intensity out of the ring cavity is derived in the time domain. Numerical results demonstrate that different microwave and millimeter signals can be achieved, such as in the case of chirp parameter C = 5 and input pulse width of 80 ps, the frequencies of generated microwave and millimeter-wave signals are ∼16.1 GHz, ∼26.3 GHz, ∼33.3 GHz, and ∼50 GHz. The results have potential application in tunable microwave/millimeter-wave generation. [ABSTRACT FROM PUBLISHER]

A kind of hollow Gaussian beams with the power-exponent-phase vortex is introduced. Based on the Collins integral, an analytical expression of a hollow Gaussian beam with the power-exponent-phase vortex passing through a paraxial optical system described by the ABCD matrix approach is derived. The analytical expressions for the beam propagation factors and the orbital angular momentum density of such hollow vortex Gaussian beam passing through a paraxial optical system described by the ABCD matrix approach are also derived, respectively. As a numerical example, the propagation properties of a hollow Gaussian beam with the power-exponent-phase vortex are demonstrated in free space. The evolutions of the normalized intensity, the phase and the orbital angular momentum density distributions are investigated, respectively. The influences of the power order and the topological charge on the beam propagation factors in the x- and y-directions are analysed. The introduced hollow Gaussian beam has potential applications in the atom manipulation and the optical trapping. [ABSTRACT FROM AUTHOR]

In this paper, we analytically investigate Hermite-cosh-Gaussian (HChG) laser beam propagation in non-degenerate germanium having space charge neutrality for the first three mode indices. The field distribution in the medium is expressed in terms of beam-width parameter f and decentred parameter b. The differential equations for the f parameter are established by a parabolic wave equation approach under paraxial approximation. Analytical solutions are obtained under the condition Rn < Rd, where Rn is the self-focusing length and Rd is the diffraction length. The behaviour of the f parameter with the dimensionless distance of propagation η for various b values is examined by numerical estimates. The results are presented graphically. [ABSTRACT FROM AUTHOR]

Recent developments in laser physics have called renewed attention to Laguerre-Gaussian (LG) beams of paraxial light. In this paper we consider the corresponding LG modes for the two-dimensional harmonic oscillator, which appear in the transversal plane at the laser beam's waist. We see how they arise as Wigner transforms of Hermite-Gaussian modes, and we proceed to find a closed form for their own Wigner transforms, providing an alternative to the methods of Simon and Agarwal. Our main observation is that the Wigner transform intertwines the creation and annihilation operators for the two classes of modes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A novel nonlinear Raman confocal microscopy utilizing Raman induced Kerr effect spectroscopy (RIKES) is presented in this paper. The imaging theory of RIKES confocal microscopy with Gaussian beam is derived. The imaging properties of RIKES confocal microscopy and the impact of different beam waist widths of Gaussian beam on the lateral and axial resolution have been analyzed in detail. It is proved that RIKES confocal microscopy has high sensitivity and high resolution, besides capability to characterize inherent structural features, such as vibration mode, vibration orientation, and optically induced molecular reorientation etc. Therefore, nonlinear Raman confocal microscopy that is based on RIKES has potential to provide a novel characteristic imaging method comparable to the existing imaging techniques based on other nonlinear optical processes, such as two-photon fluorescence, second harmonic generation (SHG) and coherent anti-Stoke Raman scattering (CARS). [ABSTRACT FROM AUTHOR]

In this paper, via the generalized beam formulation, we evaluate the scintillation index for higher-order general beams propagating through the weak atmospheric turbulence. The investigated higher-order beam types are cos-Gaussian, cosh-Gaussian and annular beams. The scintillation indices of these beams are plotted with respect to propagation length, source size and order of the beam. According to our graphical outputs, higher-order beams have less on-axis scintillation index than zero-order beams at longer propagation distances. The on-axis scintillation exhibits a slight increase when the order of even-ordered beams is made higher. Moreover, our study on the source size variation shows that, for most of the source size range, cos-Gaussian beams have a lower scintillation index than the other beams. [ABSTRACT FROM AUTHOR]

A new kind of laser beam called the decentred elliptical flat-topped light beam (DEFTB) is introduced in this paper by using a tensor method. Based on the generalized Collins integral, the propagation formula for a DEFTB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formulae for the generalized decentred elliptical Gaussian beam and elliptical flat-topped light beam under certain conditions. As a typical application example of the derived formula, the propagation characteristics of a DEFTB in a thin lens system are calculated and discussed. Furthermore, the generalized laser beam arrays with rectangular symmetry and radial symmetry by using DEFTBs as fundamental modes are constructed and the propagation properties of both a coherent and an incoherent combination of DEFTBs in the thin lens system with numerical examples are investigated. [ABSTRACT FROM AUTHOR]

The most direct and simple method to calculate analytically the propagation in the far field of a coherent beam with a rectangular symmetry and a super-Gaussian-like irradiance profile involves the use of the convolution theorem. In this paper we extend this method to a circularly symmetric beam, and hence from the Fourier transform to the zero-order Hankel transform. Then, we examine the more complex case of super-Gaussian-like beam irradiance shapes with an axial shadow, as those emitted by unstable resonators with diffraction output coupling or with a variable-reflectivity mirror. The analytical results obtained by approximating the super-Gaussian-like beam with a convolution function and applying the Hankel transform are in excellent agreement with those obtained by numerical simulations. [ABSTRACT FROM AUTHOR]

The closed-form propagation expression for the kurtosis parameter of flattened Gaussian beams (FGBs) in passage through paraxial ABCD optical systems is derived on the basis of the propagation equation of FGBs and analysed with numerical examples. A comparison of our results with those obtained by using the propagation law of irradiance moments is made, showing the advantage of the method used in this paper. [ABSTRACT FROM AUTHOR]

This paper presents an implementation of a genetic algorithm in the structural design of broken contact doublets according to a prespecified set of Gaussian characteristics and primary aberration targets. The objective of this study is to investigate the effectiveness of the algorithm in finding out global as well as useful local optima and its dependence on some parameters characterizing the genetic operators. Actual glasses are taken as variables. Some illustrative examples are given. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically demonstrate that lenses with negative spherical aberration can be used to reshape a Gaussian Schell-model (GSM) beam to uniform profiles. The numerical calculation results show that, when the coherence of the GSM beam is low, we can achieve uniform GSM beams with smooth top. As the coherence increases, some intensity modulation occurs at the top of the uniform GSM beam. This intensity modulation is caused by the interference of highly coherent light. [ABSTRACT FROM AUTHOR]

The paper presents a theoretical investigation of laser beam tailoring using a transparent diffracting phase plate. It is shown that a linear axicon is able to transform a Gaussian beam either into a super-Gaussian profile, a ring-shaped profile or a doughnut profile. All these different intensity distributions are easily obtained by only changing the width of the incident Gaussian beam. [ABSTRACT FROM AUTHOR]

Average Bit Error Rate (BER), outage probability and average channel capacity expressions of a Modulating Retro-Reflector (MRR) optical communication system based on an Airy beam under weak turbulence are derived. The effects of propagation distance, width parameter and exponential truncation factor of the Airy beam itself on the communication performance of the system are discussed. Meanwhile, the performance of the system based on the Gaussian beam is compared with the same turbulence condition and propagation distance. The simulation results show that under the same conditions, the system based on the Airy beam shows a lower outage probability, average BER and larger average channel capacity compared to the system based on the Gaussian beam. Moreover, the advantages of the Airy beam are more significant as the average signal-to-noise ratio (SNR) increases. [ABSTRACT FROM AUTHOR]

The properties of a linearly polarized cosine-hyperbolic-Gaussian beam (ChGB) propagating in a chiral medium are investigated theoretically by using the Huygens-Fresnel diffraction integral. Beam intensity distribution characteristics in the chiral medium are discussed with numerical examples. The linearly polarized ChGB is found to split into a superposition of left and right circularly polarized Gaussian components, and its intensity pattern exhibits a variable shape depending on the chirality factor and decentered parameter b. The output beam can exhibit a richer intensity pattern compared to the Gaussian beam. The results could be beneficial for the application of ChGB in beam shaping and optical micromanipulation. [ABSTRACT FROM AUTHOR]

The effects of transverse displacement parameter d and topological charge (TC) m on the beam spreading (BS) of Airy vortex beam array (AVBA) and Airy Gaussian vortex beam array (AGVBA) propagating in a moderate turbulent atmosphere are analysed and studied numerically. Due to the Gaussian function truncation and optical vortex modulation, the behaviours of the BSs of AVBA and AGVBA in turbulent atmosphere are anomalous. Compared with the AVBA, the BS of lower order AGVBA is less affected by atmospheric turbulence when d is small but more affected when d is large. With the increase of m, the BSs of two vortex beam arrays decrease nonlinearly and AVBA is broadened more seriously by atmospheric turbulence than that of AGVBA as d is set to be zero. Compared with AGVBA, the BS of AVBA with lower TC is less affected by atmospheric turbulence but more seriously affected with higher TC. [ABSTRACT FROM AUTHOR]

Based on the extended Huygens–Fresnel principle and non-Kolmogorov spectrum, the analytical expression for the effective radius of curvature of partially coherent Hermite–Gaussian (PCHG) beams propagating through non-Kolmogorov turbulence is derived, and the relative effective radius of curvature is used to describe the effect of turbulence on the effective radius of curvature. It is shown that the effective radius of curvature of PCHG beams depends on the beam and non-Kolmogorov turbulence parameters and on the propagation distance. The variation of relative effective radius of curvature with increasing generalized exponent parameter α of non-Kolmogorov turbulence is non-monotonic. The longer the propagation distance is, the larger the effect of turbulence on the effective radius of curvature of PCHG beams is. The effective radius of curvature of PCHG beams with shorter wavelength, smaller beam order, larger beam waist width or better spatial coherence is more affected by the non-Kolmogorov turbulence. The results are interpreted physically. [ABSTRACT FROM AUTHOR]

The interaction between a vortex and an edge dislocation nested in a cos‐Gaussian beam passing through a tilted lens was studied analytically and numerically. It is shown that in the presence of the tilted lens, by varying the cos‐part parameter of the beam, the slope of the edge dislocation, or the tilt coefficient of the lens, the topological charge is conserved for the case of the off‐axis edge dislocation, while charge conservation does not hold true for the case of an on‐axis edge dislocation, irrespective of the on‐axis or off‐axis vortex. The relation between the transverse positions (x, y) of vortices and the tilt coefficient is linear, and is interpreted. [ABSTRACT FROM PUBLISHER]

With the help of the extended Huygens-Fresnel principle and the spherical-wave short-term mutual coherence function, an analytical expression was derived for the short-term average intensity of a cosh-Gaussian beam through Kolmogorov turbulence. As special cases, the properties of the short-term average intensity with different propagation distances and parameters are studied. In addition, a comparison is presented of average intensity between short exposure and long exposure. The results show that the effect of turbulence on long- and short-term average intensity is different for different factors of the cosh part. [ABSTRACT FROM AUTHOR]

The functions of phase wedge and symmetric phase mask for optical vortex synthesised from a Gaussian beam are carefully analysed. The optimal linear phase dependence in the cross-section of a Gaussian beam for the singular beam with a single charge synthesis is found. The similarity of the obtained beam phase and intensity distributions in the singular beam depending on the distance of the resulting field observation is investigated. The simple original technique of the experimental realisation of the necessary phase mask for the singular beam synthesis with the help of two inclined mirrors is offered. [ABSTRACT FROM AUTHOR]

The closed-form expressions for the spectral degree of coherence and the width of the spectral degree of coherence of Gaussian-Schell model (GSM) beams propagating through atmospheric turbulence are derived. The influence of atmospheric turbulence on the spectral correlation properties of GSM beams is studied both analytically and numerically. A comparison between the width of the spectral degree of coherence and that of the spectral intensity of GSM beams propagating through atmospheric turbulence is also given. Some interesting results are obtained, which are different from those obtained previously, and are explained physically. [ABSTRACT FROM AUTHOR]

The far-field anomalous spectral behaviours of a space-time-dependent Gaussian pulsed beam passing through a rectangular aperture are studied. By expanding a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, the approximate analytical expression for the spectral intensity of a space-time-dependent Gaussian pulsed beam passing through a rectangular aperture is derived. Meanwhile, the corresponding closed-forms for the slit and the unapertured cases are also given as special cases of the general results. The red and blue shifts and the spectral intensity distribution are studied and illustrated with numerical calculations. Specifically, it is shown that the spectral switch takes place when the truncation parameter is equal to particular values or the observation position is at the critical diffraction angle. The possibility of tunable spectral switching in the far field with an apertured pulsed beam by varying the size of the rectangular aperture is highlighted. [ABSTRACT FROM AUTHOR]

We report adiabatic passage experiments with a single trapped [image omitted] ion. By applying a frequency-chirped laser pulse with a Gaussian amplitude envelope, we reach a transfer efficiency of 0.99(1) on an optical transition from the electronic ground state S1/2 to the metastable state D5/2. This transfer method is shown to be insensitive to the accurate setting of laser parameters, and therefore is suitable as a robust tool for ion-based quantum computing. [ABSTRACT FROM AUTHOR]

Based on the extended Huygens–Fresnel principle, the spreading of partially coherent flattened Gaussian beams propagating through turbulent media is studied by using the incoherent superposition of higher-order Hermite–Gaussian beams. The mean-squared width of partially coherent flattened Gaussian beams in turbulence is derived. It is shown that the spreading of partially coherent flattened Gaussian beams increases with increasing turbulent parameter and beam order N . However, the difference between the relative spreading of partially coherent flattened Gaussian beams in turbulent media and in free space reduces as N increases. Therefore, partially coherent flattened Gaussian beams with high N are less sensitive to the effects of turbulence than those with lower N . [ABSTRACT FROM AUTHOR]

A symmetrical iterative Fourier-transform algorithm (IFTA) using a combination of phase and amplitude freedom for the design of diffractive optical elements for highly precise laser beam shaping is presented. We compare this method with the basic IFTA and the symmetrical IFTA exclusively using phase freedom, and the basic IFTA using both phase and amplitude freedom, by employing these methods for super-Gaussian beam shaping. While the latter three methods fail to produce satisfactory solutions, the first method results in a beam non-uniformity error of 0.44% and a theoretical efficiency of 97.2%. Moreover, the new approach avoids the use of the trial-and-error method for finding the appropriate modified Fourier-domain constraints during the iteration, which can be difficult for some beam-shaping problems. [ABSTRACT FROM AUTHOR]

The concept of partially coherent J 0 -correlated Schell-Model (JSM) beams is extended to the nonparaxial regime. By using the generalized Rayleigh-Sommerfeld diffraction integral, analytical propagation equations of nonparaxial JSM beams in free space are derived. Under the paraxial approximation our results reduce to the corresponding paraxial ones. The free-space propagation properties of nonparaxial JSM beams are illustrated with numerical examples. A comparison with paraxial JSM beams shows that the nonparaxial approach should be used if the parameters f and s are not small. [ABSTRACT FROM AUTHOR]

By introducing a hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression for a Gaussian beam passing through a paraxial ABCD optical system with an annular aperture has been derived. The results could be reduced to the case of circular black screen or circular aperture. Some numerical simulations are also performed and illustrated for the propagation characteristics of a Gaussian beam through a paraxial ABCD optical system with an annular aperture, a circular black screen or a circular aperture. [ABSTRACT FROM AUTHOR]

The propagation characteristics of the kurtosis parameters of a standard Hermite—Gaussian (SHG) beam and of an elegant Hermite—Gaussian (EHG) beam, each passing through a fractional Fourier transformation (FRFT) system with a spherically aberrated lens, are studied in detail. Some numerical calculations are made by introducing an efficient algorithm, based on the Collins diffraction integral formula. The resulting graphs illustrate the striking difference between ideal FRFT systems and those with a spherically aberrated lens. The kurtosis parameters of both SHG and EHG beams passing through a type I Lohmann system with a spherically aberrated lens are seen to change with the fractional order periodically and the fundamental period is 4, but for type II the fundamental period is 2. Different values of spherical aberration coefficients affect the kurtosis parameters in greatly different ways. The values of the kurtosis parameters of a SHG beam passing through either type of Lohmann system with a spherically aberrated lens are no longer equal to those of an EHG beam, even when they have the same fractional orders and the same spherical aberration coefficients. [ABSTRACT FROM AUTHOR]

In the present paper bidimensional Gaussian linearly polarized beams, which are incident on an interface between an isotropic medium and a non-absorbing non-magnetic uniaxial crystal are considered. The relation between the reflection coefficients and the non-specular effects are studied. The expressions for the first order effects in the case of a beam linearly polarized in a plane perpendicular to the one containing the crystal optical axis and the normal to the interface are analytically determined. Two highly symmetric geometries are analysed and the results are compared to those obtained with isotropic interfaces. [ABSTRACT FROM AUTHOR]

For focusing the elliptical Gaussian beam directly, the effects of a non-circular aperture on the focusing properties are studied. The focusing properties for different shapes of apertures, which include a circle, an ellipse and a rectangle, are calculated and compared. Moreover, for different elliptical Gaussian beams, an empirical aperture selection rule that can be used to circularize the focusing spot is proposed. The energy transmission ratios are also considered in this paper. [ABSTRACT FROM AUTHOR]

The inverse problem of amplitude reconstruction on an inclined plane based on the values of amplitude or its module as recorded on semi-infinite plane orthogonal to the beam propagation direction is considered within the framework of 2D parabolic equation. It is demonstrated that this inverse problem, in case when the complex image plane amplitude is known, can be reduced to a singular Cauchy-type integral equation. The existence of its solutions requires that certain conditions be met but if a solution exists it is necessary unique. The obtained integral equation is then approximated piece-wisely and the resulting linear algebraic system is solved numerically while applying necessary regularization procedures to enhance the stability of its solutions. Finally, an iterative method of phase retrieval is developed and a set of numerical experiments is performed. [ABSTRACT FROM AUTHOR]

Intensity correlations in turbulent biological tissues are evaluated when collimated Gaussian laser beam is used. Variations of the intensity correlations in biological tissues are investigated versus the diagonal distance from the origin of the observation plane for various tissue distances, biological tissue types, strength coefficients of the refractive-index fluctuations, starting points at the observation plane. Also, intensity correlations in biological tissues for various biological tissue types versus the strength coefficient of the refractive-index fluctuations, small length-scale factor, fractal dimension. It is found that intensity correlations become smaller at larger diagonal distance, tissue distance, strength coefficients of the refractive-index fluctuations, and at smaller source size, small length-scale factor and fractal dimensions. Behaviour of the intensity correlations is found to depend on the type of the biological tissue. Our results can be used in tissue identification and to find the disorders in biological tissues. [ABSTRACT FROM AUTHOR]

We analyze the two-dimensional spatial intensity distribution of a CW laser light with Gaussian profile through tissue-like turbid media via calculation and experiment. The results show that the spatial intensity distribution of laser depends on the scattering coefficient, absorption coefficient, and the anisotropy factor of the turbid media. The full width at half maximum (FWHM) of the normalized intensity of the light spatial intensity distribution increases with an increase of the scattering coefficient. But the FWHM of the spatial intensities' distribution of the CW laser light through turbid media does not increase monotonously with an increase of the anisotropy factor. Besides, the spatial intensity distribution is dependent on the absorption coefficient when considering a given scattering coefficient. The two-dimensional spatial intensity distribution narrows with an increase of absorption coefficient. As one of the potential applications, we finally perform an experiment to image an object hidden behind a turbid medium. [ABSTRACT FROM AUTHOR]