Elliptical Gaussian Beam Research Articles

椭圆高斯光束的二维轴对称分数傅里叶变换特性

椭圆高斯光束的二维轴对称分数傅里叶变换特性

Optical implement of Hartley transform on elliptical Gaussian beams

The optical Hartley transform (HT) is expressed in matrix form. The analytical formula of an off-axial elliptical Gaussian beam passing through the HT system is obtained. Numerical examples show that the information about the displacement magnitude and direction of the source can be represented in the form of fringes at the output plane of the HT system.

Effects of nonlinear absorption on the Z-scan technique through beam dimension measurements

Recently we have proposed a novel Z-scan technique for measuring refractive nonlinearities, based on the direct measurement of the variations of the beam dimensions in the far field. In the present work this approach is extended to the case of simultaneous presence of nonlinear refraction and absorption, enabling the complete characterization of the materials regarding their nonlinear optical properties. In more detail we have found that nonlinear absorption induces asymmetry on the peak-valley configuration of the Z-scan curves, both in the cases of circular and elliptic Gaussian beams. We have also shown that this asymmetry grows exponentially with the values of the nonlinear phase shift and the nonlinear absorption coefficient. Further, we have found that the effects of nonlinear absorption on the Z-scan curves can be suppressed by multiplying the radius Z-scan plot with an open Z-scan curve. This result can be used for determining the nonlinear refractive index of the material through a simplified relation.

Three-dimensional simulation of a nanophotonics device with use of fullwave software

Using the FullWAVE software (www.rsoftdesign.com) that implements the finite-difference FDTD-method of solving Maxwell’s equations, we simulate the performance of a three-dimensional nanophotonics device comprising a sub-wavelength diffraction grating, a wide and a narrow planar waveguide, and a photonic crystal (PhC) Mikaelian lens located in a thin silicon film coated on a substrate containing a three-period Bragg mirror, with each period made up of silicon + silica layer. The device is intended to couple a focused laser beam with the focal spot of 3 × 4.6 μm2 and wavelength 1.55 μm into a planar waveguide of width 500 nm, resulting in a 125-fold “compression” of the input beam cross-section. The modeling has shown that the coupling efficiency amounts to 32% of the energy of the linearly polarized elliptic Gaussian beam focused onto the grating and 52% when a plane wave segment is incident onto the grating. For comparison, the grating-unaided coupling of light into the same device by the butt-coupling of light into the wide waveguide’s silicon film gives the efficiency as low as 8%.

Laser beam patterns of an optical cavity formed by two twisted cylindrical mirrors

Propagation of an elliptical Gaussian beam in a multiple-pass optical cell formed by two twisted cylindrical mirrors has been described by means of complex curvature tensors. Using the ABCD tensor approach various light patterns were computed for the use in tunable laser absorption spectroscopy with a multiple-pass optical cell. Light patterns with high beam-spot density can be also defined for a cavity formed by two twisted cylindrical high-reflectivity mirrors. In order to achieve higher cavity output intensity, a high-reflectivity cylindrical mirror cavity with at least one mirror that has a central transparent spot for laser beam injection has been described for applications in non-resonant cavity enhanced absorption spectroscopy.

Dynamic evolution of an edge dislocation through aligned and misaligned paraxial optical ABCD systems

The closed-form propagation expressions of an edge dislocation nested in a general elliptical Gaussian beam through aligned and misaligned paraxial optical ABCD systems are derived and used to study the dynamic evolution behavior of the edge dislocation propagating in free space and through a misaligned lens. It is shown that the noncanonical vortex and dynamic inversion of the topological charge, as well as a new edge dislocation may appear under certain conditions. The results are illustrated analytically and numerically.

Characteristics of elliptical sources in BEAMnrc Monte Carlo system: Implementation and application

Recently, several papers noticed that the electron focal spot of a linear accelerator (linac) could be elliptical which would cause dosimetric discrepancies between measurements and Monte Carlo simulations. To resolve the mismatch, two elliptical source models were developed in BEAMnrc code. The first was a parallel beam elliptical source with uniform distribution where the shape of the source was primarily considered. The other was a parallel beam elliptical source with Gaussian distribution whose source distribution follows the normal distribution. To validate the elliptical source models, uniform and Gaussian electron beams were impinged on a thin air target. Both models successfully reproduced the elliptical shapes and source distributions. Then, this study investigated the characteristics of the elliptical Gaussian source for a 6 MV photon beam in a Varian 21EX linac. The linac head model was implemented in the BEAMnrc/EGSnrc system and commissioned by comparing the lateral and depth dose profiles to the ion chamber measurements acquired from the annual quality assurance (QA). It was found that the circular Gaussian beam with 6 MeV/0.2 cm full width half maximum (FWHM) produces the best matches to the QA data. To explore the characteristics of the elliptical Gaussian source, this study employed an elliptical Gaussian electron source with 0.1 cm FWHM in the x axis and 0.2 cm FWHM in the y axis which was incident on the target of the linac head. Two circular Gaussian beams with 0.1 and 0.2 cm FWHM were employed to compare the differences between circular and elliptical sources. For all the sources, planar and energy fluences were acquired and analyzed. This study also compared the lateral and depth dose profiles in a water phantom by using a DOSXYZnrc user code. In results, a constricted shoulder effect was observed in both planar and energy fluence plots when the FWHM value was increased and the field size is larger than 30 x 30 cm2. The same effect was also noticed in the lateral dose profiles, while the depth dose profile did not vary much.

Scintillation properties of a rectangular dark hollow beam

The scintillation properties of a rectangular dark hollow beam (DHB) in a weak turbulent atmosphere are investigated. Explicit expression for the on-axis scintillation index of a rectangular DHB is derived. It is found that the scintillation index value of a rectangular DHB can be smaller than that of Gaussian, elliptical Gaussian and rectangular flat-topped beams in a weak turbulent atmosphere under certain conditions. Our results will be useful in long-distance free-space optical communications. The scintillation properties of a rectangular DHB are closely controlled by its initial beam parameters.

Rigorous description of holograms of particles illuminated by an astigmatic elliptical Gaussian beam

The digital holography is a non-intrusive optical metrology and well adapted for the measurement of the size and velocity field of particles in the spray of a fluid. The simplified model of an opaque disk is often used in the treatment of the diagrams and therefore the refraction and the third dimension diffraction of the particle are not taken into account. We present in this paper a rigorous description of the holographic diagrams and evaluate the effects of the refraction and the third dimension diffraction by comparison to the opaque disk model. It is found that the effects are important when the real part of the refractive index is near unity or the imaginary part is non zero but small.

Rigorous vectorial Gaussian beam modeling of spectral dispersing performance of virtually imaged phased arrays

We have developed a generalized closed-form representation of the virtually imaged phased array (VIPA) output profile based on a 3D vectorial Gaussian beam formulation. Tracing the input vectorial elliptic Gaussian beam (GB), the output profile of the VIPA is represented as an array of virtual images. Furthermore, employing GB propagation and summing up all the virtual image profiles, the VIPA output profile has been calculated on a vertical plane at an arbitrary distance from the device. Finally, the derived closed-form representation is applied to the different sources (i.e., circular and elliptic GBs) and the results are compared with previous work.

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).

The transformation of canonical vortices embedded in a general elliptical Gaussian beam to noncanonical vortices

Based on the generalized Collins integral, the transformation of canonical vortices embedded in a general elliptical Gaussian beam to noncanonical ones in free space and through a misaligned optical system is studied, and the effect of the beam parameters on the evolution behavior of noncanonical vortices is addressed. It is shown that in comparison with Gaussian background vortex beams there are richer dynamic features in the evolution of elliptical Gaussian background vortex beams, and for the latter case the noncanonical vortex transformation takes place both in free space and through a misaligned lens. In the evolution process the topological charge is not always conserved. The results are illustrated by numerical examples.

Scintillation index of astigmatic annular beams in a turbulent atmosphere

The scintillation properties of astigmatic annular beams in a weak turbulent atmosphere are investigated. Expression for the on-axis scintillation index of an astigmatic annular beam is derived. It is found that the scintillation index of an astigmatic annular beam can be smaller than that of a Gaussian beam, an elliptical Gaussian beam and a stigmatic annular beam in a weak turbulent atmosphere under certain conditions. The scintillation properties of astigmatic annular beams are closely controlled by its beam parameters.

DEASTIGMATISM AND CIRCULARIZATION OF AN ELLIPTICAL GAUSSIAN BEAM BY OFF-AXIS ELLIPSOID REFLECTOR BASED OFF-FOCUS CONFIGURATION

Abstract—Off-axis ellipsoid reflector based off-focus configuration for deastigmatism and circularization of an elliptical Gaussian beam is proposed. Mostly used off-axis ellipsoid reflector based conventional configuration is constructed by aligning the incident direction directed to one focus of the ellipsoid, which reflect the output beam to the another focus of the ellipsoid. However, such configuration is unavailable to deastigmatize and circularize an elliptical Gaussian beam. Therefore, the coupling efficiency between the reflected beam and an essentially circular beam is not well satisfied. In this case, an off-axis ellipsoid reflector based off-focus configuration is proposed to obtain better coupling efficiency. Different from the conventional configuration, in the proposed off-focus configuration, the incident beam direction is diverged from one focus of the ellipsoid. As a result, the coupling efficiency of no less than 99.9% (as compared with coupling efficiency of about 94.2% based on conventional configuration) can be obtained, which is verified with numerical calculations.

THREE-DIMENSIONAL GAUSSIAN BEAM SCATTERING FROM A PERIODIC SEQUENCE OF BI-ISOTROPIC AND MATERIAL LAYERS

The three-dimensional Gaussian beam scattering from the bounded periodic sequence of one-to-one composed isotropic magnetodielectric and bi-isotropic layers are investigated. The beam field is represented by an angular continuous spectrum of plane wave. The problem of the partial plane wave diffraction on the structure is solved using the circuit theory and the transfer matrix methods. It is found that after reflection from the structure,the circular Gaussian beam becomes,in general,an elliptical Gaussian beam,in addition to a displacement of the beam axis from the position predicted by ray optics.

Effect of Elliptical Gaussian Beam in Solid-Immersion-Lens-Based Near-Field Recording Optics

In this study, we summarized the characteristics of beam spot profiles, exit pupil images, the gap error signal and the push–pull signal obtained when using a Gaussian beam in solid immersion lens (SIL) based near-field recording (NFR) optics. As the rim intensity of the Gaussian beam decreases and the tracking direction shift of the SIL assembly increases, the intensity of the beam spot is decreases. The exit pupil image is distorted asymmetrically by the tracking direction shift of the SIL assembly. We confirmed that the tracking direction shift of the SIL assembly affects the gap error signal and push–pull signal. When using linearly polarized incident light, it is observed that a tracking direction shift of 500 µm induces a gap error signal reduction of 3.2%. The push–pull signal is offset by 18.7% in the case of a tracking direction shift of when the tracking direction is shifted by 20 µm.

Effect of beam size parameters on internal fields in an infinite cylinder irradiated by an elliptical Gaussian beam

The scattered and internal fields of an infinite, homogeneous cylinder illuminated by a linearly polarized beam depend on the following parameters: the object size parameter of the cylinder (ka, where k=2pi/lambda, lambda is the wavelength of the incident beam in the surrounding medium, and a is the radius of cylinder), the complex relative refractive index of the object, the beam size parameters (komega(1) and komega(2), where omega(1), omega(2) are the representative beam dimensions), the angle between the cylinder axis and the Poynting vector of the incident wave, and the angle between the plane of polarization and the plane of incidence. Only when the dimensions of the beam are much greater than the cylinder diameter, and hence the portion of the beam interacting with the cylinder is essentially uniform, can the plane-wave solution be used in computing the scattered and internal fields. Hence a rigorous electromagnetic approach like the generalized Lorenz-Mie theory for spheres is used to study the effect of beam size parameters on the internal fields in an infinite cylinder irradiated by elliptical Gaussian beams. The significant effects of beam size parameters on the internal fields in an infinite cylinder are presented using specific cases of (1) resonance effects in a glass cylinder (ka=45.726, transverse-electric mode 53,3) and (2) a cylindrical microchannel (ka approximately 760) irradiated by a 632.8 nm laser beam.

Hollow elliptical Gaussian beams generated by a triangular prism

Based on the tensor method, an analytical formula for hollow Gaussian beams (HGBs) generated by a triangular prism has been derived, and the propagation properties have been studied. It is shown that hollow elliptical Gaussian beams (HEGBs) can be obtained in the near field after the prism, and that the eccentricity of the output beam is affected by parameters such as the incidence angle, refractive index of the prism and the order of the HGB. It shows that by using a triangular prism one can conveniently obtain HEGBs.

Scintillation index of elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.

Decentred elliptical flat-topped light beams and their coherent and incoherent combinations

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.