super-Gaussian Beam Research Articles

Investigation into the optimum beam shape and fluence for selective ablation of dental calculus at λ = 400 nm

A frequency-doubled Ti:sapphire laser is shown to selectively ablate dental calculus. The optimal transverse shape of the laser beam, including its variability under water-cooling, is determined for selective ablation of dental calculus. Intensity profiles under various water-cooling conditions were optically observed. The 400-nm laser was coupled into a multimode optical fiber using an f = 2.5-cm lens and light-shaping diffuser. Water-cooling was supplied coaxially around the fiber. Five human tooth samples (four with calculus and one pristine) were irradiated perpendicular to the tooth surface while the tooth was moved back and forth at 0.3 mm/second, varying between 20 and 180 iterations. The teeth were imaged before and after irradiation using light microscopy with a flashing blue light-emitting diode (LED). An environmental scanning electron microscope imaged each tooth after irradiation. High-order super-Gaussian intensity profiles are observed at the output of a fiber coiled around a 4-in. diameter drum. Super-Gaussian beams have a more-homogenous fluence distribution than Gaussian beams and have a higher energy efficiency for selective ablation. Coaxial water-cooling does not noticeably distort the intensity distribution within 1 mm from the optical fiber. In contrast, lasers focused to a Gaussian cross section (< or =50-microm diameter) without fiber propagation and cooled by a water spray are heavily distorted and may lead to variable ablation. Calculus is preferentially ablated at high fluences (> or =2 J/cm(2)); below this fluence, stalling occurs because of photo-bleaching of the calculus. Healthy dental hard tissue is not removed at fluences < or =3 J/cm(2). Supplying laser light to a tooth using an optical fiber with coaxial water-cooling is determined to be the most appropriate method when selectively removing calculus with a frequency-doubled Ti:sapphire laser. Fluences over 2 J/cm(2) are required to remove calculus efficiently since photo-bleaching stalls calculus removal below that value.

Effects of the deformation of reflection volume Bragg gratings on the M2-factor of super-Gaussian laser beams

When high-power laser beams pass through a volume Bragg grating (VBG), the surface of VBG occurs distortion because of thermal effects, and it results in the decline of the grating’s performance. Considering distortion of the surface induces differences of the index and period, the scalar wave equations for super-Gaussian (SG) laser beams propagating in the reflection VBG have been solved by using finite-different and sparse matrix methods. The changes of the total power reflection coefficient, the beam width, the far-field beam angle and the M 2-factor for the laser beams through the reflection VBG with deformation have been analyzed quantitatively. It can be shown that the deformation of the VBG affects evidently on the intensity and phase distributions, the total power reflection coefficient, the beam width, the far-field divergence angle and the M 2-factor. The beam width, the far-field divergence angle, and the M 2-factor of the output beams increase significantly with the distortions of the grating. The influence of the distortions of the VBG on the power reflection coefficient, the far-field divergence angle and the M 2-factor of the output beams are smaller for higher beam orders.

Subdiffraction propagation of images using saturated absorption of optical transition

We show how well-developed saturated absorption spectroscopy could be adopted for subdiffraction propagation of optical images. We employ pump beams with appropriate spatial profiles that produce controllable inhomogeneous absorption and dispersion of the medium. We discuss advantages of using super-Gaussian and Laguerre-Gaussian pump beams.

International Scientific Laboratory for Laser-Optical Diagnostics in Service for Nondestructive Materials Testing

Abstract The latest achievements developed by the ISL-LOD in the area of elaborating and application of novel optical methods for nondestructive testing and material characterization are discussed. A special attention is given to the application of quasi-nondiffracting Bessel light beams for: i) conical beam-based profilometry for characterization of cylindrical machinery parts; ii) Stokes polarimetry based on super-Gaussian and Bessel beams; iii) Bessel beam-based interferom-etry; iv); quasi-nondiffracting speckle-photometry for remote sensing. Also the description is given of a new thermo-optical method for measurement of thermal diffusion coefficient and hardness of metal and alloys. Finally, a novel method for surface state evaluation based on three dimensional scatterometry technique is described.

Influences of pump beam distribution on thermal lensing spherical aberration in an LD end-pumped Nd:YAG laser

A numerical investigation is made on the thermal lensing and spherical aberration effect in an LD end-pumped Nd:YAG laser. Based on the finite element method (FEM), the laser rod temperature distribution is calculated and the focal length of the thermal lens is deduced, the influences of pump beam on the thermal lensing spherical aberration are mainly studied. The results show the thermal lens which focal length varied with the radial coordinate r is not an ideal lens. Given the heat dissipation boundary conditions, the radial dependent focal length will be shortened when the pump power raised or the waist radius of the pump beam reduced, meanwhile the radial differences of the focal length will decrease when the pump power increased. For a Super-Gaussian profile pump beam, the higher the exponent number, the more similar to flat top the pump beam is, and the less the radial differences of the focal length are.

Propagation of Linearly Polarized Super-Gaussian Beams through a Rectangular Relief Diffraction Grating

By using the rigorous Fourier's modal theory combining the correct Fourier factorization rules, the propagation of super-Gaussian beams through a rectangular relief grating whose characteristic size is comparable to the incideni wavelength, are studied. The influences of the centre incident angle, the incident position and the wide of beam waist on the distribution and symmetry of intensity in the grating layer are analyzed. Finally, with the comparison of the influence on the distribution of intensity according to the parameters above with errors of 1%, it is indicated that the intensity pattern is sensitive to the errors of the z coordinate of the incident spot, and is not sensitive to the errors of the beam width.

Goos-Hänchen-like shifts in atom optics

We consider the propagation of a matter wave packet of two-level atoms through a square potential created by a super-Gaussian laser beam. We explore the matter wave analog of Goos-H\anchen shift within the framework of atom optics where the roles of atom and light are exchanged with respect to conventional optics. Using a vector theory, where atoms are treated as particles possessing two internal spin components, we show that not only large negative but also large positive Goos-H\anchen shifts can occur in the reflected atomic beam.

Flattop Laser Irradiance Profile for Stimulation of Cutaneous Nociceptors

A nerve stimulator based on a CO2 laser has been developed for use in human pain research. A flattened irradiance profile was generated for safer and more uniform pain stimulation. The pain evoked by the flattened profile was compared to a TEM00 profile. The CO2 laser normally operates in TEM00 mode. This is not ideal for thermal stimulation, since the beam will generate a temperature that has a peak in the center of the irradiance profile. This will result in non-uniform activation of nerve fibers. A lens system has been designed to redistribute the energy of the beam to produce a flattened supergaussian irradiance profile for uniform heating of the skin. The lenses work by refracting the more intense central part of the beam towards the periphery. Psychophysical techniques were used to compare the pain evoked with a flattop irradiance profile and a TEM00 profile. It was found that the supergaussian beam evokes pain at a lower energy level than a TEM00 beam. A flattop irradiance profile is a safer source than a gaussian beam for evoking pain in human pain studies.

Pitchfork beam shaping for laser micorvia drilling

Laser beam shaping allows redistribution of laser power and phase across the cross-section of the beam for drilling perfectly cylindrical holes. The main purpose of this paper is to show that pitchfork beams improve the microvia quality significantly. An optical system, which comprises three lenses, is designed using conventional diffraction analysis and ray tracing technique to transform a Gaussian beam into a pitchfork beam. The first two lenses are the phase elements through which a Gaussian laser beam is transformed into a super Gaussian beam. The ray tracing technique of geometrical optics is used to design these phase elements. The third lens is the transform element which produces a pitchfork profile at the focal plane due to the diffraction effect. Another aspect of this paper is to demonstrate a pinhole scanning power meter to measure the laser beam profile at the focal plane where the irradiance is very high. This measurement technique is used to verify the existence of the pitchfork beam at the high irradiance plane.

Generation of bottle beam by focusing a super-Gaussian beam using a lens and an axicon

This study explores the characteristics of the bottle beams that are formed by super-Gaussian beams that impinge through an axicon and a positive lens. Analytical solutions for the on-axial intensity of Gaussian and apertured-plane beams were obtained. The barrier around the dark region has a larger variation of intensity for higher-order super-Gaussian profiles. Flattening the tops of the profiles increases the bottle lengths for a fixed second-order moment width or distance between the axicon and the lens.

Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms

A modified Gerchberg–Saxton algorithm, which we call symmetrical iterative Fourier transform algorithm, is presented and employed to a series of super-Gaussian beam shaping problems and arbitrary beam shaping problems. The main features of this algorithm include (1) using an amplitude-symmetric function of the failed result about the Fourier-domain constraint; (2) using both phase and amplitude freedoms in the iteration process, i.e. the noise produced outside the signal window by each iteration is kept. A formula is given to determine a critical constant in the search for the amplitude-symmetric function. The new method results in highly efficient solutions with highly precise beam profiles in the signal window for all the test problems.

Automatic symmetrical iterative Fourier-transform algorithm for the design of diffractive optical elements for highly precise laser beam shaping

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.

Collapse dynamics of super-Gaussian Beams

We investigate the self-focusing dynamics of super-Gaussian optical beams in a Kerr medium. We find that up to several times the critical power for self-focusing, super-Gaussian beams evolve towards a Townes profile. At higher powers the super-Gaussian beams form rings which break into filaments as a result of noise. Our results are consistent with the observed self-focusing dynamics of femtosecond laser pulses in air [1] in which filaments are formed along a ring about the axis of the initial beam where the initial beam did not form a ring.

Super-Gaussian mirror for high-field-seeking molecules

A matter wave mirror using a single, pulsed, super-Gaussian (SG) optical beam for specular reflection of neutral ground-state molecules is studied. The mirror has a high reflectivity close to 100% and nearly perfect specular reflection over a large incident angle. This mirror avoids the usual problems due to surface roughness and the van der Waals interactions that occur in conventional atomic mirrors. Further, it is capable of reflectance and transmittance with applications to velocity filtering and deceleration of cold molecules.

Folded diffractive laser resonators with user-defined fundamental mode

The adjustment effort required for the alignment of laser resonators with arbitrarily shaped end mirrors can be significantly reduced by folding the resonator path half-way between the two end mirrors and by slightly tilting the resonator axis. Thus the resulting resonator consists only of one diffractive mirror and a plane mirror, and the separate alignment of both diffractive end mirrors with respect to each other can be avoided. This principle is demonstrated by a Nd:YAG laser with super-Gaussian output beam. Furthermore, it is shown theoretically that the influence of phase quantization effects on the beam quality can be strongly reduced as a consequence of the tilted resonator axis.

Beam Shaping by Using the Liquid Crystal Panel of a CommercialDisplay Device

The liquid crystal (LC) panel of a commercially-available LCD projectoris successfully used for beam shaping, and a Gaussian beam is convertedto a square super-Gaussian beam using the configuration of amplitudemodulation. The additional phase modulations imposed by the LCmodulator on the shaped beams are measured precisely using aninterferometric technique. The experimental results have demonstratedthat such a commercially-available programmable spatial light modulatoris applicable to beam shaping with negligible additional phasemodulation.

Matrix formulation of axis-symmetric laser beams through a paraxial ABCD system containing hard-edged apertures: A comparative study

A matrix formulation is presented, which enables us to study the propagation of axis-symmetric beams through a paraxial optical ABCD system containing hard-edged aperture. Numerical calculation results of super-Gaussian beams passing through a multi-aperture-lens system are given to illustrate the advantage of the method. A comparison of the matrix formulation, complex Gaussian expansion and direct numerical integration of the Collins formula is made, where the propagation of apertured Laguerre–Gaussian beams is chosen as an illustrative example. It is shown that the matrix formulation provides satisfactory results in both Fraunhofer and Fresnel regions, and reduces the computational time greatly in comparison with the direct integration. However, this method is suited only to axis-symmetric optical beams and systems. By using the complex Gaussian expansion discrepancies exist in the near zone closer to the aperture, but usually its computational efficiency is higher than the matrix formulation.

Propagation of doughnut-shaped super-Gaussian beams, convolution theorem and Hankel transform

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.

Estimation of thermal lensing effect in the high-power end-pumped direct-cut crystal lasers

At this working, analytical (with Gaussian pump beam profile) and numerical FEM (with super-Gaussian pump beam profile) methods were compared for estimation of thermal lensing effect in the diode-end-pumped solid-state laser rods. These results were applied to the design and realization of a direct-cut (i.e., cut in right-angle ) crystal Nd : YVO 4 laser. The results showed that for such crystal (direct-cut), two methods obtained almost the same results, but slightly different from experimental results. However, estimation of thermal lensing effect led to realization of a diode-end-pumped Nd : YVO 4 cw high-power laser with good optical quality.

Adaptive beam profile control using a simulated annealing algorithm

We present a programmable beam-shaping method based on the combination of a deformable mirror membrane mirror and a simulated annealing algorithm. The algorithm iteratively adjusts the control voltages of 37 independent electrodes to reduce the variance between the chosen shape and the actual beam shape. The experimental results show that the system is capable of adaptively creating, on demand, Gaussian and super-Gaussian beam profiles that closely match the desired target parameters.