Self-focusing and frequency broadening of an intense short-pulse laser in plasmas.

An intense ultrafast laser pulse propagating through a plasma undergoes self-focusing and self-phase-modulation as a result of relativistic mass nonlinearity. The inclusion of a quartic (r4) term in the expansion of the eikonal in the radial coordinate r allows the modification of the shape of the radial intensity profile. The front of the pulse, under the combined effects of time-dependent self-focusing and frequency downshifting, acquires a severely distorted temporal shape. The radial profile for I(lambda)2(mu) < 2.8 x 1018 W/cm2, where I is the axial laser intensity and lambda(mu), is the laser wavelength in micrometers, is transformed from a Gaussian to a super-Gaussian because of the faster convergence of the marginal rays than the paraxial rays. In the opposite case of I(lambda)(2)(mu) > 2.8 x 10(18) W/cm2 when nonlinear plasma permittivity approaches saturation, the radial profile in the axial region becomes broader than the Gaussian.     

Diffractive shaping of excimer laser beams

Abstract

We address the problem of shaping the intensity distribution of a highly directional partially coherent field, such as an excimer laser beam, by means of diffractive optics. Our theoretical analysis is based on modelling the multi-transverse-mode laser beam as a Gaussian Schell-model beam. It is shown numerically that a periodic element, which is unsuitable for the shaping of a coherent laser beam, works well with an excimer laser beam because of its partial spatial coherence. The conversion of an approximately Gaussian excimer laser beam into a flat-top beam in the Fourier plane of a lens is demonstrated with a diffractive beam shaper fabricated as a multilevel profile in SiOl by electron-beam lithography and proportional reactive-ion etching.     

Spatial beam shaping of ultrashort laser pulses: theory and experiment

We studied the spatial intensity profile of an ultrashort laser pulse passing through a laser beam shaping system, which uses diffractive optical elements to reshape a Gaussian beam profile into a flat-topped distribution. Both dispersion and nonlinear self-phase modulation are included in the theoretical model. Our calculation shows that this system works well for ultrashort pulses (approximately 100 fs) when the pulse peak intensity is less than 5 x 10(11) W/cm2. Experimental results are presented for 136 fs pulses at 800 nm wavelength from a Ti:sapphire laser with a 6 nJ pulse energy. We also studied the effects of lateral misalignment, beam-size deviation, and defocusing on the energy fluence profile.     

Generation of sinc wave by a one-dimensional array for applicationsin ultrasonic imaging

A new solution to the 2-D scalar wave equation is presented which describes an ultrasonic beam maintaining the lateral field response expressed by the sinc function over a finite depth of field. This new beam is realizable with a linear array transducer, and less subject to diffraction spreading than conventional focused beams, physically, it is a superposition of plane waves having the same wavelength, but traveling at different angles. It is shown by numerical simulation that the beam can provide more uniform lateral beamwidth and smoother on-axis field magnitude over a greater depth of field than the rectangular transducers and Gaussian apodized transmitters which have been used to increase the limited depth of field of conventional focused beams. Compared with currently developed limited diffraction beams which must be generated by 2-D array transducers, the beam has a wider lateral beamwidth but with lower sidelobe levels. In ultrasonic medical imaging, the beam enables one to obtain a line focus using a 1-D array transducer and to eliminate the diffraction correction required in some applications such as tissue characterization     

Polarization changing and beam profile deformation of light during the isotropic Raman-nath acousto-optic interaction

A spatial Fourier transform approach is used to study the phenomena of polarization changing and beam profile deformation of light during the Raman-Nath, acousto-optic interaction in isotropic media. Starting from the vector version of the well-known Raman-Nath interaction equation and using a spatial Fourier transform allows analytic solutions that encompass the effects of polarization changing and beam-profile deformation for the multiple scattered light to be found in the spatial-frequency domain. Two kinds of sound wave, longitudinal and shear, are assumed to be interacted with the light, whose transverse spatial profile and state of polarization are arbitrary. It is shown that, for light with an arbitrary spatial profile after interaction with the sound wave in the Raman-Nath regime, the spatial profiles of the scattered light are almost the same shape as those of the input light. For the polarization changing part, it is found that the state of polarization and the direction of rotation can alter, depending not only on the sound amplitude but also on the propagation mode of the sound wave. Simulation results are provided to confirm the validity of this approach.     

Acousto-optic interaction of a Gaussian laser beam with an ultrasonic wave of cylindrical symmetry

We present experimental studies of the interaction between a narrow Gaussian laser beam and a standing cylindrical ultrasonic wave. As a theoretical approach, a Fourier-optics-based successive diffraction model is used. Depending on the ratio of the Gaussian laser beam diameter to the first nodal diameter of the cylindrical ultrasound, light refraction or diffraction is observed. We experimentally investigate the time-averaged light intensity as well as the modulation of light in the far field of light refraction-diffraction by a cylindrical ultrasound. It is revealed that significant focusing appears if the phase front of the incident light is curved. The focusing effects of the acousto-optic system depend on the width of the laser beam and curvature of the phase front. Finally, possible applications are discussed.     

Integrated diffractive andrefractive elements for spectrum shaping

Diffractive elements can be designed for spectrum shaping in the Fourier or Fresnel plane by iterative methods. It is necessary to use a Fourier lens and the wavelength for which the diffractive elements were designed to get the required spectrum shaping at the Fourier plane. Using a different wavelength will cause chromatic aberration. We deal with the combination of refractive and diffractive elements and two or more different diffractive elements on the same element to get appropriate beam shaping of light sources with a multiple spectral output. Simulations are preformed that transform the profile of a He-Ne laser with a Nd:YAG laser source, and shape the trapezoidal beam profile of an excimer laser into a Gaussian beam is also considered.     

A Large-Area PVDF Pyroelectric Sensor for CO 2 Laser Beam Alignment

We present the design of a large-area (50 mm times 50 mm) polyvynilidene fluoride (PVDF) pyroelectric sensor array for industrial CO₂ (lambda = 10.6 mum) laser beam positioning. The array dimensions were chosen to match the area typically monitored in the alignment procedure of external optics (beam steering moving arm system, for example) used to redirect the laser beam from the laser output window to a remote working station. The instrument is provided with a tilted, high reflection, ZnSe plate which partially transmits the laser beam onto the sensor array. From positioning simulations with a Gaussian laser intensity profile with a sigma = 3.2 mm standard deviation (equivalent spot size 3sigma cong 20 mm), the positional accuracy along the two orthogonal array dimensions was found to be better than 0.02 mm for an 8 times 8 array and one order of magnitude higher for a 16 times 16 array. The centroid position of a CO₂ industrial laser beam was evaluated by integrating the pyroelectric current for a time comparable to the time duration (100-200 ms) of the laser pulses used in the alignment procedure.     

Acoustooptic interaction in uniaxial gyrotropic paratellurite crystals

An analysis is made of an intermediate mode of light diffraction by ultrasound in a uniaxial gyrotropic paratellurite crystal. A system of coupled wave equations is presented to calculate the polarization and energy characteristics of the diffracted light for the Raman-Nath, intermediate, and Bragg modes of acoustooptic interaction. The diffraction of light propagating at small angles to the crystal optic axis by a slow ultrasonic shear wave propagating along the [110] crystallographic axis is studied. The amplitude-frequency characteristics of a modulator-deflector for optical radiation are investigated. Curves of the diffraction efficiency as a function of the ultrasonic wave intensity are plotted for various acoustooptic interaction lengths. Pis’ma Zh. Tekh. Fiz. 23, 84–89 (January 12, 1997)     

Gaussian beam conversion using an axicon

Abstract

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.     

Cavity with a deformable mirror for tailoring the shape of the eigenmode

We demonstrate an optical cavity that supports an eigenmode with a flattop spatial profile--a profile that has been proposed for the cavities in the Advanced Laser Interferometer Gravitational Wave Observatory, the second-generation laser interferometric gravitational wave observatory--because it provides better averaging of the spatially dependent displacement noise on the surface of the mirror than a Gaussian beam. We describe the deformable mirror that we fabricated to tailor the shape of the eigenmode of the cavity and show that this cavity is a factor of 2 more sensitive to misalignments than a comparable cavity with spherical mirrors supporting an eigenmode with a Gaussian profile.     

Diffraction of combined optical vortices

The diffraction of light on the lens of a Gaussian beam past a uniaxial crystal is equivalent to the beam diffraction on a helicoidal phase grating of two partial beams with different curvatures of the wave front. This diffraction significantly distorts the Gaussian beam profile and an extended region with three beam waists is formed near the focal plane. The beam waist region can be rectified by varying the radii of the primary beam waist and the lens pupil.     

Scattering and thermal lensing of 2.12- mum laser radiation in biological tissue

We studied light propagation of holmium:YAG laser radiation (lambda = 2.12 mum) by measuring the two-dimensional laser beam profile before and after propagation through a tissue sample with a modified fast-temperature-measurement technique. The comparison between water and cartilage tissue allowed us to differentiate between beam broadening caused by formation of a thermal lens and broadening due to light scattering. In water, beam propagation is influenced by formation of thermal lensing, whereas in cartilage the broadening was caused by a combination of light scattering and thermal lensing. Additionally, we discovered that the observed effects are subject to dynamic changes during the laser-tissue interaction.     

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.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.     

Development of a 756 nm, 3 W injection-locked cw Ti:sapphire laser

We have developed a 756 nm, 3 W single-frequency cw Ti:sapphire laser by using the technique of injection locking. A cw Ti:sapphire laser in a ring-type configuration was forced to lase unidirectionally by use of an optical diode to prevent a high-power backward laser from disturbing the injection laser. A master laser was amplified by a broad-area laser diode and coupled into a single-mode fiber to generate a 50 mW injection laser with a Gaussian beam profile, which was enough to lock the Ti:sapphire laser at full power of 3 W. Such a high-power single-frequency Ti:sapphire laser enables a watt-level blue or near-ultraviolet single-frequency laser to be generated by frequency doubling.     

Subwavelength-resolvable focused non-gaussian beam shaped with a binary diffractive optical element.

The diffraction-limited spot size limits the optical disk storage capacity and microscopic resolution. We describe a technique to shape a focused Gaussian beam into a superresolving beam by using a diffractive optical element fabricated by laser-assisted chemical etching. The focused shaped beam has a smaller width and a longer depth of focus than a similarly focused Gaussian beam. Using the diffraction-limited shaped beam along with threshold writing, we achieved a written pit size of less than 0.33 mum at a 695-nm laser wavelength, compared with a 0.7-mum focused Gaussian spot size (full width at e(-2) of the peak) with the same focusing lens. The energy conversion efficiency for the beam shaping was ~81%.     

Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere

The average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere are examined. Our research is based principally on formulating the average-intensity profile at the receiver plane for cosh-Gaussian excitation. The limiting cases of our formulation for the average intensity are found to reduce correctly to the existing Gaussian beam wave result in turbulence and the cosh-Gaussian beam result in free space (in the absence of turbulence). The average intensity and the broadening of the cosh-Gaussian beam wave after it propagates in the turbulent atmosphere are numerically evaluated versus source size, beam displacement, link length, structure constant, and two wavelengths of 0.85 and 1.55 microm, which are most widely used in currently employed free-space-optical links. Results indicate that in turbulence the beam is widened beyond its free-space diffraction values. At the receiver plane, analogous to the case of free space, this diffraction eventually leads to transformation of the cosh-Gaussian beam into an oscillatory average-intensity profile with a Gaussian envelope.     

Numerical studies of backscattering enhancement of electromagnetic waves from two-dimensional random rough surfaces with the forward-backward/novel spectral acceleration method

The forward-backward method with a novel spectral acceleration algorithm (FB/NSA) has been shown to be a highly efficient O(Ntot) iterative method of moments, where Ntot is the total number of unknowns to be solved, for the computation of electromagnetic (EM) wave scattering from both one-dimensional and two-dimensional (2-D) rough surfaces. The efficiency of the method makes studies of backscattering enhancement from moderately rough impedance surfaces at large incident angles tractable. Variations in the characteristics of backscattering enhancement with incident angle, surface impedance, polarization, and surface statistics are investigated by use of the 2-D FB/NSA method combined with parallel computing techniques. The surfaces considered are Gaussian random processes with an isotropic Gaussian spectrum and root-mean-square surface heights and slopes ranging from 0.5 lambda to lambda and from 0.5 to 1.0, respectively, where lambda is the EM wavelength in free space. Incident angles ranging from normal incidence up to 70 degrees are considered in this study. It is found that backscattering enhancement depends strongly on all parameters of interest. America     

自由电子激光中的等效折射率

推导出适用于三维自由电子激光中的电子束的等效折射率，并说明高斯平面波分布的激光场是电子束等效折射率为平方分布率即类透镜介质的结果，对指数增长区的复数增益的三次方程作了改进，而且，还选用典型的自由电子激光的参数进行了数值计算，并对结果作了简要的分析。