A neat semi-Gaussian laser beam with no diffraction fringes: Theoretical analysis

We propose a simple optical device to convert a Gaussian laser beam into a neat semi-Gaussian laser beam without any diffraction fringe by using a spatial light modulator and a thin, sharp blade, and numerically calculate the diffracted, relative intensity distributions of both the semi-Gaussian laser field and the semi-Gaussian, pseudo-thermal light. We also study the dependence of the border width of the semi-Gaussian beam on the waist of the Gaussian beam. Our study shows that the proposed scheme can be used to cancel all diffraction fringes from both the straight edge of the blade and a finite lens aperture in all the planes vertical to the z axis and obtain a neat semi-Gaussian beam without any diffraction fringe, and find that the border width w_B of the generated semi-Gaussian beam is not dependent on the waist of the incident Gaussian beam.     

Influence of laser wavelength on target irradiation uniformity

Target irradiation uniformity is very important in laser-produced plasmas experiments. The wavelength dependence of the irradiation uniformity is investigated in the joint scheme using a lens array (LA) and the technique of smoothing by spectral dispersion (SSD). It is proved that, for the long wavelength laser, lateral thermal conduction smoothing within the target is quite effective, while for the ultraviolet laser, SSD is the main smoothing mechanism. So SSD and other temporal smoothing methods are very necessary in producing uniform irradiation with laser beam of short wavelength.     

Mode profiles in resonators with a near 90° roof-top mirror

The transverse modes of a laser resonator comprising a near 90° roof-top mirror and a feedback mirror are studied theoretically. We relate this configuration to an almost plane roof-top resonator and apply the Fox and Li technique to compute the lowest-order symmetric and antisymmetric modes. The effects of perturbations to the vertex angle of the roof-top mirror, misalignments of the feedback mirror and curved feedback mirrors are examined.     

Double- and multi-photon pair production and electron-positron entanglement

We investigate entanglement of electrons and positrons produced via absorption by a vacuum of two or several photons from two external electromagnetic waves. The waves are modelled by finite-length focused pulses. Structures of the arising electron and positron wave packets are investigated in the momentum and coordinate representations. Conditional and unconditional widths of these wave packets, as well as the Schmidt number K are found, and they are used to evaluate the degree of entanglement. The conditions are found when entanglement is large. It is shown that the highest entanglement can be reached at nonrelativistic energies of electrons and positrons. Possibilities of observing the entanglement effects in experiments on pair production are discussed.     

Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon

We propose a new method for transformation of a Laguerre-Gaussian beam of azimuthal index l and radial index n = 0 (LG_l,0) into a vortex, diverging or nondiverging Bessel beam, which can have increased or decreased phase singularity order, or into a zeroth order Bessel beam, by means of a helical axicon. The Bessel beam divergence or nondivergence depends upon the waist position of the input Laguerre-Gaussian beam, regarding the plane where the helical axicon is situated.The expressions for the amplitude and the intensity distribution of the diffracted wave field, in the process of Fresnel diffraction, are deduced using the stationary phase method. The theoretical analysis for the vortex radius and the maximum propagation distance of the Bessel beams obtained is presented.     

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.     

Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources

A method of formation of the tightly confined, distortion-free, femtosecond pulses in two dimensions (2D) with the step-like decreasing of intensity after a finite length of propagation in free space is described. The pulses are formed by the Fresnel source of modes corresponding to a 2D hollow waveguide with perfectly reflecting walls (material waveguide). The source reproduces in free space a propagation-invariant pulse confined by the waveguide. Unlike the case of material waveguides, when the pulse goes out from the virtual waveguide formed by the Fresnel source its shape does not change, but the intensity immediately drops down to the near-zero level. It is also shown that there is a limit of the duration of pulse beyond which the step-like decay is not observed.     

Different field distributions obtained with an axicon and an amplitude mask

A combination of an axicon and an amplitude mask is used to obtain an intensity distribution that differs from the typical Bessel one. Experimental and numerical characterization of the field is made for different propagation distances and types of amplitude masks.     

Generation of thin and hollow beams by the axicon with a large open angle

We propose a method to produce diffraction-free thin and hollow beams. The method is based on Laguerre-Gaussian (LG) beams incident on a large open-angle axicon. We use the vector diffraction integrals and stationary phase method to deduce a simple and analytical formula of the propagating field of the linearly polarized LG beams through an axicon. The numerical results show that the hollow beams of whose diameter is in the order of the wavelength can be obtained by using the axicon with the refractive index n = 2 and the open angle α = 25°. These diffraction-free thin and hollow beams may be very useful to accurately trap and manipulate atoms. However, when the open angle is over large, the conversion efficiency from the LG beam to the diffraction-free hollow beam will decrease obviously.     

Propagation offset characteristics of annular laser beams from confocal unstable resonators through the natural atmosphere

Based on the laser field from a positive confocal unstable resonator (ab initio), the propagation characteristics of the beam through atmosphere are investigated by means of fast Fourier transform (FFT), and it is assumed that the refractive index and absorption of atmosphere are only decided by the air molecules. Considering the thermal effects of the laser beam and wind velocity of air, we evaluate the beam offsets, beam spreading, and beam qualities of the laser field transmitting from the resonator through the natural atmosphere. Meanwhile, the far-field intensity distributions of the laser beam with various intensities in the atmosphere are obtained. It is shown that the far-field diffraction patterns are deformed due to absorption of air and wind velocity. β parameter and Strehl ratio, which are usually used for high-power lasers, are introduced to estimate the beam quality characteristics. With increasing the intensity of the beam, the far-field diagram patterns are outspreaded, the peak intensities reduced, the peak centers shifted, and the beam quality characteristics greatly degraded.     

Generation of a radially polarized doughnut mode of high quality

We present an experimental set-up to generate laser beams with locally varying polarization distribution. In a linear set-up, a radially polarized beam of high quality regarding intensity distribution, polarization and phase-front distortion is generated. This beam can be used for tight focusing. Further applications are discussed.     

Propagation characteristics of the rectangular flattened Gaussian beams through circular apertured and misaligned optical systems

Based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expression for the output field distribution of a rectangular flattened Gaussian beam passing through a circular apertured and misaligned paraxial ABCD system is derived. The result brings more convenient for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of a rectangular flattened Gaussian beam through a circular apertured and misaligned optical system.     

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases.     

Smoothing effect in the broadband laser through a dispersive wedge

The propagation expression of a broadband laser passing through a dispersive wedge is derived on the basis of the Huygens-Fresnel diffraction integral. Smoothing effects caused by the phase perturbation of the dispersive wedge on the intensity profiles are investigated in detail. The phase perturbation of the dispersive wedge induces a relative transverse position shift between the diffraction patterns of different frequency components. The relative transverse position shift is of great benefit to the fill of the intensity peaks of some patterns in the valleys of others when these patterns are overlapped and thus the smoothing effect is achieved.     

A tuneable, single-mode titanium-doped-sapphire laser source with variable pulse duration in the nanosecond regime

We built and characterized a high-energy, injection-seeded, single-longitudinal-mode pulsed titanium-doped-sapphire laser with tuneable wavelength in the near-infrared and variable pulse temporal duration in the nanosecond regime. We show experimentally how the pulse duration can be easily varied either by changing the cavity length or by changing the pump energy. We successfully interpreted these results on the basis of a theoretical model which treats the operation of this type of laser as a gain-switching technique. Also, as far as the stabilization of the laser cavity, compared to the traditional techniques we employed a novel simplified solution involving the use of an avalanche photodiode.     

A continuous-mode model of the mode locking in a pump-modulated laser

The active mode-locking process of the multimode laser with an external pump modulation is theoretically investigated in the frequency domain within the framework of the continuous-mode approximation. Intermode interaction and mode-coupling effects, including both AM and FM modulations, are naturally considered in a hierarchical equation of the mode components derived from the multimode Maxwell-Bloch equations. It is reduced to a continuous-mode equation that can be solved analytically in a stationary case, and used to discuss the spectral line shape and the phase dynamics of mode-components as a function of modulation amplitude and detuning of the modulation frequency. We predict a novel oscillation existing below the threshold of the ordinary complete mode-locking: The intensity of the total electric field yields a stable pulse train but its phase varies irregularly in time. This semi-locked state is characterized by a nonlinear chirping, an asymmetric spectrum, and drifting phases of the field mode-components.     

Diffractive effects in singly resonant continuous-wave parametric oscillators

I /k_P=0.33and0.50. It is found that the ratio of pump depletion to maximal depletion as a function of the ratio of pump power to threshold power agrees with the plane-wave prediction to within 5%, for a wide range of focusing conditions. The observed trends are explained as resulting from intensity- and phase-dependent mechanisms. Received: 19 January 1998/Revised version: 13 March 1998     

Coupling laser radiation to a fabry-perot cavity with a single-mode optical fiber

Three aspects of coupling to Fabry-Perot cavities used in optical frequency standards are discussed: the use of a single-mode optical fiber to maintain coupling stability while improving vibration isolation of the cavity, the required stability of the coupling geometry, and the phase and polarization variations resulting from fiber movement. Optical fiber coupling should be useful when laser linewidths and stabilities at the Hertz level are desired.     

Interferometric method for characterizing the smile of laser diode bars

We propose an interferometric method for the characterization of the smile of laser diode bars (LDBs). The LDB is placed in a Lloyd’s mirror set-up. The beams coming from the LDB and its virtual image produce Young’s fringes, which are captured by a charge-coupled-device array, digitised and saved in a computer as an irradiance matrix. The irradiance matrix is processed in the computer and the smile parameter extracted. The theoretical basis of the method is discussed and simulated fringe patterns of practical situations are presented. A device based on the described interferometric method was mounted and the smile of a commercially available LDB was characterised.     

The discovery of nanometer fringes in laser self-mixing interference

We demonstrate the influences of optical feedback from an external mirror with high reflectivity in a He-Ne laser on self-mixing interference fringes and laser polarization states. When the external mirror is tilted to a certain level, the stable and uniform nanometer resolution fringes are generated. The fringe density is 40 times than that of the conventional self-mixing interference or two beam interference, and has still potential to be improved. Each self-mixing interference fringe corresponds to λ/80 displacement of the external mirror, i.e. 7.91 nm displacement of the external mirror. Moreover, when the movement direction of the external mirror is changed, the polarization flipping between two eigenstates will happen. The potential applications of the results are also discussed.