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.     

Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω₀. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.     

BBO晶体四倍频全固态小功率紫外激光器

 利用KTP晶体和BBO晶体,进行了激光二极管泵浦的Nd:YVO₄声光调Q激光脉冲四倍频实验。在不同绿光功率入射时,获得光束的束腰半径和紫外转换效率的依赖关系:当绿光功率为1.10 W,束腰半径为12.4 μm时,得到了210 mW的准连续266 nm紫外脉冲输出,四倍频转换效率为19.1%。实验还对紫外远场光斑分别在o光振动面和e光振动面内进行分析,指出了BBO晶体在该两平面内不同的倍频接受角是造成椭圆形紫外光斑和主光斑附近明暗条纹的主要原因。     

Diffracted field distribution from a knife-edge truncated semi-Gaussian beam as an atomic （molecular） mirror

We investigate the diffraction characteristics of an incident Gaussian beam cut by a straight edge bounding a semi-infinite opaque plane using Kirchhoff scalar wave theory in the Fresnel limit, and propose a new and simple mirror scheme to reflect atoms by using the intensity gradient induced by a blue-detuned semi-Gaussian laser beam. The optical potential of the diffracted light of the knife-cut semi-Gaussian beam for $^{85}$Rb atom and its spontaneous emission probability are calculated and compared with the performance of the evanescent-wave mirror. Our study shows that the optical potential of the diffracted light of the semi-Gaussian beam is far higher than that of the evanescent light wave, and the maximum normal velocity of the incident atoms can be far greater than that of the evanescent light wave under the same parameters, so the blue-detuned semi-Gaussian beam, as a novel atomic mirror, can be used to efficiently reflect cold atoms with a normal velocity of greater than 1 m/s. However, the intensity gradient (force) of the diffracted light of the semi-Gaussian-beam is much smaller than that of the evanescent light wave, so its spontaneous emission probability is greater than that from the evanescent-wave when the normal velocity of incident atoms is greater.     

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r)∼E²(r). For ultrathin films of thickness d?λ, the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region.     

Propagation of elegant Hermite cosine Gaussian laser beams

In this paper, a more generalized beam containing an elegant Hermite Gaussian beam and a cosine Gaussian beam, which is called elegant Hermite cosine Gaussian (EHcoG) beam, is introduced and studied. The propagation properties of the EHcoG laser beams through a first-order paraxial optical system are demonstrated analytically and numerically. The recurrence propagation equations of the EHcoG beams through a first-order paraxial optical system with and without aperture are derived, from which the analytical propagation expression for EHcoG beams of any order can be obtained by means of the recursive procedures. The validity of the analytical results is confirmed by the numerical results.     

Amplitude and phase clipping: Strehl ratio versus divergence

We consider the transverse characteristics of a Gaussian laser beam subject to a phase or amplitude clipping due to a pupil which is a π-plate or an opaque disc (stop). In particular, we consider the correlation between two features, the Strehl ratio and divergence angle, usually used for characterising the focusability of a diffracted beam. It is demonstrated that the Strehl ratio does not give systematically a global view, from a divergence point of view, on the transverse properties of a Gaussian beam suffering amplitude or phase diffraction. In addition, we consider the case of self-diffraction of a Gaussian beam upon a Gaussian phase aberration of same width, and it is found that the on-axis intensity describes correctly the whole diffracted beam cross-section, from a divergence point of view, only if the central phase shift is smaller than π. Another example showing that the focusability of a pure high-order Laguerre–Gauss TEM_p0 beam, free from any clipping, cannot be correctly described by Strehl ratio is also considered.     

全息光栅曝光系统中空间滤波器孔径与激光束腰关系的选择方法

在全息光栅制作过程中, 由空气悬浮颗粒及光学器件缺陷引起的散射光会被记录在光刻胶上, 既影响光栅衍射效率, 又会带来光栅杂散光. 为消除系统散射光, 需要对激光光束的高频成分进行滤波处理. 但是, 激光光束通过空间滤波器后发生衍射, 进而影响干涉场质量, 因此选择合适的空间滤波器孔径是搭建全息光栅曝光系统的前提条件. 根据标量衍射积分理论, 通过卷积计算滤波光束的振幅分布分析光束的相位变化, 以光束相位突变位置远离光束中心为依据确定滤波器针孔半径与光束束腰半径的比值下限; 根据滤波光束的能量守恒关系, 通过滤波光束的高斯参数变化描述光束的衍射强弱规律, 以光束发生衍射的临界条件确定滤波器针孔半径与光束束腰半径的比值上限. 结果表明, 当空间滤波器针孔半径与激光束腰半径之比满足1.52< a/ω₀<2.2时, 滤波光束曝光区域相位恒定, 光束能量通过率大于99%, 在此区间空间滤波器滤波效果最好.     

1 W tunable near diffraction limited light from a broad area laser diode in an external cavity with a line width of 1.7 MHz

A novel unstable external cavity for a broad area laser diode is presented. The cavity is based on a V-shaped setup that improves the slow axis beam quality by coupling the internal modes of a gain guided laser diode. The novelty here is the compact unstable resonator design without lenses in direction of the slow axis. For frequency stabilisation and to narrow the line width of the laser diode emission a diffraction grating in a Littrow configuration is used. With this setup up to 1 W of near diffraction limited light with a beam quality of M² ? 1.3 and a line width of 1.7 MHz could be achieved. The external cavity laser was tunable over a range of 35 nm (FWHM) around the center wavelength of 976 nm.     

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.     

Vectorial Nonparaxial Four-Petal Gaussian Beams and Their Propagation in Free Space

The vectorial nonparaxial four-petal Gaussian beam （FPGB） is introduced. The closed-form propagation expressions for the free-space propagation of FPGBs are derived and their more general applicable advantages are illustrated analytically and numerically. Some special interesting cases, in particular the paraxial one, are discussed. It is found that the parameter f = 1/kwo with the k being the wave number and wo being the waist width plays a crucial role in determining the nonparaxiallity of FPGBs. For small values of the f parameter the paraxial approximation is allowable. In the nonparaxial regime the beam order n additionally affects the vectorial and nonparaxial behaviour of FPGBs.     

Propagation of a hollow Gaussian beam through a paraxial misaligned optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a paraxial misaligned optical system in the cylindrical coordinate system, we obtain an analytical formula for a hollow Gaussian beam passing through a paraxial misaligned optical system. Furthermore, we also obtain the approximate analytical formula for a hollow Gaussian beam passing through a paraxial circularly apertured misaligned optical system by expanding the hard aperture function into a finite sum of complex Gaussian functions. As a numerical example, the propagation properties a hollow Gaussian beam through a misaligned thin lens are studied numerically.     

Biphotonic effect of azo-dye-doped liquid crystals using the sequential Z-scan technique

This study investigates the biphotonic effect of azo-dye-doped liquid crystals (ADDLCs) using the sequential Z-scan technique. A spot on the sample is illuminated by a green light for 6 s, and then the same spot is illuminated simultaneously with a red light and a green light for 6 s. Measurements are made by scanning the sample near the beam waist of the green laser. The results show that the biphotonic effect is important to the nonlinear coefficient of the sample. The variations of the optical Kerr constant with intensity of red light are measured. Measurement results demonstrate that the molecular reorientation of liquid crystals induced by the photoisomerization of the azo dyes dominates at low red-light intensity, but the thermal effect compensates for the molecular reorientational nonlinearity of the sample at high red-light intensity.     

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.     

Thermal lens determination of LD end-pumped solid-state laser with stable resonator by slit scanning method

A simple method to determine the thermal focal length of LD end-pumped solid-state laser with stable resonator is presented. The M² factor describing the quality of the beam can be obtained by scanning a slit through the multi-mode Gaussian beam field. The waist width of the beam and the corresponding TEM₀₀ under the same parameters of laser are then deduced through the law of multi-mode Gaussian beam propagation. Based on the standard matrix theory of stable resonator, the thermal focal length of the gain medium can be easily achieved. To show the application of this approach, the thermal focal length of an LD pumped Nd:YVO₄ laser is measured and the experimental results are in agreement with the theoretical prediction.     

Propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media

The propagation of four-petal Gaussian beams in strongly nonlocal nonlinear media has been studied. The analytical solution and the analytical second-order moment beam width are obtained. For the off-waist incident and the waist incident cases, the intensity pattern evolves periodically during propagation in strongly nonlocal nonlinear media. Under the off-waist incident condition, the second-order moment beam width varies periodically during propagation, whatever the input power is. But under the waist incident condition, there exists a critical power. When the input power equals the critical power, the second-order moment beam width remains invariant, otherwise the second-order moment beam width varies periodically. Numerical simulations based on the nonlocal nonlinear Schrödinger equation are carried out for comparison with the theoretical predictions. The results show that the numerical simulations are in good agreement with the analytical results in the case of strong nonlocality.     

A Novel Mirror for Cold Molecules with a Semi-Gaussian Beam

We propose a novel mirror for cold molecules with a blue-detuned semi-Gaussian beam and study the dynamic reflection process of cold molecules by Monte Carlo simulation. Our study shows that this mirror can realize a specular reflection of cold iodine molecular beam with a temperature of 30mK by a reflectivity of 58.2% when the semi-Gaussian laser power is 1.0 kW. When a semi-Gaussian CO2 laser beam with a power of 5.8 kW is used, the reflectivity of this mirror can reach about 100%.     

Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the angular spread θ _sp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition of the intensity. However, the θ _sp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition of the cross-spectral density function. For the superposition of the cross-spectral density function, θ _sp of GSM array beams with smaller coherence length σ ₀, smaller waist width w ₀, smaller beam number N, and larger separation distance x _d are less affected by turbulence than of those with larger σ ₀,w ₀,N, and smaller x _d ; while, for the superposition of the intensity, the effect of turbulence on θ _sp is independent of N and x _d . In addition, the angular spread is nearly the same for the two types of superposition when σ ₀ or w ₀ is small enough, or x _d is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence.     

Numerical Simulations on the Formation of Speckles in Nanofluids Illuminated by a TEM00 Laser Beam

On the basis of a Rayleigh scattering model for a single nanoparticle illuminated by a TEMoo laser beam, we theoretically and numerically study the speckle formation when nanofluids are illuminated by a TEMoo laser beam. The results show that the laser speckles possess a Gaussian distribution, which are in agreement with the experimental results. The results may be useful for using a laser speckle velocimetry to determine the velocitiies of nanoparticles in nanofluids.     

Smallest focal hole

We study theoretically routes toward the most confined dark channel that can be obtained using high angular aperture focusing. One possible solution is to use a radially polarized beam combined with an optical singularity. Another possibility is to use an azimuthally polarized light beam combined with an annular aperture or a phase filter. Our results suggest that a focal hole of full-width at half maximum of approximately 0.3λ₀/NA is achievable, where λ₀ is the wavelength in vacuum and NA is the numerical aperture of the focusing system. Finally, we show that by letting a phase-shifted plane wave and a focused scalar wave interfere only one point in the focal plane will exhibit zero intensity. Advantages and disadvantages of the schemes are discussed.