Multiple hot images from an obscuration in an intense laser beam through cascaded Kerr medium disks

We present a theoretical investigation on the formation of hot images in an intense laser beam through cascaded Kerr medium disks, to disclose the distribution and intensity of hot images in high-power disk amplifiers. It is shown that multiple hot images from an obscuration may be formed, instead of one hot image as reported previously in the literature. This gives a clear explanation for the curious damage pattern of hot images, namely, damage sites appearing on alternating optics in periodic trains. Further analysis demonstrates that the distribution and intensity of hot images depend closely on the number of Kerr medium disks, the distance from the obscuration to the front of the first disk downstream, the space between two neighboring disks, and the thickness and B integral of each disk. Moreover, we take two cascaded Kerr medium disks for example to detail multiple hot images from an obscuration and confirm the theoretical results by numerical simulations.     

Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.     

Propagation of (2 + 1)-dimensional solitary waves in dissipative/active saturable nonlinear media

Abstract

We investigate the propagation of (2 + 1)D bright solitary waves in a saturable nonlinear medium perturbed with gain or loss. We find that in the presence of loss (gain) the amplitude and width of the (2 + 1)D bright solitary waves may both increase (decrease) with their product varying adiabatically during evolution. This is in contrast to the (1 + 1)D Kerr bright (dark) solitons or (2 + 1)D vortex solitons whose amplitude decreases (increases) at the same rate as the width increases (decreases), keeping their product unchanged with the propagation distance. For a very weak nonlinear saturation approaching Kerr nonlinearity, it is found that the amplitude and the width change at a rate faster than the (1 + 1)D Kerr bright and dark solitons, whereas their variation in highly saturable media is slower than the (1 + 1) or (2 + 1)D Kerr dark solitons. In a medium of moderate nonlinear saturation, the beam width and amplitude may vary in the way following that of high nonlinear saturation or weak nonlinear saturation or a combination of the two, depending on loss or gain and propagation distance.     

Tunable beam focusing based on optical bistability with a composite Kretschmann configuration involving a Kerr medium

A beam focuser with a composite Kretschmann configuration involving a Kerr medium is investigated theoretically. The structure employs a silver film with four slits filled with the Kerr medium. Optical bistability and beam focusing are demonstrated, and changes to the incident intensity result in optical bistability characteristics in the reflection, focused intensity, spot size, and depth of focus. The proposed structure has the potential to be applied for optical switching and nano-illumination.     

Single Gaussian beam interaction with a Kerr microsphere: characteristics of the radiation force

We analyze the characteristics of the radiation force that is generated when a highly focused unpolarized Gaussian beam interacts with a nonabsorbing microsphere whose refractive index exhibits a first-order dependence on the beam intensity. The behavior of the force exerted on the sphere is analyzed as a function of beam power, axial distance, sphere radius, refractive-index difference between the sphere and the surrounding liquid, and wavelength. The force characteristics are compared with those of the radiation force that is generated when the electro-optic Kerr effect is absent. Our results show that a reversal in the net force direction is introduced when the Kerr effect becomes significant, which occurs at sufficiently high beam intensities.     

Optical Kerr coefficient measurement in coiled high-birefringent fibers

The optical Kerr effect in coiled high-birefringent fibers was measured based on a double-beam polarimetric method. A Q-switched Nd:YAG laser, operating at 1.064 mum (FWHM of 80 ns at 1 kHz), was used as the pump beam and a cw 0.633-mum He-Ne laser was used as the probe beam with its polarization fixed at 45 degrees with respect to the birefringent axis whereas orientation of the linearly polarized pump light varied. The phase shifts induced by an intense pump beam in a short bow-tie high-birefringent fiber were determined for different fiber lengths coiled into 15- and 30-cm-diameter drums. It was found that the induced phase shift changes drastically with the state of polarization of the pump light. A strong dependence of the phase shift on orientations of linear pump polarization is attributed to differential losses of eigenmodes peculiar to birefringent axes. Therefore, optical Kerr coefficients remain unchanged regardless of the dependence of the nonlinear response of the coiled high-birefringent fibers on pump polarization.     

Rear-Surface Laser Damage on 355-nm Silica Optics Owing to Fresnel Diffraction on Front-Surface Contamination Particles

Light intensity modulations caused by opaque obstacles (e.g., dust) on silica lenses in high-power lasers often enhance the potential for laser-induced damage. To study this effect, particles (10-250 mum) with various shapes were sputter deposited on the input surface and irradiated with a 3-ns laser beam at 355 nm. Although a clean silica surface damages at fluences above 15 J/cm(2), a surface contaminated with particles can damage below 11.5 J/cm(2). A pattern that conforms to the shape of the input surface particle is printed on the output surface. Repetitive illumination resulted in catastrophic drilling of the optic. The damage pattern correlated with an interference image of the particle before irradiation. The image shows that the incident beam undergoes phase (and amplitude) modulations after it passes around the particle. We modeled the experiments by calculating the light intensity distribution behind an obscuration by use of Fresnel diffraction theory. The comparison between calculated light intensity distribution and the output surface damage pattern showed good agreement. The model was then used to predict the increased damage vulnerability that results from intensity modulations as a function of particle size, shape, and lens thickness. The predictions provide the basis for optics cleanliness specifications on the National Ignition Facility to reduce the likelihood of optical damage.     

Risky intensity peaks resulting from nonlinear holographic imaging

A study of the maximal intensity peaks due to nonlinear holographic images of obstacles such as obscurations or phase defects in a high-power laser system is presented. It is shown that the interference of the high-power plane wave and the converging image wave results in the formation of intensity maximums in the vicinity of the image plane, the values of which significantly exceed the intensity in the image plane itself. For round obstacles, analytical expressions that describe magnitudes and locations of the maxima depending on the radius and the type of obstacle are given. A procedure of numerical modeling that allows estimation of the influence of beam size, medium thickness, type, size, and shape of obstacles onto the properties of nonlinear images is described. It is demonstrated that for a given combination of the nonlinear medium and the high-power beam parameters, there is an intrinsic size of obstacles that is most harmful for the laser system components.     

Femtosecond snapshot imaging of propagating light itself

An ultrafast imaging technique has been developed to visualize directly a light pulse that is propagating in a medium. The method, called femtosecond time-resolved optical polarigraphy (FTOP), senses instantaneous changes in the birefringence within the medium that are induced by the propagation of an intense light. A snapshot sequence composed of each femtosecond probing the pulse delay enables ultrafast propagation dynamics of the intense femtosecond laser pulse in the medium, such as gases and liquids, to be visualized directly. Other examples include the filamentation dynamics in CS2 liquid and the propagation dynamics in air related to the interaction with laser breakdown plasma. FTOP can also be used to extract information on the optical Kerr constant and its decay time in media. This method is useful in the monitoring of the intensity distribution in the nonlinear propagation of intense light pulses, which is a frequently studied subject in the field of physics regarding nonlinear optics and laser processing.     

Second-order hot image from a scatterer in high-power laser systems

A theory is developed for predicting a second-order hot-image formation in high-power laser systems. Light diffracted from a small optical scatterer interferes with an intense original wave in the nonlinear medium to produce a hologram like a Fresnel-zone plate. The theoretical model shows that the hologram produces a negative first-order diffractive wave focused to the traditional hot image and negative second-order diffraction that causes another intense image, namely, a second-order hot image. It is found by analysis that the location of the second-order hot image arises in a downstream plane with a half-distance from the medium to the scatterer. Results of the numerical calculations show that the peak intensity of the nonlinear image may reach a level high enough to damage optical components with the increase of the breakup integral (B integral), indicating that the image may also potentially damage expensive optical components in high-power laser systems.     

Radiation force on a nonlinear microsphere by a tightly focused Gaussian beam

We determine the characteristics of the radiation force that is exerted on a nonresonant nonlinear (Kerr-effect) rigid microsphere by a strongly focused Gaussian beam when diffraction and interference effects are significant (sphere radius a < or = illumination wavelength lambda). The average force is calculated from the surface integral of the energy-momentum tensor consisting of incident, scattered, and internal electromagnetic field vectors, which are expressed as multipole spherical-wave expansions. The refractive index of a Kerr microsphere is proportional to the internal field intensity, which is computed iteratively by the Rytov approximation (residual error of solution, 10(-30). The expansion coefficients for the field vectors are calculated from the approximated index value. Compared with that obtained in a dielectric (linear) microsphere in the same illumination conditions, we find that the force magnitude on the Kerr microsphere is larger and increases more rapidly with both a and the numerical aperture of the focusing objective. It also increases nonlinearly with the beam power unlike that of a linear sphere. The Kerr nonlinearity also leads to possible reversals of the force direction. The proposed technique is applicable to other types of weak optical nonlinearity.     

一种测量薄膜磁性的表面磁光克尔效应装置

介绍表面磁光克尔效应谱（SMOKE）的一种新方案。通过适当分光并测量信号束和参考束的光强比，可以明显改善由于激光的光强不稳造成的误差，还使得随机偏振激光器也能用于SMOKE装置。同时该方案中没有采用信号调制，因此对探测器等硬件要求很低。实验结果表明，采用光强稳定度为5％的普通国产He－Ne随机偏振激光器，其测量灵敏度能够达到目前国际上通常用于超薄膜磁性测量的SMOKE的同类水平。     

多模增益光纤受激布里渊散组束中散射效果的研究

提出了在计算多模增益光纤有效受激布里渊增益系数时,以优化的高斯模场面积作为光纤有效截面积的方法,并基于光强耦合微分方程,研究了多模增益光纤稳态受激布里渊散射的效果.结果表明,无论是一阶还是二阶受激布里渊散射,随着泵浦功率的增加,残余的泵浦功率都将达到饱和,而Stokes功率都线性增加;二阶Stokes功率相对较弱;光纤的有效长度随泵浦功率的增加逐渐减小.     

Near-field magnetooptics in resonant light scattering by a linear nanoprobe

A theory of the magnetooptical scattering of light by a near-field linear probe parallel to the surface of a magnet is presented. The probe is modeled by a cylindrical nanowire supporting long-lived surface plasmons. The scattering of light is considered in the longitudinal magnetooptical Kerr effect geometry (with magnetization parallel to the sample surface and the plane of light incidence). The resonant interaction of the probe + image system is taken into account in the self-consistent approximation of the multiple scattering theory, while the magnetooptical interaction is described in the linear approximation with respect to magnetization. Polarization characteristics of the scattered light and the magnetooptical modulation of light intensity, which are resonantly enhanced by the surface plasmons, have been studied.     

Simulation analysis of the restraining effect of a spatial filter on a hot image

Based on the restraining effect that spatial filtering has on the frequency spectrum of a beam, from the small-scale focusing theory of Bespalov and Talanov (B-T theory) we derive an expression for the pinhole diameter of the spatial filter corresponding to the fastest growing frequency. Then, compared with the theoretical pinhole diameter of the spatial filter, the restraining effect of the spatial filter on a hot image with different pinhole diameters is numerically investigated. The numerical results show that, if the pinhole diameter is larger than the theoretical one, the hot-image intensity will remain steady; once the pinhole diameter becomes smaller than the theoretical one, the hot-image intensity will begin to decrease. Moreover, as the pinhole diameter decreases, a more prominent restraining effect can be obtained. But reducing the diameter of the spatial filter would lead to greater beam energy loss. The parameters of the spatial filter must be chosen to guarantee that the scheme fulfills the demand for low beam energy loss and a satisfactory restraining effect simultaneously.     

Efficient analytic model to optimum design laser resonator and optical coupling system of diode-end-pumped solid-state lasers: influence of gain medium length and pump beam M2 factor

A comprehensive analytical model for optimization longitudinal pumping of ideal four-level lasers is presented for accurate analysis by removing limiting assumptions on active length and pump-beam radius in the gain medium. By taking into account the circular-symmetric Gaussian pump beam including the M2 factor, an analytical formula for the root mean square of the pump beam in the active medium is developed to relate properties of the gain medium and pump beam to the requirement on efficient optimum design. Under the condition of minimum root mean square of pump-beam radius inside the active medium, the key parameters of the optimum optical coupling system have been analytically derived. Using these parameters, optimum mode size and maximum output efficiency are derived as a function of the gain medium length, absorption coefficient, pump-beam M2 factor, and input power. Dependence of the obtained parameters on the gain medium length, absorption coefficient, pump-beam M2 factor, and input power has been investigated. The results of this theory are found to be more comprehensive than the previous theoretical investigations. The present model provides a straightforward procedure to design the optimum laser resonator and the coupling optics for maximizing the output.     

Diffusion Calculation of Change of Back-scattered Light Beam Intensity from Turbid Medium Owing to the Existence of an Inhomogeneity

Abstract

A solution to the searchlight problem on back-scattering of a narrow pencil light from a turbid medium with an inhomogeneity is presented for semi-infinite geometry in the framework of the diffusion approximation. The inhomogeneity may be an object with a given reflection coefficient or a variation of mean scattering and absorption properties of a turbid medium. A solution to the diffusion equation for mean diffuse radiant intensity with given boundary conditions is obtained by a perturbation theory method relative to the inhomogeneity effect. The spatially limited inhomogeneity contribution to the back-scattering light intensity is expressed in terms of an inhomogeneity diffuse scattering amplitude and the probability density distribution of photon paths in depth. The theoretical results obtained are applied to the interpretation of the Cui, Kumar and Chance experiment on the change of the back-scattered light beam intensity from turbid biological tissue phantom owing to the existence of small absorbers.     

Formation of nonlinear holographic images in powerful laser systems

The formation of nonlinear holographic images behind a multislab amplifier is studied. The analytical expressions describing magnitudes and locations of intensity maxima depending on the corresponding image number are derived. Comparison with numerical calculations results is given. On the basis of numerical modeling, analysis of gain saturation, slab thickness, and slab aberrations influence is carried out.     

径各平方贝赛尔函数调制高斯光束的焦移

给出变量为径向平方的贝塞尔函数调制的高斯光束（QBG光束）通过ABCD聚集光学系统的轴上光强分布公式,对QBG光束通过薄秀镜聚集系统的轴上光强分布及焦移进行了研究,得到相对焦移满足的三次方程和解析解,给出详细的数值计算结果并进行了分析讨论。     

Gaussian beam to spatial soliton formation in Kerr media

We present a detailed analysis of the generation and propagation of bright spatial soliton beams in nonlinear Kerr media, in which an input beam is assumed to be of a Gaussian or hyperbolic secant form. The problem is solved by the use of the inverse-scattering transform (IST). The analysis of the discrete spectrum obtained from the direct-scattering problem gives exact information about the parameters of the generated soliton. A condition of soliton appearance in the spectrum as a function of the complex width of the initial Gaussian beam is given numerically. The similarities and differences between the hyperbolic secant and Gaussian beams entering the Kerr medium are analyzed in detail. A case is found in which almost all (approximately 99.5%) the total intensity of the Gaussian beam entering the Kerr medium is transformed into the soliton beam. However, this analogy to the self-trapping of soliton beams occurs for higher total-intensity values than in the case of the soliton input profile. The evolution from the Gaussian to the soliton envelope is studied and the condition of self-trapping in the near field is found. The numerical method based on the IST of the solution to the nonlinear Schr?dinger equation is refined.