Investigating the Nonlinear Optical Response of Pepper Oil under Low Power Irradiation with Continuous Wave Visible Laser Beam

The nonlinear optical properties of pepper oil are studied by diffraction ring patterns and Z-scan techniques with continuous wave beam from solid state laser at 473 nm wavelength. The nonlinear refractive index of the sample is calculated by both techniques. The sample show high nonlinear refractive index. Based on Fresnel-Kirchhoff diffraction integral, the far-field intensity distributions of ring patterns have been calculated. It is found that the experimental results are in good agreement with the theoretical results. Also the optical limiting property of pepper oil is reported. The results obtained in this study prove that the pepper oil has applications in nonlinear optical devices.

Thermal-induced nonlinearities in rose, linseed, and chamomile oils using continuous wave visible laser beam

Self-diffraction rings or spatial self-phase modulation were observed in rose, linseed, and chamomile oils under 473 nm continuous wave laser irradiation. The measurements were performed by propagating the laser beam through a cell containing each sample. The number of rings as well as diameter of the outer-most ring in each pattern obtained increases monotonically with increasing input power. The diffraction ring patterns are theoretically simulated using Fresnel–Kirchhoff diffraction integral in the case of an optically thin medium. The experimental and simulation results show that when a laser beam with Gaussian profile is transmitted through an oil medium, a series of circular diffraction rings forms in the intensity distribution pattern in the far-field. The nonlinear refractive index, n2, was determined from the number of observed rings and by the Z-scan technique. The results obtained from self-diffraction rings experiment and Z-scan are compared and analyzed for the three different oils. A large value was obtained of the order of n2 = 1.32 × l0−6 cm2/W for chamomile oil using the diffraction ring pattern technique. This large nonlinearity is attributed to a thermal effect resulting from linear absorption. Moreover, the optical limiting characteristics of rose, linseed, and chamomile oils were investigated.

Electromagnetic Radiation in Accelerator Physics

This article reviews some fundamental concepts and presents several recent techniques used for calculation of radiation in various environments. They include properties of longitudinal and transverse formation lengths of radiation, usage of the parabolic equation and the Kirchhoff diffraction integral in radiation, coherent radiation and fluctuations in the beam, and the radiative reaction force resulting from coherent radiation.

Path-linking interpretation of Kirchhoff diffraction

The Kirchhoff-diffraction integral is often used to describe the (scalar) wave field from a monochromatic point source in the presence of ‘opaque’ screens. Despite criticisms that can be made of its ‘derivation’, the Kirchhoff field is an exact solution of the wave equation, and exactly obeys definite, though unusual, boundary conditions (Kottler 1923, 1965). Here, the path-integral picture of wave fields is used to interpret the Kirchhoff-diffraction field in terms of all conceivable propagation paths, whether or not they pass through the opaque screens. Specifically, it is noted that the Kirchhoff field equals Ʃ(1 ─ m )ψ m , where the sum is over all integers m , and ψ m is the wave field due to all paths from the source to the field point for which the number of outward screen crossings minus the number of backwards screen crossings is m . Expressed more topologically, m is the total linking number of a path, when closed by any unobstructed path, with the screen edge lines. Other models of diffraction by screens are compared with Kirchhoff diffraction in the path interpretation.

Computer simulation of phase of contrast of cluster atoms on support film made by sputter deposition

Based on the image formation theory, the wave function of a single atom consisting of the complex scattering amplitude |f(0)|exp{-inj(0)} and phase shift γj of spherical aberration is rigorously obtained by the Kirchhoff diffraction integral in the Fraunhofer approximation as a function of defocus. Using of the wave function w(υj,γj) of a group of atoms, which is extended the wave function of a single atom, variations of imaging phase contrast of tungsten support film in through focal series made by sputter deposition are simulated. The contrast of tungsten support film and a gold cluster atoms on the substrate made by sputter depposition, which are very close with the experiment, are calculated by the Monte-Carlo method with the aid of the inter-atomic size distribution measured by electron diffraction pattern.The contrast g for cluster atoms has been calculated by integrating the scattering wave for coherent waves, and for incoherent waves the amplitude scattered outside the limiting angle α set by the aperture respectively,