Intensity (physics)

Abstract: An approximate theory has been derived describing part of the sound field due to a concave spherical radiator, vibrating with uniform normal velocity; the radius a of the circular boundary is assumed to be large relative to the wave‐length and large relative to the depth of the concave surface. The theory describes the distribution of pressure, particle velocity, and intensity along the axis of symmetry and in the vicinity of the focal plane, perpendicular to the axis at the center of curvature. It is shown that the ratio of the intensity at the center of curvature to the average intensity at the radiating surface is nearly equal to (2πh/λ)2 where h is the depth of the concave surface and λ is the wave‐length. This ratio can be made very large by suitable choice of dimensions, and the focusing is then very sharp. The point of greatest intensity is not at the center of curvature but approaches it with increasing kh = 2πh/λ, and the greatest intensity is not much greater than the intensity at the center of ...

Abstract: An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.