Cubic B-Spline Interpolation Method for Singular Integral Equations with Logarithmic Singularities

An apparatus for compressing the spectral distribution of a coherent beam of light includes a narrowband filter for separating the coherent beam into a transmitted portion containing optical energy substantially limited to a single wavelength lambda and a reflected portion containing the remainder of the coherent beam. A photorefractive crystal is positioned to receive the transmitted and reflected portions. A mirror deflects the reflected portion toward the photorefractive crystal. The photorefractive crystal is oriented such that two-wave mixing within the crystal causes a substantial portion of the energy in the reflected portion to be converted into optical energy at the wavelength lambda and to emerge from the crystal in the direction of the transmitted portion. The spectral bandwidth of the coherent beam is less than 1/ tau , where tau is the holographic time constant of the photorefractive element. An apparatus for converting the modes of a coherent beam of light includes a mirror containing a small orifice. The mirror separates the coherent beam into a portion transmitted through the orifice containing optical energy substantially limited to the fundamental TEM00 mode and a portion reflected by the mirror containing the remainder of the coherent beam. A photorefractive crystal is positioned to receive the transmitted and reflected portions. A mirror deflects the reflected portion toward the photorefractive crystal. The photorefractive crystal is oriented such that two-wave mixing within the crystal causes a substantial portion of the energy in the reflected portion to be converted into optical energy with the fundamental TEM00 mode and to emerge from the crystal in the direction of the transmitted portion.