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We report extensive laser-induced damage threshold measurements on dielectric materials at wavelengths of 1053 and 526 nm for pulse durations ranging from 140 fs to 1 ns. Qualitative differences in the morphology of damage and a departure from the diffusion-dominated 1/2 scaling of the damage fluence indicate that damage occurs from ablation for р10 ps and from conventional melting, boiling, and fracture for Ͼ50 ps. We find a decreasing threshold fluence associated with a gradual transition from the long-pulse, thermally dominated regime to an ablative regime dominated by collisional and multiphoton ionization, and plasma formation. A theoretical model based on electron production via multiphoton ionization, Joule heating, and collisional ͑avalanche͒ ionization is in quantitative agreement with the experimental results.

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An accurate numerical method is described for solving the Helmholtz equation for a general class of optical fibers. The method yields detailed information about the spatial and angular properties of the propagating beam as well as the modal propagation constants for the fiber. The method is applied to a practical graded-index fiber under the assumptions of both coherent and incoherent illumination. A spectral analysis of the calculated field shows that leaky modes are lost and steady-state propagating conditions are established over a propagation distance of a fraction of a meter.

Laser-induced damage threshold measurements were performed on homogeneous and multilayer dielectrics and gold-coated optics at 1053 and 526 nm for pulse durations t ranging from 140 fs to 1 ns. Gold coatings were found, both experimentally and theoretically, to be limited to 0.6 J͞cm 2 in the subpicosecond range for 1053-nm pulses. In dielectrics, we find qualitative differences in the morphology of damage and a departure from the diffusion-dominated t 1/2 scaling that indicate that damage results from plasma formation and ablation for t # 10 ps and from conventional heating and melting for t . 50 ps. A theoretical model based on electron production by multiphoton ionization, joule heating, and collisional (avalanche) ionization is in quantitative agreement with both the pulse-width and the wavelength scaling of experimental results.

The spectral method utilizes numerical solutions to the time-dependent Schrödinger equation to generate the energy eigenvalues and eigenfunctions of the time-independent Schrödinger equation. Accurate time-dependent wave functions ψ(r, t) are generated by the split operator FFT method, and the correlation function 〈ψ(r, 0) ‖ ψ(r, t)〉 is computed by numerical integration. Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of ψ(r, t) with respect to time generate the eigenfunctions. Previous applications of the method were to two-dimensional potentials. In this paper energy eigenvalues and wave functions obtained with the spectral method are presented for vibrational states of three-dimensional Born–Oppenheimer potentials applicable to SO2, O3, and H2O. The energy eigenvalues are compared with results obtained with the variational method. It is concluded that the spectral method is an accurate tool for treating a variety of practical three-dimensional potentials.