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A simple numerical method based on finite differences to solve the scalar wave equation encountered in optical fibers is presented. The method uses the Ricatti transformation to the scalar wave equation and is capable of analyzing fibers of arbitrary refractive index profiles. Achieving errors as low as 0.005% for propagation constants is possible for lower-order modes. However, the error seems to increase for frequencies closer to cutoff.

Nonlinear absorption coefficients have been calculated for certain direct-bandgap semiconductors at 0.694-microm, 1.06-microm, 1.318-microm, and 10.6-microm wavelengths and compared with experimental results. The second- order perturbation theories of Braunstein and Basov yield underestimates and overestimates, respectively, of the nonlinear absorption constants. The numerical values are dependent upon the use of appropriate effective band masses, dielectric constants, and electron spin degeneracy factors. However, the Keldysh model gives second-order absorption constants that are intermediate between the two perturbation calculations. Although the Keldysh model often underestimates the value, in general, it yields the estimate of the magnitude of the two-photon absorption coefficient. The one-photon band-edge absorption in GaAs and InSb is predicted surprisingly well by the Keldysh model.

An initial-value algorithm derived from the Ricatti transformation of the scalar-wave equation is used to find the eigenvalues of inhomogeneous cylindrical dielectric waveguides. The numerical accuracy of the technique is investigated for cladded parabolic and step-index cylindrical refractive-index profiles.

Third-order time-dependent perturbation theory, utilizing parabolic and nonparabolic energy bands and calculated (from band structure) higher bands as intermediate levels, and a Keldysh first-order model are used to calculate three-photon-absorption coefficients of several direct-gap crystals. Third-order perturbation results for CdS at 1.06 microm agree well with the experimental data.

The topical meeting on Optical Phenomena in Infrared Materials, sponsored jointly by the Optical Society of America and the U.S. Air Force Office of Scientific Research, was held in December 1976. The meeting stressed research on optical effects in materials for modern IR applications such as laser windows, solar energy conversion, infrared detection and integrated optics. The November 1977 issue of Applied Optics publishes a representative selection of the papers given.

Samples of ZBLA and HBLA glasses were subjected to various fluences of neutron irradiation, and the spectral dependence of optical absorption was measured before and after irradiation. The IR edge was found to be unaffected by neutron irradiation for the fluences used. However, a red shift occurred at the UV edge which slightly recovered after three weeks.

The pressure derivative of the refractive index (dn/dP) and the elastooptic constants (P(ij)) in the transparent frequency regime of semiconducting and ionic crystals are investigated theoretically. The electronic contribution to dn/dP of semiconductors is obtained by carrying out pseudopotential calculations of the band structure as a function of hydrostatic pressure, and the results compared with experiment. The lattice contribution to dn/dP is obtained by relating dn/dP to changes in the effective ionic charge and the phonon spectrum as functions of pressure. As for the P(ij), we perform a detailed application of the theory of Humphreys and Maradudin to calculate these for a variety of cubic crystals as functions of frequency in the transparent regime. The parameters required in the calculation are determined from improved prescriptions, which relate various microscopic functions to experimental data on the pressure dependence of phonon frequencies. The theoretical results are checked employing a relatio between dn/dP and the P(ij). Overall, one finds that frequency dispersion is most important for the ionic materials and is generally negligible for the more highly covalent materials.

The mixed crystal system KCl(1-x)Br(x) shows a one-mode type behavior. The variation of the long-wavelength transverse optical (TO) mode frequency at 1 atm pressure can be understood in terms of the virtual crystal model. The variation of the frequency with pressure or the mole fraction x can be expressed in terms of volume change alone. The slopes of the vTO mode vs P are highest for the end numbers, and are less for intermediate values of x, and may be understood in terms of a nonlinear variation of the compressibility with x.

Solid solution hardening has been reviewed with respect to existing experimental data. It is shown with the aid of new experimental data on two inorganic systems (NiO-CoO and CaF(2)-SrF(2)) that the large increase in hardness of intermediate compositions correlates qualitatively and can also be quantitatively justified by the use of selected values of the parameters in a previously developed atomistic hardness formula. The key parameters are the variations in the unit cell dimensions, the eigenfrequency, and anharmonic factor of the structure.