CONTENTS 1. Introduction 2. Theory 3. Experiment and data 3.1. Experiment 3.2. Data 4. Comparison of ß2 values to theory 4.1. Two-photon absorption theory 4.2. Comparison to theory 5. Self-refraction 6. Optical limiter 7. Conclusion 8. Acknowledgments 9. References Abstract. Two-photon absorption coefficients ß2 of ten direct gap semiconductors with band-gap energy Eg varying between 1.4 and 3.7 eV were measured using 1.06 pm and 0.53 pm picosecond pulses. ß2 was found to scale as E93, as predicted by theory for the samples measured. Extension of the empirical relationship between ß2 and Eg to InSb with Eg = 0.2 eV also provides agreement between previously measured values and the predicted ß2. In addition, the absolute values of ß2 are in excellent agreement (the average difference being <26 %) with recent theory, which includes the effects of nonparabolic bands. The nonlinear refraction induced in these materials was monitored and found to agree well with the assumption that the self-refraction originates from the two-photon-generated free carriers. The observed self-defocusing yields an effective nonlinear index as much as two orders of magnitude larger than CS2 for comparable irradiances. This self-defocusing, in conjunction with twophoton absorption, was used to construct a simple, effective optical limiter that has high transmission at low input irradiance and low transmission at high input irradiance. The device is the optical analog of a Zener diode.

Using nonparaxial vector diffraction theory derived using the Hertz vector formalism, integral expressions for the electric and magnetic field components of light within and beyond an apertured plane are obtained for an incident plane wave. For linearly polarized light incident on a circular aperture, the integrals for the field components and for the Poynting vector are numerically evaluated. By further two-dimensional integration of a Poynting vector component, the total transmission of a circular aperture is determined as a function of the aperture radius to wavelength ratio. The validity of using Kirchhoff boundary conditions in the aperture plane is also examined in detail.

We discuss the origins and regions of validity of various near-field diffraction models. The complete Rayleigh-Sommerfeld model is found to accurately represent intensity distributions for axial distances up to and including the location of the aperture, a region where commonly used models fail. We show that near-field diffraction theory can be applied to the refraction of light at an interface between two different media yielding results that demonstrate the validity of Snell's law in the presence of diffraction. Calculations using near-field diffraction and Fourier optics are compared to experimentally measured intensity distributions.

We present full-band structure calculations of temperature-and wavelength-dependent two-photon absorption coefficients and free-carrier absorption cross sections in GaAs, InP, and 0.92 eV-band gap Ga 64 In 36 As and InP 60 As 40 alloys. The calculated coefficient decreases with increasing wavelength and band gap but increases with temperature. Using detailed band structure analysis, we identify various contributions to the free-carrier absorption in GaAs and InP. Although the free-carrier absorption is found to arise predominantly from hole absorption, we show that direct absorption by excited electrons is possible, leading to an enhanced free-carrier absorption coefficient. This excited state absorption could be exploited to modulate the transmission of light at communication wavelengths ͑of 1.33 or 1.55 m͒ with, for example, the more commonly available 0.8 m diode laser. We further show that the high-intensity transmission calculated with our values of nonlinear parameters in GaAs agrees very well with the measured values.