A sensitive single-beam technique for measuring both the nonlinear refractive index and nonlinear absorption coefficient for a wide variety of materials is reported. The authors describe the experimental details and present a comprehensive theoretical analysis including cases where nonlinear refraction is accompanied by nonlinear absorption. In these experiments, the transmittance of a sample is measured through a finite aperture in the far field as the sample is moved along the propagation path (z) of a focused Gaussian beam. The sign and magnitude of the nonlinear refraction are easily deduced from such a transmittance curve (Z-scan). Employing this technique, a sensitivity of better than lambda /300 wavefront distortion is achieved in n/sub 2/ measurements of BaF/sub 2/ using picosecond frequency-doubled Nd:YAG laser pulses. >

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Sensitive measurement of optical nonlinearities using a single beam

We present a simple yet highly sensitive single-beam experimental technique for the determination of both the sign and magnitude of n2. The sample is moved along the z direction of a focused Gaussian beam while the repetitively pulsed laser energy is held fixed. The resultant plot of transmittance through an aperture in the far field yields a dispersion-shaped curve from which n2 is easily calculated. A transmittance change of 1% corresponds to a phase distortion of ≃ λ/250. We demonstrate this method on several materials using both CO2 and Nd:YAG laser pulses.

High-sensitivity, single-beam n(2) measurements.

CRYSTALLINE MATERIALS Introduction Physical Properties Optical Properties Mechanical Properties Thermal Properties Magnetooptic Properties Electrooptic Properties Elastooptic Properties Nonlinear Optical Properties GLASSES Introduction Commercial Optical Glasses Specialty Optical Glasses Fused Silica Fluoride Glasses Chalcogenide Glasses Magnetooptic Properties Electrooptic Properties Elastooptic Properties Nonlinear Optical Properties Special Glasses POLYMERIC MATERIALS Optical Plastics Index of Refraction Nonlinear Optical Properties Thermal Properties Engineering Data METALS Physical Properties of Selected Metals Optical Properties Mechanical Properties Thermal Properties Mirror Substrate Materials LIQUIDS Introduction Water Physical Properties of Selected Liquids Index of Refraction Nonlinear Optical Properties Magnetooptic Properties Commercial Optical Liquids GASES Introduction Physical Properties of Selected Gases Index of Refraction Nonlinear Optical Properties Magnetooptic Properties Atomic Resonance Filters APPENDICES Safe Handling of Optical Materials Abbreviations, Acronyms, and Mineralogical or Common Names for Optical Materials Abbreviations for Methods of Preparing Optical Materials and Thin Films Fundamental Physical Constants Units and Conversion Factors

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Handbook of Optical Materials

A two-hand model is used to calculate the scaling and spectrum of the nondegenerate nonlinear absorption. From this, the bound electronic nonlinear refractive index n/sub 2/ is obtained using a Kramers-Kronig transformation. The authors include the effects of two-photon and Raman transitions and the AC Stark shift (virtual band blocking). The theoretical calculation for n/sub 2/ shows excellent agreement with measured values for a five-order-of-magnitude variation in the modulus of n/sub 2/ in semiconductors and wide-gap optical solids. Beam distortion methods were used to measure n/sub 2/ in semiconductors. The observations result in a comprehensive theory that allows a prediction of n/sub 2/ at wavelengths beneath the band edge, given only the bandgap energy and the linear index of refraction. Some consequences for all-optical switching are discussed, and a wavelength criterion for the observation of switching is derived. >

Dispersion of bound electron nonlinear refraction in solids

A substantial amount of work has been carried out in the area of nanocomposite materials for optical applications. Composites are typically constructed by embedding an optically functional phase into a processable, transparent matrix material. By doing so, the optical properties can be utilized in more technologically important forms such as films and fibers. This review covers many areas of optical composite research to date. Composites with second- and third-order nonlinearities and laser amplification properties are discussed with examples from the recent literature. Other composites, including transparent magnets, may be made using similar structures. The principles used to construct these composites may have important technological applications soon and are therefore summarized in this review.

Nanocomposite Materials for Optical Applications

The nonlinear refractive indices (${n}_{2}$) of a large number of optical crystals have been measured at a wavelength near one micrometer with use of nearly degenerate three-wave mixing. The measurements are compared with the predictions of an empirical formula derived by Boling, Glass, and Owyoung. This formula, which relates ${n}_{2}$ to the linear refractive index and its dispersion, is shown to be accurate to within about 30% for materials with nonlinear indices ranging over 3 orders of magnitude. Measurements for a number of binary oxide and fluoride crystals have been analyzed under the assumption that the hyperpolarizability of the anion is much larger than that of the cation. It is found that the hyperpolarizability of oxygen varies by a factor of 10, and that of fluorine varies by a factor of 7, depending on the size of the coordinating cation. This behavior is similar to that of the linear polarizability, although the hyperpolarizability is much more sensitive than the linear polarizability to the identity of the cation. The measured halide ion hyperpolarizabilities for several alkali-halide crystals are in reasonable agreement with recent self-consistent calculations. A semiempirical model was proposed by Wilson and Curtis to account for the dependence of the linear anionic polarizability on the radius of the cation. This model also accounts quite well for the variation of the hyperpolarizability of both fluorine and oxygen, except for cation partners that have filled or unfilled d-electron shells. The nonlinear indices of a number of complex oxides (i.e., those with more than one cation) have been calculated from the partial hyperpolarizabilities deduced from the data for the binary oxides. The calculated and measured values of ${n}_{2}$ agree to within an average error of 13%.

Nonlinear refractive index of optical crystals.

We have developed a rapid and accurate method for measuring the nonlinear refractive index of transparent materials. It is based on a version of three-wave mixing in which the frequencies of the two input beams are adjusted to differ by about 60 cm−1. The nonlinear index of a material is measured relative to that of a standard with a known index. Our measurements of 27 glasses are in good agreement with previous results, where available, and with the n2 values calculated empirically from linear index parameters. We also discuss the relationship between the observed nonlinear index and the structure and composition of the glasses.

Nonlinear refractive-index measurements of glasses using three-wave frequency mixing

One of the important parameters in the design of high power lasers is the nonlinear refractive index n2 defined by the expression n = n0 + n2(E2), where n0 is the familiar linear index and E is the optical electric field.

Dispersion of the nonlinear refractive index of optical crystals

https://www.osapublishing.org/viewmedia.cfm?uri=CLEO-1987-THE5&seq=0

Robert Adair

Papers

Nonlinear refractive index of optical crystals.

Nonlinear refractive-index measurements of glasses using three-wave frequency mixing

Dispersion of the nonlinear refractive index of optical crystals

Dispersion of the nonlinear refractive index of optical crystals

Nonlinear refractive-index measurements of glasses and crystals using three-wave frequency mixing