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.

Nonlinear Optical Crystals: A Complete Survey

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.

The propagation of intense optical beams through dielectric media induces changes in the refractive index which cause self-focusing and beam breakup in high-power laser systems. After a brief discussion of the origin and spatial anisotropy of refractive-index nonlinearities, methods for measuring the nonlinear refractive index coefficient are reviewed. The use of time-resolved interferometry is described in detail. Nonlinear indices for optical glasses and crystals measured at 1064 nm by this technique are tabulated. From these data, an empirical expression is given which, using the linear refractive index and partial dispersion, provides a good estimate of the nonlinear index of optical materials in the long-wavelength limit.

Nonlinear Refractive Index of Glasses and Crystals

We used 20 ns, 248 nm pulses to study surface and bulk damage in bare, polished samples of UV-transmitting glasses, fluoride crystals, and isomorphs of potassium dihydrogen phosphate (KDP). The intent was to test enough samples to establish the safe operating limits for currently available windows and crystals finished by routine techniques for optical fabrication. In fluoride crystals, thresholds for bulk inclusion damage and for rear-surface damage were comparable. The median rear-surface threshold was 16 J/cm2. The fluence limit in fused silica windows was determined by the threshold for rear-surface damage, which ranged from 5 to 9 J/cm2. For the isomorphs of KDP, the limiting fluence was the threshold for front-surface damage, which ranged from 3 to 9 J/cm2.

Bulk And Surface Damage Thresholds Of Crystals And Glasses At 248 nm

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Nonlinear Refractive Index of Glasses and Crystals

Bulk And Surface Damage Thresholds Of Crystals And Glasses At 248 nm