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Within the framework of classical beam theory it is shown that a strain-independent surface stress has no effect on the natural frequency of a thin cantilever beam. Therefore, the experimental results of Lagowski, Gatos, and Sproles must have a different explanation.

Ultrasonic wave velocities in single-crystal quartz have been measured as a function of temperature and pressure by means of a pulse superposition method described in J. Acoust. Soc. Am. 33, 12 (1961). In order to make good use of all the experimental data, a set of "adjusted" velocities and initial pressure derivatives was obtained which satisfies all the cross-checks exactly, while minimizing a weighted sum of the squares of the adjustments from the measured values. These adjusted values were then used to calculate the elastic moduli as functions of temperature and pressure. Values of "zero-field" moduli at zero pressure and the initial pressure derivatives determined in this way are shown below.

Clad rods have been investigated for use as long delay lines because they offer isolation of the signal from the surface and low dispersion. In addition, single-mode propagation is achieved with a larger (and hence more conveniently transduced) cross section than is possible with a homogeneous rod at the same frequency. This paper describes the modes that have a steady-state sin(ωt−βz) dependence on (t,z), with emphasis on the modes and ranges of parameters that are of interest for delay lines. Only rods of circular cross section, and isotropic, linear elastic materials are considered. Attention is drawn to correspondences with homogeneous rods and with the hypothetical case of infinite thickness cladding, which is most useful as a model for understanding the behavior of corresponding modes in an actual clad rod. Written for the nonspecialist, the paper includes a tutorial review of the concepts and results needed to understand wave propagation in rods and clad rods. In addition, the following new results are reported: (1) for homogeneous rods, a representation of the lowest flexural mode dispersion curve that is for practical purposes independent of Poisson’s ratio; (2) for homogeneous rods, displacement distributions of the first three high-frequency shear modes, i.e., the ’’flexural’’ modes that are asymptotic to the shear velocity (it was found that the distribution previously attributed to the lowest such mode actually belongs to the next); (3) for clad rods, the first demonstration of interface modes of the Stoneley type for nonaxially symmetric waves; (4) classification of clad rods according to the nature and ordering of their asymptotic velocities showing that there are eight types of clad rod, rather than four as stated in the previous literature; (5) for infinitely clad rods having the same shear modulus, proof that the dispersion of torsional waves and their penetration into cladding are universal functions of f/fc∞. The ratio of the shear velocities of the two materials affects the cutoff frequency fc∞, but not the universal penetration and dispersion functions. Subjects on which significant tutorial or descriptive material is given include typical waveguide dispersion, characteristic velocities of an isotropic elastic material, the effect of coupling of dilatational and shear waves at a boundary, waves in homogeneous rods, the connection of isolation to total internal reflection (with Love waves and SH waves in a clad plate as an example), Stoneley waves at a plane interface, and previous results on the clad rod.

We present evidence of soliton propagation by 185-fsec dark pulses at a wavelength of 0.62 /zm in a 1.4-m length of single-mode optical fiber. Our experiments utilize specially shaped, antisymmetric input pulses, which closely correspond to the form of the fundamental dark soliton. At appropriate power levels the dark pulses propagate without broadening. Our measurements are in quantitative agreement with numerical solutions to the nonlinear Schrodinger equation and constitute the first clear observation of the fundamental dark soliton in optical fibers. PACS numbers:42.50.Qq, 42.65.Re, 42.81.Dp Although soliton phenomena arise in many distinct areas of physics, the single-mode optical fiber has been found an especially convenient medium for their study. Hasegawa and Tappert proposed in 1973 that the nonlinear refractive index in glass optical fibers could be utilized to compensate for group velocity dispersion (GVD), resulting in optical solitons which could propagate without distortion. 1 Since then, soliton propagation of bright optical pulses has been verified in a number of elegant experiments performed in the negative GVD region of the spectrum (X>\.3jjmin standard singlemode fibers) 2 ; most recently, transmission of 55-psec optical pulses through 4000 km of fiber was achieved, by use of a combination of nonlinear soliton propagation to avoid pulse spreading and Raman amplification to overcome losses. 3 For positive dispersion (A,<1.3//m), bright pulses cannot propagate as solitons, and the interaction of the nonlinear index with GVD leads to spectral and temporal broadening of the propagating pulses. These effects form the basis for the fiber-and-grating pulse compressor, 4 ' 5 which was utilized to produce the shortest optical pulses (6 fsec) ever reported. 6 For both signs of GVD, the experimental results are in quantitative agreement with the predictions of the nonlinear Schrodinger equation (NLSE).Although bright solitons are allowed only for negative dispersion, the NLSE admits other soliton solutions for positive GVD. 1,7 These solutions are "dark-pulse solitons," consisting of a rapid dip in the intensity of a broad pulse or a cw background. The fundamental dark soliton, for which we report here the first experimental observation, is predicted to be an antisymmetric function of time, with an abrupt K phase shift and zero intensity at its center. Other dark solitons with a reduced contrast and a lesser, more gradual phase modulation also exist. Throughout the text we will use the terms "black" and "gray" soliton, respectively, to refer to the fundamental and to the lower-contrast dark-soliton solutions.As a result of difficulty in generating the required input dark pulses, previous experimental evidence for dark-soliton propagation in fibers is limited. Krokel et al* reported the evolution of an even-symmetry, 300fsec dark pulse into a complementary pair of lowcontrast dark pulses, which they interpreted as gray solitons. Emplit et al. 9 performed experiments utilizing odd-symmetry dark pulses -...