Laser characterization of ultrasonic wave propagation in random media.

Lasers can be used to excite and detect ultrasonic waves in a wide variety of materials. This allows the measurement of absolute particle motion without the mechanical disturbances of contacting transducers. In an ultrasound transmission experiment, the wave field is usually accessible only on the boundaries of a sample. Using optical methods, one can measure the surface wave field, in effect, within the scattering region. Here, we describe noncontacting (laser source and detector) measurements of ultrasonic wave propagation in randomly heterogeneous rock samples. By scanning the surface of the sample, we can directly visualize the complex dynamics of diffraction, multiple scattering, mode conversion, and whispering gallery modes. We will show measurements on rock samples that have similar elastic moduli and intrinsic attenuation, but different grain sizes, and hence, different scattering strengths. The intensity data are well fit by a radiative transfer model, and we use this fact to infer the scattering mean free path.

1D energy transport in a strongly scattering laboratory model.

Radiative transfer (RT) theory is often invoked to describe energy propagation in strongly scattering media. Fitting RT to measured wave field intensities is rather different at late times, when the transport is diffusive, than at intermediate times (around one extinction mean free time), when ballistic and diffusive behavior coexist. While there are many examples of late-time RT fits, we describe ultrasonic multiple scattering measurements with RT over the entire range of times--from ballistic to diffusive. In addition to allowing us to retrieve the scattering and absorption mean free paths independently, our results also support theoretical predictions in 1D that suggest an intermediate regime of diffusive (nonlocalized) behavior.

Extracting the Green function from diffuse, equipartitioned waves.

A ballistic pulse launched in a strongly scattering random medium becomes diffusive after a few mean-free times. In this regime of diffusive propagation there is a net flux of energy away from the source. Eventually the flux goes to zero, in the equipartitioned regime, in which the signal consists of equal amounts of energy propagating in all directions. In this regime the two-point, two-time correlation of the wave-field should equal the sum of the advanced and retarded Green functions associated with the average medium. We observe the emergence of the Green function from this correlation at about 9 mean-free times in a highly heterogeneous rock sample.

A system for measuring complex dielectric properties of thin films at submillimeter wavelengths using an open hemispherical cavity and a vector network analyzer.

Quasi-optical (QO) methods of dielectric spectroscopy are well established in the millimeter and submillimeter frequency bands. These methods exploit standing wave structure in the sample produced by a transmitted Gaussian beam to achieve accurate, low-noise measurement of the complex permittivity of the sample [e.g., J. A. Scales and M. Batzle, Appl. Phys. Lett. 88, 062906 (2006); R. N. Clarke and C. B. Rosenberg, J. Phys. E 15, 9 (1982); T. M. Hirovnen, P. Vainikainen, A. Lozowski, and A. V. Raisanen, IEEE Trans. Instrum. Meas. 45, 780 (1996)]. In effect the sample itself becomes a low-Q cavity. On the other hand, for optically thin samples (films of thickness much less than a wavelength) or extremely low loss samples (loss tangents below 10(-5)) the QO approach tends to break down due to loss of signal. In such a case it is useful to put the sample in a high-Q cavity and measure the perturbation of the cavity modes. Provided that the average mode frequency divided by the shift in mode frequency is less than the Q (quality factor) of the mode, then the perturbation should be resolvable. Cavity perturbation techniques are not new, but there are technological difficulties in working in the millimeter/submillimeter wave region. In this paper we will show applications of cavity perturbation to the dielectric characterization of semi-conductor thin films of the type used in the manufacture of photovoltaics in the 100 and 350 GHz range. We measured the complex optical constants of hot-wire chemical deposition grown 1-µm thick amorphous silicon (a-Si:H) film on borosilicate glass substrate. The real part of the refractive index and dielectric constant of the glass-substrate varies from frequency-independent to linearly frequency-dependent. We also see power-law behavior of the frequency-dependent optical conductivity from 316 GHz (9.48 cm(-1)) down to 104 GHz (3.12 cm(-1)).