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Nonlinear optical effects can be enhanced in tapered optical fibers with diameters less than the wavelength of the propagating light. Here we report on the observation of two-photon absorption using tapered fibers in rubidium vapor at power levels of less than 150 nW. Transit-time broadening produces two-photon absorption spectra with sharp peaks that are very different from conventional line shapes.Tapered optical fibers with small diameters can produce relatively high intensities at low incident power levels due to their small mode area. This has allowed a number of recent demonstrations of nonlinear optical effects at low power levels [1][2][3][4]. Here we describe an experiment in which enhanced two-photon absorption [5,6] was observed in tapered optical fibers in the presence of rubidium vapor. Two-photon absorption was observed at power levels of less than 150 nW. To put this in perspective, these power levels correspond to less than 20 photons on average in the tapered region of the fiber at any given time.Aside from its fundamental interest, two-photon absorption at low intensities may be useful for all-optical switching [2,7-10] or for quantum logic gates based on the Zeno effect [11][12][13]. The tapered optical fibers used in these experiments had diameters of 350 nm, which is less than half the wavelength of the light propagating in the fiber. As a result, atoms moving at thermal velocities pass through the evanescent field of the tapered region in a few nanoseconds, which produces interesting features in the shape of the two-photon absorption lines due to transit-time broadening.Two-photon absorption in a three-level atom is illustrated schematically in Fig. 1. A photon at frequency 1  is detuned from the resonant frequency of the first atomic transition by an amount  , which produces a virtual population of the second atomic state. A second photon at frequency 2  gives a detuning of the sum of the photon energies from the energy of the upper atomic state. We typically held for fixed power levels [5] and is thus considerably smaller than resonant two-photon absorption. We observed both types of two-photon absorption although the off-resonant two-photon absorption required somewhat higher power levels in order to maintain the signal to noise ratio. Tapered optical fibers were fabricated from standard single-mode fiber using the well-known flame brush technique [17]. Our setup was designed to consistently fabricate tapered fibers with diameters of approximately 350 nm over a length of 5 mm. This diameter was chosen to coincide with the optimal combination of mode compression and evanescent power [5,18] for nonlinear interactions using the 5S 1/2 to 5P 3/2 to 5D 5/2 transitions in rubidium, which have wavelengths of 780 and 776 nm, respectively.To heat and pull the fibers to the desired diameter, we used an air and propane flame with a ¼" diameter nozzle with three 1 mm holes in a line perpendicular to the fiber axis. The air and fuel flow were stabilized using regulators in combination with digita...

The diffusion characteristics of water in brain white matter were studied in patients with benign and secondary progressive multiple sclerosis (MS), and also in normal controls. In the MS patients, both lesions and normal-appearing white matter (NAWM) were examined to assess whether pathological differences might be evident from the diffusion behavior. A volume-selective technique was used to reduce data acquisition time and improve the reliability and precision of the measurements. This also allowed the time-dependence of apparent diffusion coefficients to be assessed. While lesions from both patient groups showed an elevated diffusion coefficient, no differences between the two groups were found. In addition, NAWM was elevated for both patient groups compared with the control group, although this was only statistically significant for patients with a benign disease course. The degree of elevation of the diffusion coefficient within the individual lesions measured was not related to the disability of the patient. Pathological differences between lesions in patients with different disease courses, if they exist, have not been detected in this study of brain water diffusion.

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