How thin can a microfiber be and still guide light?

For the adiabatically deformed optical fiber the intermode transmission amplitudes and loss vanish exponentially with the characteristic length of the fiber's nonuniformity. For this reason smoothly deformed optical fiber tapers can have very small losses. However, losses dramatically increase with a thinning of the microfiber down to a diameter much smaller than the radiation wavelength. The theory of nonadiabatic intermode transitions is briefly discussed and, by using this theory, the problem of the smallest diameter of a microfiber that can transmit evanescent radiation is studied. It is shown that even for an extremely high uniformity of microfiber the ability of light transmission does not leave much space for microfiber thinning: the propagating mode vanishes at a threshold value of the microfiber's diameter, that is smaller than the radiation wavelength by only an order of magnitude.     

How does the substrate affect the Raman and excited state spectra of a carbon nanotube?

We study the optical properties of a single, semiconducting single-walled carbon nanotube (CNT) that is partially suspended across a trench and partially supported by a SiO₂-substrate. By tuning the laser excitation energy across the E ₃₃ excitonic resonance of the suspended CNT segment, the scattering intensities of the principal Raman transitions, the radial breathing mode (RBM), the D mode and the G mode show strong resonance enhancement of up to three orders of magnitude. In the supported part of the CNT, despite a loss of Raman scattering intensity of up to two orders of magnitude, we recover the E ₃₃ excitonic resonance suffering a substrate-induced red shift of 50 meV. The peak intensity ratio between G band and D band is highly sensitive to the presence of the substrate and varies by one order of magnitude, demonstrating the much higher defect density in the supported CNT segments. By comparing the E ₃₃ resonance spectra measured by Raman excitation spectroscopy and photoluminescence (PL) excitation spectroscopy in the suspended CNT segment, we observe that the peak energy in the PL excitation spectrum is red-shifted by 40 meV. This shift is associated with the energy difference between the localized exciton dominating the PL excitation spectrum and the free exciton giving rise to the Raman excitation spectrum. High-resolution Raman spectra reveal substrate-induced symmetry breaking, as evidenced by the appearance of additional peaks in the strongly broadened Raman G band. Laser-induced line shifts of RBM and G band measured on the suspended CNT segment are both linear as a function of the laser excitation power. Stokes/anti-Stokes measurements, however, reveal an increase of the G phonon population while the RBM phonon population is rather independent of the laser excitation power.     

Are Leptons, Quarks or Both Highly Relativistic Bound States of a Minimally Interacting Fermion and Scalar?

The possibility that leptons, quarks or both might be highly relativistic bound states of a spin-0 and spin-1/2 constituent bound by minimal electrodynamics is discussed in the context of the two-body, bound-state Bethe?CSalpeter equation. For most interactions, strongly bound solutions exist only when the coupling constant is on the order of or greater than unity. However, for the bound-state system discussed here, in the strong-binding limit there exist two classes of boundary conditions that could yield solutions with coupling constants on the order of the fine structure constant. In both classes only bound states with spin 1/2 can exist, thus providing a possible explanation for the absence of higher spin leptons and quarks. Also, a mechanism for the suppression of the decay??? ?? e?+??? exists.     

How does the s(E + N) equation work? Comparisons with a modified Swain–Scott equation (E + sN) and revision of the N1 scale of solvent nucleophilicity

Modifications of the Swain–Scott equation (log k/k₀) = sn) give an equation log k₁ = (E + sN₁′); k₁ is the rate constant, E is an electrophilicity parameter, N₁′ is a solvent nucleophilicity parameter and s is an electrophile‐specific sensitivity parameter. The equation is tested using over 300 published first‐order rate constants (k₁) for decay of a range of benzhydrylium cations in various solvents, on which the published N₁ scale of solvent nucleophilicity is based (S. Minegishi, S. Kobayashi and H. Mayr, J. Am. Chem. Soc. 2004, 126, 5174–5181) using the alternative equation log k = s(E + N₁), in which s is a nucleophile‐specific parameter. The modified (E + sN₁′) equation provides a revised N₁′ scale of solvent nucleophilicity, and a more precise fit, with less than half the number of adjustable parameters. It is found that the sensitivities of the benzhydrylium cations to changes in solvent nucleophilicity decrease slightly as reactivity increases, in contrast to s(E + N) equations, which show no trends in s values. It is proposed that more reliable N scales can be defined using (E + sN), because N is determined directly from definitions, and residual errors (e.g. experimental or due to solvation effects) can be incorporated into the slope and intercept. The complex reasons for the success of equations of the type log k = s(E + N) are discussed. Copyright © 2009 John Wiley & Sons, Ltd.