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.

MicroRNAs (miRNAs) play crucial roles in regulating gene expression. Many studies show that miRNAs have been linked to almost all kinds of disease. In addition, miRNAs are well preserved in a variety of specimens, thereby making them ideal biomarkers for biosensing applications when compared to traditional protein biomarkers. Conventional biosensors for miRNA require fluorescent labeling, which is complicated, time-consuming, laborious, costly, and exhibits low sensitivity. The detection of miRNA remains a big challenge due to their intrinsic properties such as small sizes, low abundance, and high sequence similarity. A label-free biosensor can simplify the assay and enable the direct detection of miRNA. The optical approach for a label-free miRNA sensor is very promising and many assays have demonstrated ultra-sensitivity (aM) with a fast response time. Here, we review the most relevant label-free microRNA optical biosensors and the nanomaterials used to enhance the performance of the optical biosensors.

The Hermitian Cartesian quantum momentum operator $\mathbf{p}$ for an embedded surface $M$ in $R^{3}$ is proved to be a constant factor $-i\hbar $ times the mean curvature vector field $H\mathbf{n}$ added to the usual differential term. With use of this form of momentum operators, the operator-ordering ambiguity exists in the construction of the correct kinetic energy operator and three different operator-orderings lead to the same result. PACS: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization

The use of subwavelength diameter tapered optical fibers (TOFs) in warm rubidium vapor has recently been identified as a promising system for realizing ultralow-power nonlinear optical effects. However, at the relatively high atomic densities needed for many of these experiments, rubidium atoms accumulating on the TOF surface can cause a significant loss of overall transmission through the fiber. Here we report direct measurements of the time scale associated with this transmission degradation for various rubidium density conditions. Transmission is affected almost immediately after the introduction of rubidium vapor into the system, and declines rapidly as the density is increased. More significantly, we show how a heating element designed to raise the TOF temperature can be used to reduce this transmission loss and dramatically extend the effective TOF transmission lifetime.