Analytical description of high-aperture STED resolution with 0-2π\pi vortex phase modulation

Stimulated emission depletion (STED) can achieve optical super-resolution, with the optical diffraction limit broken by the suppression on the periphery of the fluorescent focal spot. Previously, it is generally experimentally accepted that there exists an inverse square root relationship with the STED power and the resolution, yet without strict analytical description. In this paper, we have analytically verified the relationship between the STED power and the achievable resolution from vector optical theory for the widely used 0-2$\pi$ vortex phase modulation. Electromagnetic fields of the focal region of a high numerical aperture objective are calculated and approximated into polynomials, and analytical expression of resolution as a function of the STED intensity has been derived. As a result, the resolution can be estimated directly from the measurement of the saturation power of the dye and the STED power applied.Comment: (19 pages

Complex electronic states in double layered ruthenates (Sr1-xCax)3Ru2O7

The magnetic ground state of (Sr$_{1-x}$Ca$_x$)$_3$Ru$_2$O$_7$ (0 $\leq x \leq$ 1) is complex, ranging from an itinerant metamagnetic state (0 $\leq x <$ 0.08), to an unusual heavy-mass, nearly ferromagnetic (FM) state (0.08 $< x <$ 0.4), and finally to an antiferromagnetic (AFM) state (0.4 $\leq x \leq$ 1). In this report we elucidate the electronic properties for these magnetic states, and show that the electronic and magnetic properties are strongly coupled in this system. The electronic ground state evolves from an AFM quasi-two-dimensional metal for $x =$ 1.0, to an Anderson localized state for $0.4 \leq x < 1.0$ (the AFM region). When the magnetic state undergoes a transition from the AFM to the nearly FM state, the electronic ground state switches to a weakly localized state induced by magnetic scattering for $0.25 \leq x < 0.4$, and then to a magnetic metallic state with the in-plane resistivity $\rho_{ab} \propto T^\alpha$ ($\alpha >$ 2) for $0.08 < x < 0.25$. The system eventually transforms into a Fermi liquid ground state when the magnetic ground state enters the itinerant metamagnetic state for $x < 0.08$. When $x$ approaches the critical composition ($x \sim$ 0.08), the Fermi liquid temperature is suppressed to zero Kelvin, and non-Fermi liquid behavior is observed. These results demonstrate the strong interplay between charge and spin degrees of freedom in the double layered ruthenates.Comment: 10 figures. To be published in Phys. Rev.