A nanoscale plasmonic metal film can amplify free-electron evanescent fields, leading to strongly enhanced light emission via Smith-Purcell effect through a mechanism analogous to the 'poor-man's superlens' for optical evanescent field enhancement. We demonstrate that a layer of silver a few tens of nanometers thick can amplify the evanescent field of free electrons in the same way that the plasmonic metal acts on the evanescent field of light. The enhancement of the evanescent field of free electrons is studied by analyzing the far-field emission from nano-gratings on the tips of optical fibers in a scanning electron microscope ( Fig. 1) and through numerical simulations showing an order of magnitude increase in Smith-Purcell radiation. The enhancement exhibited here for Smith-Purcell radiation may readily be applied to other forms of electron-beam-induced light emission.The electromagnetic energy of the evanescent field of free electrons exists in the form of evanescent waves and can be decoupled into light only when they are in close proximity to a slow-wave medium or optical inhomogeneity. The former gives rise to what is famously known as Cerenkov radiation, the latter to diffraction or Smith-Purcell radiation [1]. Since the exponential decay rate of such evanescent waves is proportional to the ratio of the frequency of the electromagnetic field to the velocity of the particle, high velocity, relativistic particles are more efficient in generating light in the optical part of the spectrum. Here, rather than increasing the energy of particles to achieve higher levels of conversion, we utilize a thin silver layer to amplify the rapidly decaying evanescent waves of nonrelativistic free electrons. In analogy to the 'poor-man's superlens' where the evanescent component of light from an object is restored by a thin silver layer to beat the diffraction limit [2], we consider a thin silver layer for the amplification of the free electron evanescent field before it is decoupled into light by a nano-grating. The period of the grating is chosen so that the Smith-Purcell emission wavelength in the surface-normal direction coincides with the plasmonic resonance

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A focused Laguerre–Gaussian beam scattered by a homogeneous prolate spheroidal particle is studied for on-axis incidence. An approach to expanding a focused Laguerre–Gaussian beam in terms of the spheroidal wavefunctions in spheroidal coordinates is presented. By using the localized approximations method, the beam-shape coefficients are evaluated and the results agree with the cases of on-axis incidence. Calculations of the far-field scattering intensity are performed to study the shaped beam scattered by a spheroid, which has different size parameters and eccentricities.

Partial reflection of linearly polarized Laguerre-Gaussian beams incident at a dielectric interface are studied beyond the paraxial regime. Based on the angular spectrum method and Taylor series expansion, we derive exact analytical expressions for the reflected electric field. This result holds in both the paraxial and nonparaxial regimes. The result is then extended to beams of arbitrary polarization and used to analytically calculate the transverse and longitudinal shifts of the beams' center of gravity. Finally, several numerical examples are performed to verify the analytical formulas we derived near the Brewster angle.