Quantum theory of spontaneous and stimulated emission of surface plasmons

We introduce a quantization scheme that can be applied to surface waves propagating along a plane interface. An important result is the derivation of the energy of the surface wave for dispersive non-lossy media without invoking any specific model for the dielectric constant. Working in Coulomb's gauge, we use a modal representation of the fields. Each mode can be associated with a quantum harmonic oscillator. We have applied the formalism to derive quantum-mechanically the spontaneous emission rate of surface plasmon by a two-level system. The result is in very good agreement with Green's tensor approach in the non-lossy case. Green's approach allows also to account for losses, so that the limitations of a quantum approach of surface plasmons are clearly defined. Finally, the issue of stimulated versus spontaneous emission has been addressed. Because of the increasing density of states near the asymptote of the dispersion relation, it is quantitatively shown that the stimulated emission probability is too small to obtain gain in this frequency region.Comment: 14 pages, 5 figures, submitted to Phys. Rev. B

Balanced homodyne detection in second-harmonic generation microscopy

We demonstrate the association of two-photon nonlinear microscopy with balanced homodyne detection for investigating second harmonic radiation properties at nanoscale dimensions. Variation of the relative phase between second-harmonic and fundamental beams is retrieved, as a function of the absolute orientation of the nonlinear emitters. Sensitivity down to approximately 3.2 photon/s in the spatio-temporal mode of the local oscillator is obtained. This value is high enough to efficiently detect the coherent second-harmonic emission from a single KTiOPO4 crystal of sub-wavelength size.Comment: 9 pages to appear in Applied Physics Letter

Two-photon real-time device for single-particle holographic tracking (red shot)

Three-dimension real-time tracking of single emitters is an emerging tool for assessment of biological behavior as intraneuronal transport, for which spatiotemporal resolution is crucial to understand the microscopic interactions between molecular motors. We report the use of second harmonic signal from nonlinear nanoparticles to localize them in a super-localization regime, down to 15 nm precision, and at high refreshing rates, up to 1.1 kHz, allowing us to track the particles in real-time. Holograms dynamically displayed on a digital micro-mirror device are used to steer the excitation laser focus in 3D around the particle on a specific pattern. The particle position is inferred from the collected intensities using a maximum likelihood approach. The holograms are also used to compensate for optical aberrations of the optical system. We report tracking of particles moving faster than 30 $\mu$m/s with an uncertainty on the localization around 40 nm. We have been able to track freely moving particles over tens of micrometers, and directional intracellular transport in neurites