Francesco Papoff

Geometrical Mie theory for resonances in nanoparticles of any shape

We give a geometrical theory of resonances in Maxwells equations that generalizes the Mie formulae for spheres to all scattering channels of any dielectric or metallic particle without sharp edges. We show that the electromagnetic response of a particle is given by a set of modes of internal and scattered fields that are coupled pairwise on the surface of the particle and reveal that resonances in nanoparticles and excess noise in macroscopic cavities have the same origin. We give examples of two types of optical resonances: those in which a single pair of internal and scattered modes become strongly aligned in the sense defined in this paper, and those resulting from constructive interference of many pairs of weakly aligned modes, an effect relevant for sensing. This approach calculates resonances for every significant mode of particles, demonstrating that modes can be either bright or dark depending on the incident field. Using this extra mode information we then outline how excitation can be optimized. Finally, we apply this theory to gold particles with shapes often used in experiments, demonstrating effects including a Fano-like resonance.We give a geometrical theory of resonances in Maxwells equations that generalizes Mie formulae for spheres to any dielectric or metallic particle without sharp edges. We show that the electromagnetic response of a particle is given by a set of modes of internal and scattered fields and reveal a strong analogy between resonances in nanoparticles and excess noise in unstable macroscopic cavities. We give examples of two types of optical resonances: those in which a single pair of internal and scattered modes become strongly aligned in the sense defined in this paper, and those resulting from constructive interference of many pairs of weakly aligned modes, an effect relevant for sensing. We demonstrate that modes can be either bright or dark depending on the incident field and give examples of how the excitation can be optimized. Finally, we apply this theory to gold particles with shapes often used in experiments.

Calculation of internal and scattered fields of axisymmetric nanoparticles at any point in space

We present a method of simultaneously calculating both the internal and external fields of arbitrarily shaped dielectric and metallic axisymmetric nanoparticles. By using a set of distributed spherical vector wavefunctions that are exact solutions to Maxwells equations and which form a complete, linearly independent set on the particle surface, we approximate the surface Green functions of particles. In this way we can enforce the boundary conditions at the interface and represent the electromagnetic fields at the surface to an arbitrary precision. With the boundary conditions at the particle surface satisfied, the electromagnetic fields are uniquely determined at any point in space, whether internal or external to the particle. Furthermore, the residual field error at the particle surface can be shown to give an upper bound error for the field solutions at any point in space. We show the accuracy of this method with two important areas studied widely in the literature, photonic nanojets and the internal field structure of nanoparticles.

Plasmon modes in single gold nanodiscs

Optical properties of single gold nanodiscs were studied by scanning near-field optical microscopy. Near-field transmission spectra of a single nanodisc exhibited multiple plasmon resonances in the visible to near-infrared region. Near-field transmission images observed at these resonance wavelengths show wavy spatial features depending on the wavelength of observation. To clarify physical pictures of the images, theoretical simulations based on spatial correlation between electromagnetic fundamental modes inside and outside of the disc were performed. Simulated images reproduced the observed spatial structures excited in the disc. Mode-analysis of the simulated images indicates that the spatial features observed in the transmission images originate mainly from a few fundamental plasmon modes of the disc.

Chaotic transients in a CO2 laser with modulated parameters: Critical slowing-down and crisis-induced intermittency

Abstract Chaotic transients have been experimentally observed in a CO 2 laser with modulated losses, a system which exhibits generalized bistability and chaos with different kinds of crises. In addition to the expected critical slowing down obtained when the laser modulation is switched towards a point in the vicinity of a bifuraction point, transients of different kinds appeared depending on the region of the bifuraction diagram which was explored. In particular, long-lived transients and crisis-induced intermittency were obtained when the control parameter is switched to a value for which the chaotic attractor has undergone a crisis. Switching inside one chaotic region allows to temporarily observe the unstable cycles which were predicted in previous theoretical studies. The existence of crisis-induced intermittency and of the unstable cycles is clearly related to the excitation caused by the switching and not to noise-induced jumps between different attractors. All the observed behaviours are consistent with those which were obtained in numerical simulations on a two-level model of the CO 2 laser with modulated losses.

The geometrical nature of optical resonances: from a sphere to fused dimer nanoparticles

We study the electromagnetic response of smooth gold nanoparticles with shapes varying from a single sphere to two ellipsoids joined smoothly at their vertices. We show that the plasmonic resonance visible in the extinction and absorption cross sections shifts to longer wavelengths and eventually disappears as the mid-plane waist of the composite particle becomes narrower. This process corresponds to an increase of the numbers of internal and scattering modes that are mainly confined to the surface and coupled to the incident field. These modes strongly affect the near field, and therefore are of great importance in surface spectroscopy, but are almost undetectable in the far field.

Coherent control of radiation patterns of nonlinear multiphoton processes in nanoparticles

We propose a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. We derive conditions on the external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. The control introduces narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts.

Evaluation of E. M. fields and energy transport in metallic nanoparticles with near field excitation

We compare two ways of calculating the optical response of metallic nanoparticles illuminated by near field dipole sources. We develop tests to determine the accuracy of the calculations of internal and scattered fields of metallic nanoparticles at the boundary of the particles and in the far field. We verify the correct transport of energy by checking that the evaluation of the energy flux agrees at the surface of the particles and in the far field. A new test is introduced to check that the surface fields fulfill Maxwells equations allowing evaluation of the validity of the internal field. Calculations of the scattering cross section show a faster rate of convergence for the principal mode theory. We show that for metallic particles the internal field is the most significant source of error.

Optical control of scattering, absorption and lineshape in nanoparticles

We find exact conditions for the enhancement or suppression of internal and/or scattered fields in any smooth particle and the determination of their spatial distribution or angular momentum through the combination of simple fields. The incident fields can be generated by a single monochromatic or broad band light source, or by several sources, which may also be impurities embedded in the nanoparticle. We can design the lineshape of a particle introducing very narrow features in its spectral response.

Signal amplification and control in optical cavities with off-axis feedback

We consider a large class of optical cavities and gain media with an off-axis external feedback which introduces a two-point nonlocality. This nonlocality moves the lasing threshold and opens large windows of control parameters where weak light spots can be strongly amplified while the background radiation remains very low. Furthermore, transverse phase and group velocities of a signal can be independently tuned and this enables us to steer it nonmechanically, to control its spatial chirping, and to split it into two counterpropagating ones.

Enhancing ultraviolet spontaneous emission with a designed quantum vacuum

We determine how to alter the properties of the quantum vacuum at ultraviolet wavelengths to simultaneously enhance the spontaneous transition rates and the far field detection rate of quantum emitters. We find the response of several complex nanostructures in the 200 - 400 nm range, where many organic molecules have fluorescent responses, using an analytic decomposition of the electromagnetic response in terms of continuous spectra of plane waves and discrete sets of modes. Coupling a nanorod with an aluminum substrate gives decay rates up to 2.7 × 103 times larger than the decay rate in vacuum and enhancements of 824 for the far field emission into the entire upper semi-space and of 2.04 × 103 for emission within a cone with a 60° semi-angle. This effect is due to both an enhancement of the field at the emitters position and a reshaping of the radiation patterns near mode resonances and cannot be obtained by replacing the aluminum substrate with a second nanoparticle or with a fused silica substrate. These large decay rates and far field enhancement factors will be very useful in the detection of fluorescence signals, as these resonances can be shifted by changing the dimensions of the nanorod. Moreover, these nanostructures have potential for nano-lasing because the Q factors of these resonances can reach 107.9, higher than the Q factors observed in nano-lasers.