Excitation Mechanisms of Whispering Gallery Modes with Direct Light Scattering

AbstractIn optics, whispering gallery modes (WGMs) are modes of light that arise in cylindrically symmetric structures. Their intensity profile is strongly confined around the interface of the structure, and their Q‐factors are some of the highest ever measured with light. Here, the physical mechanisms governing the coupling of a tangential beam into a WGM of a microsphere are analytically demonstrated. For that, Mie theory and the symmetries of light are made use of. It is demonstrated that the coupling mechanism is not related to any evanescent tunnelling effect. Rather, it is shown that it has to do with the angular momentum matching between the available inner WGMs of the sphere and the angular momentum content of the incident beam. The model is valid for any homogeneous sphere, for any wavelength, and for any incident cylindrically symmetric beam, focused or not. It quantitatively predicts the optical coupling efficiency to the resonator for any tangential position of the incident beam. And it sketches four different regimes of interaction depending on the beam position with respect to the sphere, properly matching experimental resonance spectra observed with free‐space laser scattering

Purcell factor of Mie resonators featuring electric and magnetic modes

We present a modal approach to compute the Purcell factor in Mie resonators exhibiting both electric and magnetic resonances. The analytic expressions of the normal modes are used to calculate the effective volumes. We show that important features of the effective volume can be predicted thanks to the translation-addition coefficients of a displaced dipole. Using our formalism, it is easy to see that, in general, the Purcell factor of Mie resonators is not dominated by a single mode, but rather by a large superposition. Finally we consider a silicon resonator homogeneously doped with electric dipolar emitters, and we show that the average electric Purcell factor dominates over the magnetic one

The role of the angular momentum of light in Mie scattering. Excitation of dielectric spheres with Laguerre-Gaussian modes

We present a method to enhance the ripple structure of the scattered electromagnetic field in the visible range through the use of Laguerre-Gaussian beams. The position of these enhanced ripples as well as their linewidths can be controlled using different optical beams and sizes of the spheres.Comment: 10 pages, 4 figures, 1 table, http://dx.doi.org/10.1016/j.jqsrt.2012.10.01

Control and characterization of nano-structures with the symmetries of light

Light beams can be symmetric under different transformations: translations, rotations, mirror symmetries, duality transformations, etc. In this thesis, a systematic way of characterizing these symmetries is presented. Then, it is shown that light beams symmetric under different transformations can be used to control light-matter interactions at the nano-scale. Particular applications are developed, both theoretically and experimentally. Inducing a dual behaviour on a non-dual sample, the excitation of high multipolar order resonances and the measurement of circular dichroism using vortex beams are among them.Comment: PhD Thesis, Department of Physics and Astronomy, Macquarie University. PhD Supervisor: Gabriel Molina-Terriz

Angular momentum-induced circular dichroism in non-chiral nanostructures

Circular dichroism (CD), i.e. the differential response of a system to left and right circularly polarized light, is one of the only techniques capable of providing morphological information of certain samples. In biology, for instance, CD spectroscopy is widely used to study the structure of proteins. More recently, it has also been used to characterize metamaterials and plasmonic structures. Typically, CD can only be observed in chiral objects. Here, we present experimental results showing that a non-chiral sample such as a sub-wavelength circular nano-aperture can produce giant CD when a vortex beam is used to excite it. These measurements can be understood by studying the symmetries of the sample and the total angular momentum that vortex beams carry. Our results show that CD can provide a wealth of information about the sample when combined with the control of the total angular momentum of the input field

On the transformations generated by the electromagnetic spin and orbital angular momentum operators

We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and frequency and that the "orbital angular momentum" operators generate transformations which are a sequence of this kind of translations and rotations. We give some examples of the use of these operators in light matter interaction problems. Their relationship with the helicity operator allows to involve the electromagnetic duality symmetry in the analysis. We also find that simultaneous eigenstates of the three "spin" operators and parity define a type of standing modes which has been recently singled out for the interaction of light with chiral molecules. With respect to the relationship between "spin angular momentum", polarization, and total angular momentum, we show that, except for the case of a single plane wave, the total angular momentum of the field is decoupled from its vectorial degrees of freedom even in the regime where the paraxial approximation holds. Finally, we point out a relationship between the three "spin" operators and the spatial part of the Pauli-Lubanski four vector

Dual and anti-dual modes in dielectric spheres

We present how the angular momentum of light can play an important role to induce a dual or anti-dual behaviour on a dielectric particle. Although the material the particle is made of is not dual, i.e. a dielectric does not interact with an electrical field in the same way as it does with a magnetic one, a spherical particle can behave as a dual system when the correct excitation beam is chosen. We study the conditions under which this induced dual or anti-dual behaviour can be induced.Comment: 13 pages, 5 figure

Far-field measurements of vortex beams interacting with nanoholes

We measure the far-field intensity of vortex beams going through nanoholes. The process is analyzed in terms of helicity and total angular momentum. It is seen that the total angular momentum is preserved in the process, and helicity is not. We compute the ratio between the two transmitted helicity components, $\gamma_{m,p}$. We observe that this ratio is highly dependent on the helicity ($p$) and the angular momentum ($m$) of the incident vortex beam in consideration. Due to the mirror symmetry of the nanoholes, we are able to relate the transmission properties of vortex beams with a certain helicity and angular momentum, with the ones with opposite helicity and angular momentum. Interestingly, vortex beams enhance the $\gamma_{m,p}$ ratio as compared to those obtained by Gaussian beams

Transverse multipolar light-matter couplings in evanescent waves

We present an approach to study the interaction between matter and evanescent fields. The approach is based on the decomposition of evanescent plane waves into multipoles of well-defined angular momentum transverse to both decay and propagation directions. We use the approach to identify the origin of the recently observed directional coupling of emitters into guided modes, and of the opposite Zeeman state excitation of atoms near a fiber. We explain how to rigorously quantify both effects, and show that the directionality and the difference in excitation rates grow exponentially with the multipolar order of the light-matter interaction. We also use the approach to study and maximize the transverse torque exerted by an evanescent plane wave onto a given spherical absorbing particle. The maximum occurs at the quadrupolar order of the particle, and for a particular polarization of the plane wave. All the obtained physical insights can be traced back to the two main features of the decomposition of evanescent plane waves into transverse multipolar modes: A polarization independent exponential dominance of modes with large transverse angular momentum, and a polarization controlled parity selection rule.Comment: Last version with slight changes in the figures and tex