Optical micro-manipulation and trapping of micro-particles delivers a mechanical system in direct interaction with a beam of light. In this interaction, the optical properties such as polarisation, beam profile and wavelength of the trapping beam are important. Different beams are associated with different momentum transfer, trap stiffness and stabilisation properties, for example. One method to determine the best beam profile is through the use of the optical eigenmode approach. To use this method, we employ Mie scattering theory which enables the exact determination of the scattered field as a function of the incident field. More precisely, this approach allows us to calculate the Hermitian relationship between the incident field and the optical forces acting on the scattering objects. This Hermitian relationship defines also a set of orthogonal optical eigenmodes which deliver a natural basis to describe momentum transfer in light-matter interactions. This relationship defines also a set of orthogonal optical eigenmodes. Using these modes it is possible to define, for each numerical aperture, particle size or geometry, the optimal trapping beam.
We show that the fundamental eigenmode of a shallow optical bottle microresonator (also called a SNAP microresonator) can be made exceptionally uniform along its axial length. The introduced microresonator has the effective radius variation resembling the profile of a bat with ears and wings. Remarkably, reduction of the axial size of this microresonator by cutting the wings does not alter the uniformity of its fundamental eigenmode. Being of general interest, our findings pave a way for improving the perceptibility of micro/nanoparticle sensing. These results also suggest a bottle microresona…
We investigate the radiation patterns of sharp conical gold tapers, designed as adiabatic nanofocusing probes for scanning near-field optical microscopy (SNOM). Field calculations show that only the lowest order eigenmode of such a taper can reach the very apex and thus induce the generation of strongly enhanced near-field signals. Higher order modes are coupled into the far field at finite distances from the apex. Here, we demonstrate experimentally how to distinguish and separate between the lowest and higher order eigenmodes of such a metallic taper by filtering in the spatial frequency dom…
We present a method to determine the complex coupling parameter of a two-coupled-modes system by directly measuring the coupled eigenmodes rather than their eigenvalues. This method is useful because mode-mixing can be observed even if frequency shifts can not be measured. It also allows to determine the complex coupling parameter, from which we conclude that the observed coupling is mainly conservative. We observe mode-mixing in an optical microcavity, where the modes couple primarily at the mirror surface, as confirmed by AFM measurements. The presented method is general and can be applied t…
We determine the fundamental limit of the microresonator field uniformity. It can be achieved in a specially designed microresonator, called a bat microresonator, fabricated at the optical fiber surface. We show that the relative nonuniformity of an eigenmode amplitude along the axial length $L$ of an ideal bat microresonator cannot be smaller than ${{\frac{1}{3}}}{π}^2n^4_r{λ}^{-4}Q^{-2}L^4$, where $n_r,\ λ$ and $Q$ are its refractive index, the eigenmode wavelength and Q-factor. In the absence of losses ($Q=\infty $), this eigenmode has the amplitude independent of axial coordinate and zero …
The theoretical work of V.B. Braginsky predicted that radiation pressure can couple the mechanical, mirror-eigenmodes of a Fabry-Perot resonator to it's optical modes, leading to a parametric oscillation instability. This regime is characterized by regenerative mechanical oscillation of the mechanical mirror eigenmodes. We have recently observed the excitation of mechanical modes in an ultra-high-Q optical microcavity. Here, we present a detailed experimental analysis of this effect and demonstrate that radiation pressure is the excitation mechanism of the observed mechanical oscillations.
The resonant buildup of light within optical microcavities elevates the radiation pressure which mediates coupling of optical modes to the mechanical modes of a microcavity. Above a certain threshold pump power, regenerative mechanical oscillation occurs causing oscillation of certain mechanical eigenmodes. Here, we present a methodology to spatially image the micro-mechanical resonances of a toroid microcavity using a scanning probe technique. The method relies on recording the induced frequency shift of the mechanical eigenmode when in contact with a scanning probe tip. The method is passive…
A photonic molecule (PM) is a miniature diffractive optical structure composed of resonance microcavities called atoms (e.g., cylinders or spheres) supporting a set of high-quality eigenmodes. All atoms in a PM are coupled by the electromagnetic fields of eigenmodes, which form collective supermodes of the whole PM. We consider a particular type of mirror-symmetric PMs being optically excited simultaneously via two light channels (tapered fibers). Based on the numerical simulations, we show that the spectral composition of supermodes in such PM can be effectively manipulated by changing the ph…
We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields in free space and including scattering interactions. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of the intensity to define specific Optical Eigenmodes (OEi) that are pertinent to the interaction considered. Key applications include the optimization of the size of a focused spot, the transmission through sub-wavelength apertures, and of the optical force acting on microparticles. We verify experimentally the …
We demonstrate the stimulated Raman near-field microscopy of few molecules, measured only using near-field optical forces thereby eliminating the need for far-field optical detection. The molecules were excited in the near-field without resonant electronic enhancement. We imaged gold nanoparticles of 30 nm diameter functionalized with a self-assembled monolayer (SAM) of 4-nitrobenzenethiol (4-NBT) molecules. The maximum number of molecules detected by the gold-coated nano-probe at the position of maximum field enhancement could be fewer than 20 molecules. The molecules were imaged by vibrating…
Quantitative infrared nanoscopy: Probe-cavity eigenmodes and nano-gap polaritons for strongly coupled nanoscale optics
School of Physics and Astronomy, University of Minnesota Twin Cities（明尼苏达大学双城分校物理与天文学学院）；Dept. of Physics, University of California San Diego（加州大学圣地亚哥分校物理系）；Advanced Light Source, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室先进光源中心）；Dept. of Physics, Columbia University（哥伦比亚大学物理系）
Hot alkali metal vapors enclosed in sub-micron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at nanoscale. Here, we propose a novel approach for calculating the eigenmodes of a thin-vapor-layer beyond the limitations of the first-order perturbation theory in optical density for the case of quenching of atomic polarization upon collisions of atoms with dielectric walls. We show that higher-order optical density corrections lead to a remarkable density-dependent blue shift and deformation of the spectral line shapes of reflection…
We provide detailed comparisons between experimental findings and numerical simulations of large cooperatively interacting, spatially disordered metamaterial arrays, consisting of asymmetrically split rings. Simulation methods fully incorporate strong field-mediated inter-meta-atom interactions between discrete resonators and statistical properties of disorder, while approximating the resonators' internal structure. Despite the large system size, we find a qualitative agreement between the simulations and experiments, and characterize the microscopic origins of the observed disorder response. …
We have measured the photonic bandstructure of GaAs photonic-crystal waveguides with high energy and momentum resolution using near-field scanning optical microscopy. Intriguingly, we observe additional bands that are not predicted by eigenmode solvers, as was recently demonstrated by Huisman et al. [Phys. Rev. B 86, 155154 (2012)]. We study the presence of these additional bands by performing measurements of these bands while varying the incident light power, revealing a non-linear power dependence. Here, we demonstrate experimentally and theoretically that the observed additional bands are c…
Based on the scalar Helmholtz equation and the finite-difference approximation, we formulate a matrix eigenvalue problem for the calculation of propagation constants, beta(omega), in micro-structured optical fibres. The method is applied to index-guiding fibres as well as air-core photonic bandgap fibres, and in both cases qualitatively correct results are found. The strength of this approach lies in its very simple numerical implementation and its ability to find eigenmodes at a specific eigenvalue, which is of great interest, when modelling defect modes in photonic bandgap fibres.
Optical energy flow inside a dielectric microsphere exposed to an optical wave is usually codirected with its wave vector. At the same time, if the optical field in a microparticle is in resonance with a high-quality spatial eigenmode, referred to as the whispering-gallery mode (WGM), at least two regions of reverse energy flow emerge in the illuminated and shadow particle hemispheres. These areas are of considerable practical interest due to their enhanced optical trapping potential provided they should be previously cleared from particle material. In this paper, we consider a perforated micr…
The coupling of distinct systems underlies nearly all physical phenomena and their applications. A basic instance is that of interacting harmonic oscillators, which gives rise to, for example, the phonon eigenmodes in a crystal lattice. Particularly important are the interactions in hybrid quantum systems consisting of different kinds of degrees of freedom. These assemblies can combine the benefits of each in future quantum technologies. Here, we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with close…
