Optical Coupling of Mie Particles Adsorbed on a Whispering Gallery Resonator

We present an experimental observation on particles adsorbed to a whispering gallery mode (WGM) optical resonator produced from a glass sphere ≅100 μm in radius. For spherical adsorbates of radius a ≅100 nm (meso-optic, 2πa/λ ~1) we find a striking nonlinear dependence of the induced wavelength shift on the adsorbed particle density, whereas for Rayleigh particles with dimensions much smaller than the infrared wavelength the dependence is linear with particle density. An explanation of the anomalous effect based on optical coupling between meso-optic adsorbates is suggested. Ever since the pioneering work on high Q whispering gallery resonances in spherical micrometer sized resonators by Ashkin and Didzkic [1] there have been a plethora of articles [2] which have extended the measured “ultimate Q” [3] to ~10. The interest in such resonators has been fueled by a diversity of areas from studies of strong coupling in quantum electrodynamics [4] to ultra-sensitive bio-sensing [5]. The latter interest, which has produced a record sensitivity, depends on the shift in resonance frequency due to the perturbation by adsorbed nanoparticles (i.e. protein molecules, DNA, etc.). The recent experiments on DNA hybridization [6] and specific protein interactions [5] deal with adsorbates ~10 nm in size for which a first order perturbation theory of Rayleigh scattering has successfully been applied [7, 8]. Herein we present experiments on adsorbates in transition toward Mie sizes (meso-optic, size ~100 nm) and find an anomalous enhancement over the first order theory. In addition, our results have a fundamentally different form. Although the Rayleigh theory predicts a resonant wavelength shift in proportion to surface density, with meso-optic adsorbates the effect has a predominant density squared component. It appears that the new phenomenon is due to resonantly enhanced coupling between the adsorbed particles. In what follows we briefly describe our experimental approach, present the anomalous results on meso-optical particles and outline a theoretical approach based on the multiple scattering of the WGM by adsorbed particles. In our experiments we use a microsphere cavity as an ideal optical resonator for WGMs. Smaller particles can be bound to such a cavity. Such adsorbed particles perturb the WGM by interaction with the associated evanescent field. We use highly polarizable polystyrene spheres (called nanospheres) with a refractive index of n = 1.59 of varying size to perturb the WGM (Fig.1). We excite WGMs inside the silica microsphere cavity (n = 1.46) of typical radius R = 110 μm by evanescent coupling to a single mode fiber [9] which is eroded into its core by etching with hydrofluoric acid. [10]. The microspheres are made by melting the tip of a single mode fiber in a butane/nitrous oxide flame [11]. The fabricated sphere is mounted on a xyz stage and positioned in mechanical contact with the eroded fiber core, to enable evanescent coupling. Coherent light is transmitted through the single mode fiber from a current tunable distributed feedback laser operating at a nominal wavelength λ = 1312 nm. The fiber-transmitted intensity is detected by a photodetector at the other fiber end. We identify the resonance wavelength from the minima of a Lorentzian-shaped dip in the transmission spectrum [12]. This microsphere-fiber system is operated in an aqueous environment (salted phosphate buffer PBS, pH 7.4) with a Q ~2 x 10. The resonance wavelength is determined with a precision ~1/50 of the linewidth from a parabolic minimum fit of the resonance dip. A suspension of nanospheres of a given size is then injected into the liquid filled sample cell whereupon the nanospheres diffuse to and stably adsorb on the surface of the microsphere cavity. The resonant wavelength vs. nanosphere surface density is continually monitored from the point of injection. We use fluorescent, carboxylated polystyrene nanospheres to study the perturbative effect. The sample cell is examined with a standard fluorescence microscope equipped with a Xenon lamp and fluorescent filter set. The surface density of adsorbed yellow-green fluorescent nanospheres (Molecular Probes) is determined from an image taken with a cooled CCD camera. We plot the recorded wavelength shift versus the nanosphere surface density. For nanospheres of meso-optical size ~100 nm radius we observe an anomalous shift of the resonant line (Fig. 2). The wavelength shift is much larger than expected from our first order perturbation theory developed for Rayleigh particles. Furthermore, we observe a pronounced nonlinear dependence of the resonant line shift with nanosphere surface density . This effect is not seen for nanospheres of radii ~50 nm or smaller where the Rayleigh theory [7] applies. The mean field approximation to multiple scattering of nanospheres gives rise to the linear scattering, which is represented in Fig.2 by a solid line for the Rayleigh limit and by the dashed line when the evanescent field penetration depth is taken into account. For the larger nanospheres the theoretical explanation of the observed effect is challenging because of its departure from the Rayleigh regime and the relatively large polarizability of the adsorbates. A model for this strong nonlinear dependence of the resonant wavelength shift on the density of meso-optic adsorbates will be constructed below. The electromagnetic field induced in the cavity and the solution by the eroded optical fiber is determined by the macroscopic Maxwell equations with an inhomogeneous dielectric function,