Observation of Normal and Anomalous Dispersions in a Microsphere Taper Fiber System

Abstract

A dielectric microsphere may be considered as an artificial photonic atom. The electromagnetic modes in the microsphere are completely assigned with indexes similar to those used to characterize simple atomic systems. Microsphere modes, as well as microring or microdisk, trap light in circular orbits near the sphere surface and strongly modify the phase of the interacting light, resulting in very steep dispersions. Pulse propagation experiments were performed in a system consisting of a fiber taper coupled with a silica glass microsphere, and it was shown that the light velocity in the system can be largely changed through the control of the coupling strength. Slow light was also demonstrated in a system in which two ultrahigh-Q silica microspheres of different diameters were coupled in tandem to a fiber taper demonstrating classical analog of electromagnetically induced transparency in atomic system. Here, we employed interferometric techniques based on the Mach-Zehnder interferometer for examining extremely steep dispersions induced by whispering gallery modes with a quality factor on the order of Q 1⁄4 10. Such a narrow resonance in the dielectric microsphere is comparable to that in cooled atomic systems. We successfully observed both normal and anomalous dispersions at the resonant frequency, depending on the coupling strength between the sphere and the fiber. Figure 1 shows our experimental system based on an interferometric setup. We used the second harmonics of a single mode ring cavity Nd3þ yttrium aluminum garnet (Nd3þ:YAG) laser with a line width of 1 kHz at 532 nm. The laser frequency was tuned using thermal control of the ring cavity length, over a mode-hop-free range of greater than 10GHz. The reference arm was empty, while the sample arm contained the microsphere-fiber system. Silica microspheres were fabricated from standard telecommunication optical fiber. The end of the etched fiber was fused using a CO2 laser and the microsphere formed due to the surface tension. The experiments were performed with a microsphere 60 mm in diameter. The fiber taper was also fabricated from the same telecommunication fiber. The typical fiber waist diameter at the coupling region was 0.5 mm. A large number of spectrally overlapping resonance modes exist within a microsphere. The fiber taper method is essential for coupling the incident light to a specific whispering gallery mode selectively and efficiently. The microsphere was attached to a translation stage controlled by a piezo actuator. The relative position between the sphere and the fiber were carefully adjusted so that we could observe spectrally isolated whispering gallery modes with proper coupling strength. The optical path length and dispersion were equalized in each arm as completely as possible. The fringe pattern was captured using a charge-coupled device (CCD) camera for each frequency increment. The observed interference patterns appeared as concentric circles due to the interference between the plain reference wave and the spherical wave from the sample arm. A least square fit for each fringe pattern was performed to extract the phase information in the transmitted light. Figures 2(a) and 2(b) show examples of transmission spectra through the microsphere fiber taper coupled system. These spectra were taken in two different whispering gallery modes at different laser frequencies in the mode-hop-free laser tuning range. The transmission dips appear when the incident laser frequencies are resonant at specific whispering gallery modes in the microsphere. The two whispering gallery modes shown in Figs. 2(a) and 2(b) are denoted as WG1 and WG2, respectively. The transmission minimum was Tmin 1⁄4 0:12, and the resonance width was 1⁄4 BS