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Journal of Nonlinear Optical Physics & Materials

SLOW LIGHT IN A TWO MICROSPHERE OPTICAL FIBER SYSTEM

Jing Zhang, Yundong Zhang, Xuenan Zhang, Bo Yu, DAN WU, He Tian, Ping Yuan, Nan Wang, Jinfang Wang

Published Dec 1, 2009• 12 citations
Publisher

Abstract

The condition of being undercoupled and overcoupled for the lower microsphere is investigated respectively in two microspheres coupled with a fiber taper system. The effective phase shift curves which could occur in normal dispersion to generate slow light are different based on both situations. The influence of the loss coefficient and coupler parameter for each microsphere is interpreted in detail.

DOI
10.1142/s0218863509004920

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The condition of being undercoupled and overcoupled for the lower microsphere is investigated respectively in two microspheres coupled with a fiber taper system. The effective phase shift curves which could occur in normal dispersion to generate slow light are different based on both situations. The influence of the loss coefficient and coupler parameter for each microsphere is interpreted in detail.
The dispersion relation in a system of a fiber taper coupled with a microsphere is investigated. On the undercoupling condition, in which the coupling strength between the sphere and the fiber is weak compared with the round-trip loss in the sphere, the system shows anomalous dispersion. On the other hand, on the overcoupling condition, in which the coupling strength is strong compared with the loss, the system shows normal dispersion. We performed pulse propagation experiments and observed both the slow light and the fast light relevant to the normal and anomalous dispersions in the single microsphere-fiber taper system, controlling the coupling strength between the sphere and the fiber. The observed pulse propagation times show good agreement with theoretical calculations based on a directional coupling theory.
We discuss the mechanism of fast and slow light generation when optical pulses propagate through a fiber taper coupled to an ultrahigh-Q microsphere system in the time domain. Fast and slow light are explained as interference effects between ballistic light through the fiber and circulated light within the sphere. One of the striking effects predicted by this model is dynamic pulse splitting in the transmitted pulse at the critical coupling condition, where the coupling strength between the sphere and fiber equals the round-trip loss in the sphere. By realizing this critical coupling condition experimentally, we observed this dynamic pulse splitting effect.
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
We performed optical pulse propagation experiments in a system in which two ultrahigh-Q silica microspheres of different diameters were coupled in tandem to a fiber taper to yield coupled-resonator-induced transparency. Nearly Gaussian-shaped optical pulses propagated with a large positive delay of 8.5 ns through a transparent frequency window, without significant attenuation, amplification, or pulse deformation, demonstrating classical analogy of the extremely slow light obtained with electromagnetically induced transparency.