Slow Light in Coupled-Resonator-Induced Transparency

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.

Figure 1

Schematic illustration of the double microsphere system coupled to a fiber taper. $S_1$ and $S_2$ are the first and second spheres, respectively.

Figure 2

(a)–(f) The transmission spectra in the double sphere-fiber system as a function of the laser frequency detuning for different separation gap distances. The separation gap decreases from the top to the bottom figures. The solid circles are the experimental observations and the solid curves are the theoretical calculations based on Eq. (2). The frequency origin $\Delta \nu =0$ is taken at the resonance frequency of the first sphere, ${\nu }_1$. The parameters used are $x_1=0.999820$ and $y_1=0.999899$, (b) $y_2=0.999999999$, (c) $y_2=0.9999999974$, (d) $y_2=0.999999992$, (e) $y_2=0.999999986$, and (f) $y_2=0.999999965$, while $x_2=0.999975\pm 0.000010$. (g)–(l) The theoretical calculation of the transmission phase shift as a function of the frequency detuning. The parameters used in (g)–(l) are same as those in (a)–(f), respectively.

Figure 3

(a) The transmission spectrum as a function of the laser frequency detuning at a specific gap distance. The solid circles are the experimental observations and the solid curve is the theoretical calculation, where the parameters are $x_1=0.999820$ and $y_1=0.999899$, $x_2=0.999975$, $y_2=0.999999986$, and $\Delta {\nu }_{12}=13\mathrm{MHz}$. (b) The pulse propagation delay time through the double sphere-fiber system as a function of the frequency detuning. The solid circles are the experimental observations and the solid curve is the theoretical calculation based on Eq. (2). The parameters used are the same as for (a). (c) Transmitted pulse profiles through the double sphere-fiber system. The solid, dashed, and dotted curves are the pulse profiles at three laser detuning frequencies denoted as $A$, $B$, and $C$ in Fig. 3a, where $\Delta \nu =-240$, 13, and 41 MHz, respectively.

Figure 4

The open circles, solid diamonds, and solid squares are the experimentally observed propagation delay time (left scale), frequency width of the induced transparency window $\Delta {\nu }_{\mathrm{ind}}$ (inner right scale), and transmission peak of the transparency window $T_{\mathrm{ind}}$ (outer right scale), respectively. The solid, dashed, and dotted curves are the theoretical calculations, where $x_1=0.999820$, $y_1=0.999899$, and $x_2=0.999975$.