Direct observation of stopped light in a whispering-gallery-mode microresonator

We introduce the definition of group velocity for a system with a discrete spectrum and apply it to a linear resonator. We show that a positive, negative, or zero group velocity can be obtained for light propagating in the whispering-gallery modes of a microspherical resonator. The associated group delay is practically independent of the ring-down time of the resonator. We demonstrate “stopped light” in an experiment with a fused silica microsphere.

Figure 1

(Color online) (a) WGM frequencies of a microsphere with radius $R=150\mu \mathrm{m}$ and index of refraction $n=1.4$. The carrier frequency is equal to ${\nu }_0=478\mathrm{THz}$ (wavelength $\lambda =635\mathrm{nm}$), $l_0=2078$. The frequency difference between modes $a$ ($l_a=15$, $q_a=5$) and $b$ ($l_b=4$, $q_b=6$) is equal to $\delta {\nu }_{ab}=48\mathrm{GHz}$. (b) An interference pattern on the surface of the microsphere is created by modes $a$ and $b$. We have assumed that the modes are fundamental azimuthal, i.e., $m=l$ for each mode.

Figure 2

(a)–(d) Interference patterns observed on the surface of a $300\text{−}\mu \mathrm{m}$-diameter optically pumped microsphere. Note the static interference pattern that exists despite the traveling-wave (clockwise) excitation. Light coupling is achieved with angle-cleaved fibers. The second output beam is due to precession of light in the WGM resonator. (c) and (d) are the same pattern observed by focusing the microscope on either the front or the back surface of the microsphere. The transitions between patterns (a), (b), and (c) were realized by tuning the coupling to allow the input light to interact with different mode families.

Figure 3

Theoretical model of the pattern in Fig. 2a. Six degenerate modes were taken into consideration.