References [17�C19] describe a detailed review of recent MDR applications. The MDR are optical modes that are observed in dielectric resonator, and are excited by coupling light from a tunable laser into the resonator using a single mode optical fiber.A simplified description of the MDR phenomenon can be obtained by using geometric optics as shown in Figure 1. This description is valid when the wavelength of the light used to excite the optical modes is much smaller than the size of the optical cavity. In this geometric view, light coupled into the microsphere (for example using a single mode optical fiber) circles the interior of the sphere through total internal reflection as long as the refractive index of the sphere is larger than that of the surrounding medium.Figure 1.
Ray optics description of MDR in a sphere.The condition for optical resonance is 2�� Rn = l��, where �� is the vacuum wavelength of the light (supplied by a laser), l is an integer, R is the sphere radius, and n is the sphere refractive index. An external effect applied to the sphere that induces a change in both the radius, ��R, (mechanical strain) and the refractive index, ��n, (due to mechanical stress) leads to a shift in the optical resonance (MDR) as follows:��RR+��nn=���˦�(1)Therefore, any change in the index of refraction and radius of the microsphere induced by the external effect can be sensed by monitoring the change (shift) in the resonance (MDR) of the microsphere. Our earlier studies on MDR have shown that for most sphere materials (silica and polymers), ��R/R dominates over ��n/n and the latter can be neglected .
The general optical arrangement for these sensors is depicted in Figure 2. The optical modes are excited by coupling light from a tunable laser (with nominal power of a few mW) into the sphere using a single mode optical fiber as shown in Figure 2a. The optical fiber which carries light from the tunable laser serves as an input/output port for the microsphere. Brefeldin_A When the microsphere is brought in contact with a tapered section of the optical fiber its optical resonances are observed as sharp dips in the transmission spectrum at the end of the fiber as illustrated in Figure 2b.Figure 2.(a) Schematic of sensor system and (b) observed transmission spectrum.A key factor that makes this phenomenon attractive for sensor applications is the very large optical quality factors, Q, of the optical resonances. The observed line-width, �Ħ�, is related to the optical quality factor as Q = ��/�Ħ�. In our laboratories we can routinely achieve optical quality factor of 107.Here, we investigate the effect of angular velocity on the MDR shifts of spherical resonators that are used as sensing element as described above.