Simple fiber-optic couplers have been devised for use in coupling light into and out of the "whispering-gallery" electromagnetic modes of transparent microspheres. The need for this type of coupling arises in conjunction with the use of transparent microspheres as compact, high-Q (where Q is the resonance quality factor) resonators, delay lines for optoelectronic oscillators (including microlasers), and narrow-band-pass filters.
In the whispering-gallery modes of a transparent microsphere, light orbits inside the sphere, where it is confined by total internal reflection. The high degree of confinement results in high Q (up to about 1010 in the absence of loading). To couple light into or out of the microsphere, it is necessary to utilize overlapping of (1) the evanescent field of the whispering-gallery modes with (2) the evanescent field of a phase-matched optical waveguide or of an optimized total-internal-reflection spot in a prism or similar component. Heretofore, such coupling has been implemented, variously, by use of tapered optical fibers, side-polished optical fibers, or prisms, all of which entail disadvantages:
- Tapered optical fibers are fragile, bulky, and difficult to fabricate.
- Side-polished optical fibers offer low efficiency.
- Prisms are bulky and require collimation and focusing optics to work with optical fibers.
In contrast, the present fiber-optic couplers are simple, compact, and relatively inexpensive. A coupler of this type is essentially a hybrid of a waveguide and a prism coupler, and provides direct coupling with high-Q whispering-gallery modes. The coupler is fabricated by cleaving and polishing the tip of a single-mode optical fiber at an angle to form a microscopic coupling prism integral with the fiber. The cleaved and polished surface lies at a small angle (π/2φ F) with the longitudinal axis of the fiber (see Figure 1). The angle is chosen to secure matching of phases of the waveguide and whispering-gallery modes; by Snell's law, the angle is given by φ = arcsin(nsphere/nfiber), where nsphere is the effective index of refraction for the whispering-gallery modes propagating around the sphere in closed circumferential orbits and nfiber is the effective index of refraction for the guided wave in the truncated region of the fiber-optic core.
In the absence of a nearby microsphere, light propagating along the fiber is totally internally reflected at the angled surface and then escapes through the end face of the fiber. If a microsphere is placed near the angled surface and within the evanescent field of the fiber-optic core, then there is an efficient exchange of energy in resonance between the waveguide mode of the fiber and a whispering-gallery mode of the sphere. Inasmuch as the angle-cut area of the fiber coincides, to a close approximation, with the area of overlap of the evanescent fields, the present coupler is functionally equivalent to a prism coupler, without need for collimation and focusing optics.
Figure 2 depicts an experimental setup that was used for testing this coupling method. Efficiency of input and output coupling was measured by simultaneous monitoring of the intensity of the light escaping from the end of the input optical fiber and the power transmitted to the output optical fiber. In the experiments, the gaps between the microsphere and the angled coupling faces of the optical fibers were adjusted to optimize contrast of resonances in input coupling and maximize the power transmitted to the output optical fiber.
The experiments showed that this method of coupling works well, allowing to couple, at resonance, up to 60 percent of the light from the input fiber into the microsphere. The total fiber-to-fiber insertion loss at resonance was about 6 dB, with the quality-factor ~108 at the wavelength 1.55 µm.
This work was done by Lute Maleki, Vladimir Iltchenko, and Steve Yao of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Physical Sciences category.