A diffraction grating consisting of a periodic gradient in the index of refraction of a thin surface layer has been shown to be effective as a means of far-field coupling of monochromatic light into or out of the "whispering-gallery" electromagnetic modes of a transparent microsphere. This far-field coupling can be an alternative to the near-field (evanescent-wave) coupling afforded by prism- and fiber-optic couplers described in the immediately preceding article. Far-field coupling is preferable to near-field coupling in applications in which there are requirements for undisturbed access to the entire surfaces of microspheres. Examples of such applications include (1) a proposed atomic cavity in which cold atoms would orbit in a toroidal trap around a microsphere and (2) a photonic quantum logic gate based on coupling between a high-Q (where Q is the resonance quality factor) microsphere and trapped individual resonant ions.
In preparation for experiments to demonstrate this concept, fused silica microspheres with a diameter of about 180 μm were fabricated, then coated with layers of molten germanium-doped glass powder 3 to 5 µm thick. The purpose served by the germanium doping was to increase the photosensitivity of the surface layers for the grating-fabrication step described next. An index-of-refraction grating was formed in the surface layer of each microsphere by exposing the layer to ultraviolet light (wavelength = 244 nm) from a frequency-doubled argon laser. The laser beam power was 40 mW, the exposure time was 5 to 10 minutes, and the expected index modulation was (1 to 3) × 10-4. The spatial period and length of the grating were ≈2 µm and ≈15 µm, respectively. The spatial period was chosen to provide first-order phase matching between a whispering-gallery mode of the microsphere and a free-space beam oriented at ≈45° to the surface of the microsphere.
Figure 1 schematically depicts the experimental setup used to demonstrate the grating-based coupling scheme. Laser light at a wavelength of ≈1,550 nm was coupled into the whispering-gallery modes of a microsphere by a standard prism coupler, then coupled out of the microsphere by the grating. The laser was gradually tuned over a frequency range that included some whispering-gallery-mode resonances. The resulting measurements (see Figure 2) showed that at the resonances, some light was depleted from the input beam and there were corresponding increases in the amount of light emitted from the microsphere through the surface grating.
From the measurement data, the maximum grating coupling efficiency was calculated to be 14 percent. The grating loaded the resonance sufficiently to decrease the Q of the microsphere to a value in the range of (0.2 to 2) × 106. [The initial Q (without the grating) was 1.2 × 108.] Higher Q could be obtained by reducing the strength of the grating. Efficiency of coupling could be increased by optimizing the exposure to ultraviolet light, improving the grating profile, and minimizing scattering losses. Parasitic coupling to low-Q higher-order modes in the microsphere could be prevented by decreasing the diameter of the microsphere.
This work was done by Vladimir Iltchenko and Lute Maleki 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.
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