April 1, 1996 / Vol. 21, No. 7 / OPTICS LETTERS
Ultimate Q of optical microsphere resonators
M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko
Department of Physics, Moscow Slole University. Moscow. 119899, Russia
Received November 15, 1995
We demonstrate the quality factor Q = (0.8 ^ 0.1) x 1010 of whispering-gallery modes in fused-silica microspheres at 633 nm, close to the ultimate level determined by fundamental material attenuation as measured in optical fibers. The lifetime of ultimate Q is limited by adsorption of atmospheric water. Monitoring of adsorption kinetics with submonolayer sensitivity by Q factors and frequencies of whispering-gallery modes is demonstrated. The possibility of supermaterial Q's owing to intrinsic suppression of scattering losses in micropheres is discussed. £ 1996 Optical Society of America
Microspheres of fused silica with high-Q whispering-gallery (WG) modes (hereafter called microspheres,)1'3 are a novel type of optical resonator that are attractive for different applications. Most applications, especially projected cavity QED experiments,'!'5 require the realization of the highest possible Q. Since its first demonstration in 1987, microsphere Q has been improved from nearly 1 x 106 to (2-3) x 109 in the red and near-IR areas of spectrum.3'5 This Q was, however, at least three times smaller than the limit determined by intrinsic material losses. It was also reported that in regular laboratory conditions the Q factor deteriorates within a 1-h time scale, presumably because of deposition ofmicrodust or water vapors upon the microsphere surface.5 Thus far it has remained unclear whether a material-limited Q can be realized in experiment.
The quality factor of \VG modes is deter^i"0^. ^y several factors:
Q"=Q^+Q;.l+Q^^Q^,
where Qra^ denotes intrinsic radiative (curvature) losses; Qg's1, scattering losses on residual surface inhomogeneities; Qcom, losses introduced by surface contaminants; and Qniat, material losses. As frequently described, Qra^ vanishes exponentially with increasing size, so with D/\ >. 15, Qrad > 1011 {D is the microsphere diameter;
Ë is the wavelength). Q^ can prevail in intermediate-sized spheres. Calculations based on the model of Rayleigh scattering by molecular-sized surface clusters under grazing incidence and total internal reflection yield the following estimate for Qs.s.'-Qs.s=
”<ss
2^25where cr and
 are the rms size and the correlation length of surface inhomogeneities, respectively. With the numerical values o- = 0.3 nm and 5=3 nm reported for glass surfaces6 we obtain that Q^ “ 1 x 10"10 may be expected only in large spheres, D ” 100 fim. In the absence of contaminants the Q of large spheres may reach the limit defined by material losses. Optical attenuation in fused silica, investigated inten-sively in the context of fiber transmission optimization, at 633 nm is "7 dB/km (5 dB is bulk Rayleigh scatter-ing and 2 dB is absorption).' Therefore the principal limit for microsphere Q at 633 nm is
10
=0.9 x 10
a\
We measured the Q in microspheres of high-purity fused silica 500-1000 <um in diameter fabricated by an oxygen-hydrogen microburner. The Q factor was measured by means of energy damping time - = Q Iw of the \\G mode in the undercoupled regime. The radiation of the probe He-Ne laser ^swept in frequency by piezotranslation of one of the resonator mirrors) was fed into WG modes by a prism coupler. The necessary two-port configuration for selective measurement of WG mode output with only a single prism coupler was facilitated by use of "processing" modes'^ E, J7;,,, , ? = '"
ÒÚðñð mrirlps are characterized by two-lobe emission patterns with a prism coupler (mode index I is approximately equal to the number of wavelengths packed around the circumference of the microsphere; q is the number of field variations along the radius; all the above estimates are valid with I = ÿ-.Dn/A, g=l, and arbitrary ò è I). Unlike for the case of Fabry-Perot cavities with their fixed coupling to external beams, one can gradually turn off coupling to \VG modes ë zero by increasing the tunneling gap between the microsphere and the prism. This permits clear observation of saturation of the measured Q up to its intrinsic (unloaded) value. The ringdown signals were observed when we switched off the input beam by an acousto-optic modulator shutter. The latter was triggered by the increase of mode output as the probe laser was swept in the vicinity of the selected WG mode. The combined speed of the shutter and of the photodetector permitted measurement with a 10% error of Q ã 3 x 10®; below this value Q could be easily measured with the same uncertainty by means of the resonance linewidth of the modes.Figure 1 presents the energy damping curve for a record-Q 750-/^m microsphere, recorded ~ 1 min after fabrication. The exponential fit gives the value
ò = 2.7 ± 0.1 p.s, which together w^th instrumental errors yields Q = (0.8 ± 0.1) x 1010. This value ofQ closely approaches the ultimate prediction determined by material losses, and it was reproduced with 20% scatter in three resonators 600 to 900 /xm in diameter,454 OPTICS LETTERS / Vol. 21. No. 7 / April 1. 1996
5 t,^s
Fig. 1. Mode energy damping curve for a WG mode in a 750-^m sphere. Estimated damping time - = 2.7 ^is:
A = 633 nm.
each time between the 50th and the 60th second after fabrication.
Figure 2(a) shows a typical time dependence of Q. with the t = 0 point coinciding with the fabrication of microsphere (its removal from the flame after formation of sphere by surface tension forces). The Q-versus-t plot indicates quick decay of the record Q within the first 5 min toward ~•20r( of the record Q and slow-er saturation toward Q
=ã 1 x 109 with a much longer lifetime on a many-hour scale. Bakeout of the resonator at 400^ for 30 s resulted in partial restoration of Q [Fig.2(b)1, in favor of the water adsorption hypothesis.To obtain additional information on the kinetics of surface contamination, we also measured the time variation ofWG mode frequencies [Fig. 2<ci]. We provided a stable reference for measurement of the shift of WG mode frequencies by beating the probe laser light with an additional frequency-stabilized He-Ne laser. Resolution of the measurement was limited by the temperature drift of the microsphere in passive heat isolation (total dri.ft of the frequency of a selected mode in a saturated microsphere 5 h after fabrication smaller than 1 MHz for 20 min).
According to a current model of two-stage chemosorp-tion,9 after fast adsorption of oxygen upon a fresh SiO^ surface the following hemosorption of atmospheric water leads to formation of a layer of OH groups chemically bound to the surface. The reported duration of this process,10 of the order of 100 s, agrees both with the parameter of logarithmic fit of the Ar-versus-t plot [solid curve in Fig. 2(c)] and with the characteristic time of the initial fast drop of Q in our experiment. The resulting hydrated surface is a substrate for further adsorption of molecular water. After this stage, presumably completed in 20-30 min, only slow deposition of microdust particles is responsible for long-term degradation of Q. (In a hermetic box, we have observed Q °= 1 x 109 of a 350-/Lim resonator preserved during t 2 6 months.)
The results of measurement of WG mode frequency variation can be interpreted in terms of the thickness iSofan adsorbed layer:
/A^JXHzT
Ë 800 .where ^v is the current-frequency shift, v = 475 THz is the optical frequency, n^\ and nads are refractive
indices of silica and of the adsorbed layer, respectively, a numerical estimate is given for n^\ = 1.46, "ads = 1.33, and D = 750 /^m. According to results shown in Fig. 1(c), the total change in thickness of the adsorbed layer between 1 and 30 min is ~0.2 nm and corresponds to 1.5 monolayers.
Extrapolation of the results in Figs. 1 and 2 (to estimate the quality factor of a fresh microsphere) cannot be based on the logarithmic fit of the A v-versus-t plot. The kinetics of the initial stages of adsorption near t = Q can be different and requires specially arranged measurements close to the formation time, with attention to the possibility of laser-induced effects. (In our experiments the time interval between formation and first measurement points was limited by the transfer of the ready microsphere from the torch to the optical table and by alignment of the setup). However, the absence of an apparent shelf at the level Qmai in a Q-versus-f curve may indicate that Q > Qmat = 0.9 x 1010 can be expected at t = 0. We cannot rule out this possibility because scattering losses in microspheres can be smaller than in bulk material or fibers, in which the lowest attenuation in fused silica has been measured.
Indeed, the Rayleigh losses in fused silica are attributed to scattering of an electromagnetic wave on thermal and frozen fluctuations of density. For a free traveling wave this mostly paraxial scattering produces irreversible losses of energy by coupling the initial wave to the radiative modes of space. In a microsphere, because of its narrow angular distribution, this scattering must predominantly couple the initial mode to other close-frequency WG modes with similar configuration. However, this process is suppressed because of the rare spectrum and high Q of the modes. The only modes that efficiently couple to each
10 20 t,min
t,mm
Fig. 2. (a), (b) Effect of adsorption of atmospheric water on the damping time and (c) frequency of a WG mode in a 750-^m microsphere. (b) Illustrates the effect of 30-s bakeout at 400
"Ñ.other are originally degenerate opposite-rotating high-Q WG modes. This effect ofbackscattering results not in losses but in the splitting of resonances reported earlier."-12
Independently, larger Q can be expected closer to the minimum of attenuation in fused silica, promising at least 1.5 X 1011 at A = 1.55 //m. And, apparently, to preserve the record Q for applications, microspheres have to be prepared and contained in evacuated or dry-gas-filled chambers. Another possibility for preservation of the record Q is chemical treatment to prevent surface hydration in the atmosphere.
This research has been performed as part of collaborative project with the University of California and the Los Alamos National Laboratory and supported in part by the Quantum Optics Lab, California Institute of Technology. The authors are grateful to V. B. Braginsky, H. J. Kimble, H. Mabuchi, and S. Habib for helpful discussions.
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