Optical whispering-galle microresonators ABSTRACT

Transcription

1 Optical whispering-galle microresonators Vladimir B. Braginsky, Mikhail L Gorodetsky, VladimirS. lichenko Moscow State University, Department of Physics, Moscow, Russia ABSTRACT Quality-factor at the wavelength VO.63,zrn is reported in -1OOum spherical resonators of fused silica with whispering-gallery modes (equivalent finesse 26 ). Quality-factor and effective thermal tunability of modes (up to 0.1%) is demonstrated in whispering-gallery microresonators of opticai glass. Dispersive bistability and other nonlinear effects are observed at the level of input power about tens of rnicrowatts. Nonlinear properties of optical whispering-gallery modes are investigated by mode cross-modulation technique. Prospects of applications in linear signal processing and quantumnondemolition measurements are outlined. Development of integrated and fiber optics stimulates the search for new types of compact devices. For several problems such as semiconductor laser stabilization, multiplexing and high-resolution spectrumanalysers, of special interest is the creation of a small (submillirneter) size high-q optical solid state resonator. In the existing types of resonators including Fabry-Perot and DBR cavities, the quality-factor substantially decreases with the reduction of resonator length. Q>106 are not available in resonators with dimensions less then 1000 L However, there exists a possibility to create an ultra-high resonator with dimensions D 100 L It can be realized on the basis of whispering-gallery (WG) modes - closed waves in axially symmetric dielectric bodies, undergoing total internal reflection [1J. At microwave frequencies sapphire disks of diameter D = cm possess at the wavelength % 1 3 cm [2,3J. If the radius of resonator exceeds several wavelength and surface quality is sufficient, the Q-factor is limited only by material losses. Transfer of this idea to the opticai area results in the creation of the optical whispering-gallery microresonators (OWGMR) 141. Initially optical structural resonances in rnicrospheres have been observed indirectly in the experiments on lasing in spherical samples of active crystals and later, in experiments on elastic and inelastic scattering on liquid droplets [5,6,7]. Estimated quality factor did not exceed 10. It can be easily shown that in resonators made of optically transparent materials, the quality-factor can be several orders of magnitude higher. In this paper we present a short review of our results concerning experimental realization and study of properties of specially prepared spherical microresonators of fused silica and optical glass with the radius R pm 14,8,91. Whispering gallery modes are E,H1 modes of dielectric sphere (see for example [1OJ) with l-m<<l and small q (q1, 2, 3... ), where 1 2mR/A is radial mode number, m - is azimuthal mode number and q - is mode order. These modes have the minimal volume of field localization and usually largest quality-factor. The e.m. field of these modes is concentrated near the surface of the resonator in the ' equator" area. Three main mechanisms limiting the Q-factor of spherical resonators operated at WG modes are i) internal absorption and scattering losses in dielectric, ii) radiative (bend) losses, iii) surface scattering: Q = Q,' + Q; + (1) The value of Q1a2/2rn (a is attenuation in the material, n - refractive index) does not depend significantly on the mode type and for modern optical materials Q can be extremely small. For fused /941$6.00 SPIE Vol Laser Applications (1993) / 283

2 silica Q. 6x10 for A. = 0.63 um and Q. do not prevent achieving of Q fxlo8. Radiative losses vanish exponentially with growing radius (index 1): Qr = e21_tll+v2)_( 2 for 2 = 1.55pm. For glass resonators, internal losses Here 1 for H1 and n2 for E1 modes, t are q-th zeroes of spherical bessel function of the order 1. According to this formula, Q>10 when R/A>20 and for q1. The third mechanism of losses in real resonators - surface scattering. It can be analyzed by methods that have been earlier developed for planar waveguides: 2Rr2 BV1 Q =i[j-tj' irq. (3) Here 0 - is the mean size of inhomogeneities and B - is the correlation length. For molecular size roughness cr O.3nm in resonator 100 pm in diameter one can count on Q>3x10. The above estimates demonstrate that the quality-factor Q>10 can be obtained in microresonators of fused silica several tens of microns in diameter. It is appropriate to note here that this figure is equivalent to Q-factor of meter-length Fabry-Perot resonator with 99% reflection of mirrors. For effective excitation of WG modes it is suitable to use prism coupler with refractive index np>n7. (Fig 1). (2) I Fig. 1 The scheme of prism coupler for excitation of high-quality WG modes in spherical microresonators 1 - reflected beam; 2 - output beam. The analysis for this coupler for WG modes in spherical resonators was presented in [8J. It was shown in particular, that effective coupling can be obtained with Gaussian-Hermittian wave beams focused on the prism inner surface under optimal angle O=arcsin(n/n). Critical coupling (100% absorption of incident power) is possible for resonators with the unloaded Q>10 6 and the diameter For larger resonators, higher unloaded Q are necessary to obtain critical coupling. 284 ISPIE Vol LaserApplications (1993)

3 We have experimentally studied spherical microresonators wn in thameter. They were fabricated of fused silica or glass in the flame of miniature burner or in focus of CO2 laser beam. For support and temperature control, resonators were formed on top of short stems with the diameter 1/10 1/3 that of the resonator. For measurement of the Q factor, we used a single-frequency He-Ne laser operated at the wavelength O.63ixra, with the frequency swept in the range of He-Ne mixture gain curve by piezo drive of the output mirror. Calibration of frequency sweeping was made by using the mixing of the probe laser output with RF modulated beam of additional He-Ne laser. Typical resonance corresponding to one of WG modes in fused silica sphere is shown in Fig.2; the second trace in the oscillogram is 7 MHz frequency marks obtained by optical mixing. The quality-factor of this resonance is lxlo 8 Maximum value of 2 was obtained in resonators of UV grade fused silica ("KUVI"). This Q-factor is only 2.5 times smaller than the limit imposed by fundamental internal scattering at this given wavelength. In terms of equivalent fmesse F, this demonstrated Q in 14Own resonators corresponds to the record up-to-date value of FQ/l 2.5x106. Typical modes have easily reproducable quality-factors with coupling of 5 10% (non-optimal beam matching). Mode spacing varied depending on size of OWGMR ( um) between 10 and 10 10Hz :::::JJ::-? TiJ Fig.2 Typical resonance curve of an optical whispering gallery mode of fused silica microresonator at the wavelength 633 nm (frequency 475 Thz); second trace is 7MHz frequency marks obtained by optical mixing. We have also tested WG microresonators of optical glass K8 and obtained at.%=o.631urn. High thermal coefficient of refraction index in glasses gives an opportunity to use glass rnicroresonators as tunable narrow-band optical filters. Demonstrated thermal tuning was 0. 1% of the mode with the relative resonance bandwidth of 10 ' and 150K temperature span of resonator [8]. Strong optical fields obtained in these resonators with relatively small pumping power, in combination with high Q-factor, translate into easily observable dispersive optical bistabiity and mode interaction, even with materials having small nonlinearity, such as fused quartz. In case when two modes are taken into consideration, linear dependence of mode's resonance frequency on the energy stored in another mode, can be employed for realization of quantum-nondemolition (QND) photon number measurement experiment [4]. As it was shown experimentally and theoretically [9], the small third-order Kerr nonlinearity (y3)=1x1o 14 esu) in fused quartz microresonators is added by two stronger nonlinear effects caused by SPIE Vol Laser Applications (1993)1 285

4 thermally induced refraction index changes due to nonzero absorption of light The first ("fast") type of thermal nonlinearity is associated with the thermal relaxation of the field localization area to the rest of the resonator. The second ("slow") thermal nonlinearity is caused by thermal relaxation of the resonator as a whole. - (5R)2 VT1 D j3) n(n2 1)o.n1 dn Ti 87tCvQa (4) R2 T2 = DNu' J3) n(n2 1)an2 dfl Vjr LT2 87t2CvQa (5) Here D - is thermal conductivity, Q=im/a2 is determined by absorption in resonator material, c, - specific thermal conductivity, V - and Veff are correspodingly the physical volume of the resonator and the volume of field localization, SR - is the effective thickness of the layer occupied by e.m. field. Nonlinearity of whispering-gallery modes was studied experimentally in the two-mode scheme. Signal laser radiation fed into one mode of the resonator was intensity-modulated by variable duration pulses. The shift of the resonance frequency of another mode caused by third-order nonlinearity was registered using additional probe laser tuned on the slope of the resonance curve. The results of this study are presented in Fig.3 [91 in form of time dispersion of equivalent y'3) measured for 200pm fused silica (3)(esu) v s 10-f 10-s t(s) Fig.3. Time dispersion of equivalent third-order succeptibility to describe nonlinearity-produced cross-modulation of WG modes. resonator. Solid line in Fig.3 is a theoretical prediction on mode cross modulation response, taking into account resonator decay time?q/co. The presence of three types of nonlinearity is obvious from Fig.3. Experimental results are in good agreement with theoretical predictions for '3T1 T1 and %'3T2 T2 given by formulas (4) and (5) for resonator of the given dimension. 286 ISPIE Vol LaserApplications (1993)

5 At the levels of absorbed power above tens of microwatts, most of the modes displayed dispersive optical bistability. In presence of two closely spaced modes (typical separation 5-20MHz; these pairs were usualy the result of coupling of counter-rotating modes via backscattering), Instability regimes were observed (Fig. 4). In several cases, we observed quasi-periodical and chaotic oscillations (Fig.5) corresponding to cyclic or random skips of resonator between two neighboring modes. 10 MH& Zms Fig.4. A nonlinear dublet of WG modes, provi ding conditions for optical tnistamllty Fig.5. Quasipeniodical oscillations, produced by cyclic jumps between two WG modes To conclude this report, let us make the following two remarks. 1) Despite the presence of two parasitic slow nonlmearities, high-q WG microresonators can be used for high-frequency low-controlling energy all-optical switching. In fused silica resonators, the best demonstrated threshold of bistabiity due to Kerr nonlinearity (j3' 1x1O 14 esu) was W=5O1uW, with the response time limited by resonator ringdown z1x1o 8s. It corresponds to the controlling energy of switching E1.5 pj. The estimates show that in WG microresonator of semiconductor-doped glass (yf3)=lxlo -9 esu [1 11; absorption allows Q10 7) of optimal dimension, the controlling energy can be reduced to a few photons at the rate about 1GHz. Slow thermal effects in semiconductor glass resonator will not be larger than those produced by intrinsic fast 3) In the two-mode scheme of QND photon-number measurements, semiconductor glass resonators also promise improvement of sensitivity down to few photons. 2) Low threshold of nonlinear, mainly thermal effects produces difficulties for "linear" applications of ultra-high-q OWGMRS. It is appropriate to note however that in many cases there is no nesessity to operate the cavity at power levels above few microwatts. Otherwise, strong thermal effects can be avoided either by moderate reduction of Q (loading), or by modifying resonator design to provide better cooling of field localization area. The latter can be achieved for example by embedding the sphere into lower refraction substrate. REFERENCES 1. R.D.Richtmyer, "Dielectric resonators," J.Appl.Phys., vol.10, pp , V.B.Braginsky, V.S.Ilchenko, Kh.S.Bagdasarov, "Experimental observation of fundamental microwave absorption in high-quality dielectric crystals," Phys.Lett.A, vol. 120, pp , A.N.Luiten, A.G.Mann, D.G.Blair, "Improved sapphire dielectric resonators for ultrastable oscillators," Ann.Symp.Freq.Control, Salt Lake City, V.B.Braginsky, M.L.Gorodetsky, V.S.Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys.Lett.A, vol. 137, pp , SPIE Vol LaserApplications (1993) /287

6 5. C.G.B.Garrett, W.Kaiser, W.LBond, "Stimulated emission into whispering-gallery modes of spheres" Phys.Rev., vol.124, pp.l8o7-l8og, AAshkin, J.M.Dziedzic "Observation of resonances in the radiation pressure on dielectric sphere," ys, vol.38, pp , R.E.Benner, P.W.Barber, J.F.Owen, R.K.Chang, "Observation of structural resonances in the flourescence spectra from microspheres," Phys.Rev.Lett.,vol.44,pp , S.P.Vyatchanm, M.LGorodetsky, V.S.Ilchenko, "Tunable narrow-band optical filters with whispering gallery modes," Zh.Prikl.Spektrosk. (russian), vol. 56, pp , V.S.Ilchenko and M.L Gorodetsky, "Thermal nonlinear effects in optical whispering gallery microresonators, Laser Physics, vol.2, pp , J.A.Straton, Electromagnetic theory, McGraw-Hill, New York, B.J.Ainsley, H.P.Girdlestone and D.Cotter, "Semiconductor-doped fiber waveguides exhibiting picosecond nonlinearities," Electron.Lett., vol.23, pp , / SPIE Vol Laser Applications (1993)