Self-focused beams to couple light into a whispering-gallery mode resonator
Kien Phan Huy, Jassem Safioui, Jean-Yves Rauch, Patrice Féron, Mathieu Chauvet
SSelf-focused beams to couple light into a whispering-gallerymode resonator ∗ Kien Phan Huy, Jassem Safioui, Jean-Yves Rauch, Patrice F´eron, and Mathieu Chauvet FEMTO-ST Institute, UMR CNRS 6174, Universit´e de Franche-Comt´e, 16 Route de Gray, 25000 Besan¸con, France FOTON-Syst`emes Photoniques (CNRS-UMR 6082), ENSSAT,6 rue de Kerampont, CS 80518, 22305 Lannion cedex, France compiled: November 12, 2018We propose an original method to couple light into a whispering-gallery mode resonator. This method benefitsfrom the mode selectivity and robustness of the prism-coupling along with the single-mode propagation ofthe fiber taper. It consists in a prism shaped crystal with a waveguide inscribed inside it. The waveguide isself-inscribed in-situ by beam self-trapping to allow an optimum coupling to a given resonator.
Since the seminal paper of Tien and Ulrich [1], prismcoupling has been a very successful coupling method. Itwas the natural choice in the late 80’s to characterizehigh-Q resonators [2]. Later on, a new method involv-ing side-polished or fused-fiber taper took over with thebenefit of optical fiber compatibility [3, 4]. In the prism-coupling method, the total internal reflexion (TIR) uponthe internal face of a prism is used to produce an evanes-cent field that couples with a whispering-gallery mode(WGM). A proper adjustment of the angle of incidenceenables to fine tune the propagation constant and insurethe phase matching with the WGM. For best coupling,the incident-beam size should be as close as possible tothe WGM size. To satisfy this criterion, light is usuallyfocused upon the coupling surface. However, focusingtoo much eventually leads to the coupling of neighbourWGMs with close propagating constants. Consequently,a compromise had to be found leading to an awkwardmethod. In the tapered fiber method, a standard opticalfiber is pulled when heated by a gas-burner or an electricheater. The waist of the fiber is then adiabatically re-duced along the fiber. As the guided mode propagates,it reaches the smallest diameter region (typically 1 µ m)where the light is guided by TIR at the interface be-tween silica and air. Due to the small core diameter, theevanescent field extents in air, thus couples to the WGMresonator. Unfortunately, this method suffers from theinherent fragility of the device. All the more, a goodcontrol of the fusion-pulling process is needed to reachthe proper propagating constant, hence, a less flexiblemethod compared to the prism coupling [4].In this paper, we propose an alternative method com-bining the flexibility of the prism-coupling and a guidedpropagation. We use a prism-coupling set-up that in- ∗ Corresponding author: [email protected] volves a prism made of a nonlinear material. The prism-coupling configuration enables to fine tune the phasematching at low power. At high power, the light beaminduces its own waveguide thanks to the optical nonlin-earity and is thus self-confined, and travels like a mode,that is a typical feature of the tapered fiber couplingmethod. As the beam goes through TIR, it is coupledto a silica micro-sphere resonator. The reflected beamat the output of the prism is confined and the WGMresonance is observed.An isosceles prism is diced from a z-cut stoichiomet-ric LiNbO refractive index isabout n=2.2, the two equal angles of the isosceles prismare chosen to be 37.4 ◦ to match the refractive index ofthe silica microsphere. The optical set-up is described inFig. 1(a). The polarized beam of a tunable laser with a650-660nm wavelength range (Newfocus Velocity 6305)is coupled into a Polarization Maintaining Fiber (PMF)in order to get spatial filtering and a convenient controlof the polarization. The output of the fiber is imaged atthe input face of the prism with two lenses (L2-L3) anda diaphragm D1 enables fine tuning of the beam waistat the prism input. Part of the beam is reflected at theprism input and is imaged through L4 on a CCD cam-era. The launched beam profile can thus be monitored.The transmitted light propagates inside the prism and is a r X i v : . [ phy s i c s . op ti c s ] J u l TunableLaser PMFL1 D1z (c-axis)x yE(b) (c)
Negative chargesPositive chargesInduced optical waveguide - --+ + z (c-axis)x y - - - - - - - - - -- - -+ + + + + + + + + + ++++++- + + ++
OD L2
C C D C a m e r a CCD C a m e r a L3 L4 L5resonatorPrism(a) PE
Fig. 1. (a) Experimental setup for writing and probingwaveguides inscribed by self-trapped beams. D1,D2: Di-aphragms. PC: Polarization controller. OD: Optical density.L1 ,L2, L3, L4 and L5 lenses. PBS: Polarizing Beam Splitter.HWP: Half-Wave plate. PE: Peltier Element. (b) Diffractingbeam at low power. (c) Self-trapped beam. subject to TIR on the opposite face where the couplingwith the micro-resonator occurs. The relative positionbetween the resonator and the prism is controlled by a3-axis stage. After reflection upon the coupling area, thereflected beam reaches the ouput face of the prism andis imaged on a second CCD thanks to lens L5.The optimum coupling angle is found in two steps.First we search for the proper angle that enlighten themicro-resonator at binocular sight. Then the beam is fo-cused with L3 at the TIR point to optimize the couplingsurface area, and we search for resonances. Once theproper angle is found, we pull back L3 to focus on theprism input with the desired beam width for the nonlin-ear regime. The self-trapped beam is obtained thanksto the photorefractive effect that will be discussed in thefollowing paragraph.In the linear regime, the light diffracts freely in thecrystal as shown in Fig 1(b). In the non-linear regime,we slightly increase the temperature of the LiNbO crys-tal. A pyroelectric internal electric field ∆ E py appearsand decreases the refractive index all over the crystalbecause of the Pockels effect. However, at the inputof the crystal, the focused beam generates free elec-trons because of the photoelectric effect. Those optical-generated free carriers drifts along the c-axis becauseof the pyroelectric field and recombine. The resultingspace-charge field E partially screens ∆ E py . In the areawhere the field is screened, the refractive index is less af-fected which results in a localized high refractive indexthat eventually traps the light beam (Fig. 1(c).). Be-cause the space-charge field E results from deep-centerrecombination, the resulting waveguide lasts even if the temperature is lowered. In our set-up, a Peltier elementis placed under the crystal to control its temperature asdepicted in Fig 1(a). In LiNbO crystals, a moderatetemperature increase ∆ T = 20 ◦ C leads to an internalelectric field as high as ∆ E py = 47kV/cm [7, 9]. For x(mm) y ( mm ) (a) Injectedbeam−0.2 0 0.2−0.200.2 x(mm) y ( mm ) (b) Outputdiffractedbeam−0.2 0 0.2−0.200.2 x(mm) y ( mm ) (c) Outputfocusedbeam−0.2 0 0.2−0.200.2 Fig. 2. (a) Injected beam profile. (b) Diffracting beam pro-file at low power. (c) Self-trapped beam in nonlinear regime. strong-coupling efficiency, the beam profile should be assimilar as possible to the microsphere mode size to max-imize the overlap between the evanescent part of thefields. However, for WGMs, a weak-coupling regime isusually preferred to keep the Q-factor high. Analyticcalculations show that high-Q WGMs are present in ourlaser tuning range with a beam FWHM around 5 µ m [10].We choose a trade-off input beam of 18 µ m FWHM thatis typical for self-focussing experiment in LiNbO as de-picted in Fig. 2(a). In Fig. 2(b), the beam observedat the output face is reported in the linear regime aswitnessed by the diffraction of the beam. Note that noresonance was observed in this configuration, because ofthe poor overlap between the diffracted beam and theWGM. To reach the nonlinear regime, the pyroelectriceffect is triggered with a temperature increase of theLiNbO sample of ∆ T = 33 ◦ C and the light power israised to 152 µ W. In about an hour, the beam is self-focused thanks to the photorefractive effect. In Fig. 2(c),the crystal output beam is shown, a clear confinementis seen. It has a 16 . µ m FWHM along the vertical axis(c-axis) and 42 . µ m along the horizontal one. As aresult, the overlap between the beam and the WGM isimproved and WGM resonances can be measured. Theoutput camera is replaced with a photodiode and thelaser frequency is periodically swept over few tens of GHzas depicted in the inset of Fig. 3. The measurement istypical of a high-Q resonator hysteretic frequency re-sponse. The WGM resonance is broader for increas-ing frequency sweep as the thermal nonlinearity of theresonator shifts the resonance in the same direction asthe laser frequency. When the laser frequency is shiftedbackward, the resonance is still shifted upward and doesnot follow the resonance anymore, as a consequence athiner resonance peak is obtained[2, 11]. The resonancedip reported in Fig. 3 corresponds to a forward sweep.A raw Q-factor of the WGM over 90000 is deduced fromthe 5 GHz width of the dip in transmission. An analyticcalculation of the WGMs of the sphere with parameters(l,m,n) as described by Little et al. [10] shows that for500 < l <
900 up to 11 modes can be found within the −80 −60 −40 −20 0 2011.81212.212.412.6 detuning (GHz) T r a n s m i tt e dp o w e r ( a . u . ) −0.2 −0.1 0 0.1 0.2 0.3−101 time (s) I a n d l a m bd a ( a . u . ) transmittedpowerwavelength Fig. 3. Detail of the whispering-gallery-mode resonance.Inset: Large-scale scanning of the resonance. Dashed lineshows the wavelength scanning with respect to time.
100 GHz scanning range of our experiment. However,only one of these modes is a fundamental mode ( l = m ).The presence of only one dip in the measured spectrumis therefore a confirmation of the good modal selectivityof our method.Note that once the writing phase is realized a waveg-uide is inscribed in the prism. This waveguide has theproper characteristics to guide light with the right tra-jectory and the adapted mode profile to couple effi-ciently to the resonator. It takes advantage of the uniqueproperties of self-alignment and confinement provided bytrapped beams.To conclude, we have reported light coupling in aWGM resonator with the help of a self-trapped beam.This original configuration gathers both the flexibilityof the prism coupling and the benefit from the waveg-uide confinement. In addition, it is mechanically morerobust than the fiber-taper method. Improvements ofthe method are foreseen by optimizing the output beamshape through a better control of the dynamic of thenonlinear effect. The concept can be extended to otherphotosensitive materials such as photopolymers to fab-ricate permanent sturdy coupling to resonators.We are grateful for financial support by Agence Na-tional de la Recherche for project ORA (ANR 2010BLAN-0312). This work was realized in the frameworkof the French Labex Action and was partly supported bythe RENATECH network and its FEMTO-ST techno-logical facility. Kien Phan Huy thanks Thibaut Sylvestrefor his technical help on the injection. References [1] P. K. Tien and R. Ulrich, J. Opt. Soc. Am., (10),1325–1337 (1970).[2] V. B. Braginsky, M. L. Gorodetsky and V.S Ilchenko,Phys. Lett. A, (7), 393–397 (1989). [3] G. Griffel, S. Arnold, D. Taskent, A. Serpeng¨uzel,J. Connolly and N. Morris, Opt. Lett., (10), 695–697(1996).[4] J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks,Opt. Lett., (15), 1129–1131(1997).[5] E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chau-vet, W. Ramadan, A. Petris, and V. I. Vlad, Appl. Phys.Lett. , 2193–2195 (2004).[6] M. Chauvet, J. Opt. Soc. Am. B, , 2515–2522 (2003).[7] J. Safioui, F. Devaux, and M. Chauvet, Opt. Express , 22209–22216 (2009).[8] K. Phan Huy, J. Safioui, B. Guichardaz, F. Devaux, andM. Chauvet, Appl. Opt. , 4353–4358 (2012).[9] K. K. Wong, “Properties of Lithium Niobate”, (Aca-demic, 2002)[10] B. E. Little, J.-P. Laine, and H. Haus, J. Lightw. Tech-nol. (4), 704–715, (1999).[11] T. Carmon, L. Yang, and K. J. Vahala, Opt. Express (20), 4742–4750, (2004). References [1] P. K. Tien and R. Ulrich, “Theory of Prism-Film Cou-pler and Thin Film Light Guides,” J. Opt. Soc. Am., (10), 1325–1337 (1970).[2] V. B. Braginsky, M. L. Gorodetsky and V.S Ilchenko,“Quality-factor and nonlinear properties of opticalwhispering-gallery modes,” Phys. Lett. A, (7), 393–397 (1989).[3] G. Griffel, S. Arnold, D. Taskent, A. Serpeng¨uzel, J.Connolly and N. Morris, “Morphology-dependent reso-nances of a microsphereoptical fiber system,” Opt. Lett., (10), 695–697(1996).[4] J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks,“Phase-matched excitation of whispering-gallery-moderesonances by a fiber taper,” Opt. Lett., (15), 1129–1131(1997).[5] E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chau-vet, W. Ramadan, A. Petris, and V. I. Vlad, “Screeningphotovoltaic bright solitons in lithium niobate and asso-ciated single-mode waveguides,” Appl. Phys. Lett. , 2193–2195 (2004).[6] M. Chauvet, “Temporal analysis of open-circuit darkphotovoltaic spatial solitons,” J. Opt. Soc. Am. B, ,2515–2522 (2003).[7] J. Safioui, F. Devaux, and M. Chauvet, “Pyroliton:pyroelectric spatial soliton,” Opt. Express , 22209–22216 (2009).[8] K. Phan Huy, J. Safioui, B. Guichardaz, F. Devaux, andM. Chauvet, “Writing and probing light-induced waveg-uides thanks to an endlessly single-mode photonic crys-tal fiber,” Appl. Opt. , 4353–4358 (2012).[9] K. K. Wong, “Properties of Lithium Niobate”, (The In-stitution of Engineering and Technology, 2002)[10] B. E. Little, J.-P. Laine, and H. Haus, “Analytic theoryof coupling from tapered fibers and half-blocks into mi-crosphere resonators,” J. Lightw. Technol. (4), 704–715, (1999).[11] T. Carmon, L. Yang, and K. J. Vahala, “Dynamical ther-mal behavior and thermal self stability of microcavities,”Opt. Express12