Thermally tunable whispering-gallery mode cavities for magneto-optics

We report the experimental realization of magneto-optical coupling between whispering-gallery modes in a germanate (56GeO2-31PbO9Na2O-4Ga2O3) microspherical cavity due to the Faraday effect. An encapsulated gold conductor heats the resonator and tunes the quasitransverse electric (TE) and quasi-transverse magnetic (TM) polarized modes with an efficiency of 65 fm/V at a peak-to-peak bias voltage of 4V. The signal parameters for a number of heating regimes are quantified to confirm sensitivity to the generated magnetic field. The quasi-TE and quasi-TM resonance frequencies stably converge near the device’s heating rate limit (equivalently, bias voltage limit) in order to minimize inherent geometrical birefringence. This functionality optimizes Faraday rotation and thus enables the observation of subsequent magneto-optics. VC 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0006367 Optical devices that exploit whispering-gallery modes (WGMs) have gradually become ubiquitous. The WGM cavity has demonstrated strong optomechanical interactions, lased at ultralow thresholds, established parity-time symmetric systems, and detected single atomic ions near plasmonic nanoantennae. Tuning of WGMs outside of irreversible modification has been achieved by refractive index modulation, such as from mechanical strain/pressure, electrooptics, or thermal effects. Thermo-optical control is typically realized by selecting a high-thermo-optic coefficient material for the cavity or relying on absorption based heating, wherein the former involves an integrated heating element. Tuning of glass WGM cavities through an internal metallic conductor, however, can be intractable due to glass crystallization during fabrication. While melting the dielectric at a temperature below the conductor’s melting point, nucleation sites develop and with crystal growth inhibit WGM circulation. For sensing applications in a stochastic environment, there is also a need for laser jitter suppression when detecting nanoparticles and the removal of background drift when thermally characterizing polymers. By way of optomechanics and magnetostriction, on-chip WGM based magnetometers have detected magnetic fields with sensitivities as small as hundreds of pT/ ffiffiffiffiffiffi Hz p : More generally, magneto-optical coupling in a WGM resonator has been studied for transported magnetic fluids and for the resonator material itself. Cavity optomagnonics in yttrium iron garnet (YIG) microspheres offers coherent magnon-to-photon interconversion at optical and microwave frequencies, justifying the use of magnons as information carriers. An applied magnetic field B modifies the cavity dielectric tensor by first and second order magnetization, respectively, known as the Faraday and Voigt effects. The quasi-transverse electric (TE) and quasi-transverse magnetic (TM) WGM resonance frequencies are split by the cavity boundary conditions, i.e., by a geometrically induced birefringence Dng , and are mixed by the Faraday effect. 31 One conclusion that was drawn in Ref. 31 was that Dng quenches the overall Faraday rotation. Minimizing Dng in turn maximizes the magnetic field sensitivity and so polarization rotation at the output coupler becomes significant. Cavity-enhanced polarimetry is an extension of this operational principle through which chiral measurement can be considered. In this paper, we present a WGM sensing platform that dually incorporates thermal tuning and magneto-optical responsivity. A germanate (56GeO2-31PbO-9Na2O-4Ga2O3) microsphere with a high Verdet constant is fabricated with a central gold conducting wire to modulate the WGM resonance via heating and induce a magnetic field on the order of 1G. The cavity-wire structure is fashioned by inserting Appl. Phys. Lett. 116, 161110 (2020); doi: 10.1063/5.0006367 116, 161110-1 VC Author(s) 2020 Applied Physics Letters ARTICLE scitation.org/journal/apl

Optical devices that exploit whispering-gallery modes (WGMs) have gradually become ubiquitous. 1 The WGM cavity has demonstrated strong optomechanical interactions, 2,3 lased at ultralow thresholds, 4 established parity-time symmetric systems, 5 and detected single atomic ions near plasmonic nanoantennae. 6 Tuning of WGMs outside of irreversible modification 7,8 has been achieved by refractive index modulation, such as from mechanical strain/pressure, [9][10][11][12] electrooptics, [13][14][15] or thermal effects. [16][17][18][19][20] Thermo-optical control is typically realized by selecting a high-thermo-optic coefficient material for the cavity 18,19 or relying on absorption based heating, 16,17 wherein the former involves an integrated heating element. Tuning of glass WGM cavities through an internal metallic conductor, however, can be intractable due to glass crystallization during fabrication. While melting the dielectric at a temperature below the conductor's melting point, nucleation sites develop and with crystal growth inhibit WGM circulation. For sensing applications in a stochastic environment, there is also a need for laser jitter suppression when detecting nanoparticles 21 and the removal of background drift when thermally characterizing polymers. 22 By way of optomechanics and magnetostriction, on-chip WGM based magnetometers 23 have detected magnetic fields with sensitivities as small as hundreds of pT/ ffiffiffiffiffiffi Hz p : 24 More generally, magneto-optical coupling in a WGM resonator has been studied for transported magnetic fluids 25,26 and for the resonator material itself. 27 Cavity optomagnonics in yttrium iron garnet (YIG) microspheres 28,29 offers coherent magnon-to-photon interconversion at optical and microwave frequencies, justifying the use of magnons as information carriers. An applied magnetic field B modifies the cavity dielectric tensor by first and second order magnetization, respectively, known as the Faraday and Voigt effects. 30 The quasi-transverse electric (TE) and quasi-transverse magnetic (TM) WGM resonance frequencies are split by the cavity boundary conditions, i.e., by a geometrically induced birefringence Dn g , and are mixed by the Faraday effect. 31 One conclusion that was drawn in Ref. 31 was that Dn g quenches the overall Faraday rotation. Minimizing Dn g in turn maximizes the magnetic field sensitivity and so polarization rotation at the output coupler becomes significant. Cavity-enhanced polarimetry 32 is an extension of this operational principle through which chiral measurement can be considered.
In this paper, we present a WGM sensing platform that dually incorporates thermal tuning and magneto-optical responsivity. A germanate (56GeO 2 -31PbO-9Na 2 O-4Ga 2 O 3 ) microsphere with a high Verdet constant is fabricated with a central gold conducting wire to modulate the WGM resonance via heating and induce a magnetic field on the order of 1 G. The cavity-wire structure is fashioned by inserting a sub-millimeter diameter gold wire into a germanate capillary, then a capillary segment with a wire protrusion is melted inside a ceramic microheater. Convection and surface tension promote the formation of a germanate microspherical profile around the wire (with the cavity radius on the order of hundreds of lm) and glass isotropy is ensured by the germanate's slower crystallization rate. The wire geometry creates a B-field that is parallel or antiparallel to the WGM propagation direction throughout current reversal in time. Critically, as the cavity refractive index (n c ) profile guides quasi-TE and quasi-TM modes differently, we show that Dn g decreases with thermal conductance throughout the cavity with the increasing root-mean-square amplitude of the oscillating bias voltage. This WGM tunability scheme excludes large and expensive electromagnets in order to limit the device footprint.
Scans were performed across WGM resonances using a tunable external cavity laser of central wavelength k ¼ 642 nm in the geometry shown in Fig. 1. Light is focused onto the internal surface of a rutile prism and, through frustrated total internal reflection, couples to the germanate microsphere at 5% efficiency in order to excite WGMs. We note that the prism is birefringent with an ordinary refractive index n o and an extraordinary refractive index n e above that of the germanate (n c < 2 < n o < n e ) within the chosen optical bandwidth. The WGM microsphere in contact with this prism is doubly clamped above a metal-on-insulator biasing chip [ Fig. 1(a)] and the enclosed 150-lm diameter gold wire supports actuating currents of up to a few amperes. Spectral characterization of the germanate's Verdet constant [ Fig.  1(b)] determined a value of $ 25 rad/(Tm) near WGM resonances. Nevertheless, initial peak tracking of the resonance line shape in Fig.  1(c) for a triangular bias voltage VðtÞ suggests dominant thermal influences. In principle, for a local temperature change DT, signal rectification arises from Joule heating Linewidth narrowing and broadening follows the heating cycle with a p phase delay with respect to the resonant wavelength k Res . When the suspended microsphere contacts the prism, forces acting on the sphere-stem cantilever 33 from capacitance at the soft glass interface and flexion from heating can vary the coupling to the WGM and hence alter the linewidth. The magnetic field oscillation frequency f M is not equal to that of the recorded response of Fig. 1(c)-what is instead observed is a WGM perturbation at 2f M due to heat conduction that is independent of the current direction. The trace's noise floor in the tens of fm range, in this case derived from the cavity quality factor Q ¼ k Res =dk % 2 Â 10 5 , exceeds the laser phase noise. Further investigation of the perturbed WGM resonance was carried out by frequency domain analysis. The entire resonance trace of Fig. 2(a) was decomposed into its frequency components [ Fig.  2(b)], revealing the expected DC component and 2f M peaks for a fullwave rectified resonance signal response. These peaks originate from thermal nonlinearities; however, f M peaks also exist within the spectrum. Normalized spectral peak amplitude vs frequency curves in Fig.  2(b) for the two separate series of peaks differ in bandwidth, thus indicating separate time constants. The model proposed in Ref. 31 derived from the coupled mode theory contextualizes this disparity: once the B-field is sufficient to overcome the geometrical birefringence Dn g , mode mixing produces deviations in quasi-TE and quasi-TM WGM eigenfrequencies away from degeneracy. Consequently, a partial-wave rectified resonance shift pattern from a weak intracavity Faraday effect would exhibit the f M peak seen in our experiment. With lower Dn g , coupling between quasi-TE and quasi-TM WGMs is detected at lower magnetic field thresholds.
Faraday rotation h F is optimized in the unquenched regime (Dn g ¼ 0) and highly dependent on the magnetic field strength. Calculations in Fig. 3(a) outline that h F and hence the shift Dk Res for a tellurite WGM microsphere are linear with the B-field. Simulated fundamental quasi-TE and quasi-TM WGMs with azimuthal mode order m ¼ 975 (i.e., near the experimental operating wavelength) places the operating points at Dn g ¼ 0:00146, neglecting the cavity index profile variation from thermo-refractivity and thermal expansion. Accounting for this tuning, on the other hand, can lead to a displacement in the radial position of the guided WGM intensity maxima. Figure 3(b) depicts the experimental resonance trace when increasing the root-mean-square amplitude of the bias voltage. By fixing the duty cycle of the electrical signal, the time-averaged heating of the  microsphere enforces a radial thermal gradient that equalizes the quasi-TE and quasi-TM WGM eigenfrequencies. These modes begin with different penetration depths into the external dielectric, and with precise thermal feedback, may converge toward minimal geometrical birefringence. At a peak-to-peak bias voltage V pp ¼ 4 V, the tuning efficiency reaches $ 65 fm/V and the modes differ in resonant wavelength by less than 1 pm. The amplitude of in-phase shift Dk Res for these modes scales linearly with V pp and the signal undergoes a steeper rise toward the peak, in agreement with thermal and intracavity Faraday effect superposition. WGM resonant linewidths are similar in oscillation and close in value ( 0.5 pm at V pp ¼ 4 V), remaining synchronous irrespective of the superimposed perturbations.
The findings in this study provide preliminary evidence for the optical WGM resonator analog of polarization rotation in a soft glass cavity. A cost-effective microheater with electrical interfacing was used to tune the WGM resonances and reduce geometrically induced birefringence. The latter enhances the quasi-TE and quasi-TM polarization coupling per round trip in the presence of a proximate magnetic field aligned with mode propagation. Magnetization dynamics could be explored, such as the possibility of lasing by way of magnon Brillouin scattering. Nonreciprocal Brillouin scattering can bring selective creation and annihilation of magnons in the Kittel mode, alongside chiral features embedded in the spin dynamics of a ferromagnetic YIG microcavity. 28,29 Due to the solubility of the germanate glass, any WGM measurement in solution may require the coating of a protective layer [e.g., a perfluoro(1-butenyl vinyl ether) polymer] around the cavity. By satisfying this criterion, we anticipate future chiral sensing of enantiomer layers on the cavity surface. Distinguishing the chirality of and detecting Faraday rotation from single molecules will, however, necessitate greater specificity and signal enhancement. Single-molecule chirality is largely unattainable in cavity polarimetry schemes 30 as the requisite resolution falls below the shot noise. A signal-reversing WGM biosensor based on the intracavity Faraday effect may circumvent this pitfall by isolating for a weak yet local chiral signal. This is afforded by exceptional points 5 and/or mode hybridization through coupling to localized surface plasmons of metallic nanoparticles. 6 Plasmonic nanoantennae from Ref. 6 may be functionalized with organic molecules possessing a substantial Verdet constant {e.g., 1,3,5trimethyl-2,4,6-tris[2-(4-nitrophenyl)ethynyl]benzene/TTB 34 } as they would be individually detectable and responsive to magnetic field fluctuations in the optoplasmonic system. Another promising avenue is the detection of magnetic field-dependent protein behavior, such as cryptochrome signaling. 35 Spin states correlated with such biochemical reactions could be manipulated with the local magnetic field and probed according to the magneto-optical coupling of the resonator, i.e., through resolvable discrepancies between the quasi-TE and quasi-TM WGM resonance response.
The authors would like to thank R emy Soucaille for his contribution in characterizing the glasses' Verdet constants. S.V. also thanks Peter Rakitzis and Matthew Foreman for their valuable discussions. Resonance peaks in the measured spectra were tracked and analyzed using software developed by Martin Baaske. This work was supported by a H2020 FET Open grant (ULTRACHIRAL, No. 737071) issued by the European Research Council.