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Sub-Pico-Liter Magneto-Optical Cavities Sub-pico-liter magneto-optical cavities J. A. Haigh,1, ∗ R. A. Chakalov,2 and A. J. Ramsay1 1Hitachi Cambridge Laboratory, Cambridge, CB3 0HE, United Kingdom 2Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom (Dated: September 10, 2020) Microwave-to-optical conversion via ferromagnetic magnons has so-far been limited by the optical coupling rates achieved in mm-scale whispering gallery mode resonators. Towards overcoming this limitation, we pro- pose and demonstrate an open magneto-optical cavity containing a thin-film of yttrium iron garnet (YIG). We achieve a 0.1 pL (100 µm3) optical mode volume, ∼50 times smaller than previous devices. From this, we estimate the magnon single-photon coupling rate is G ≈ 50 Hz. This open cavity design offers the prospect of wavelength scale mode volumes, small polarization splittings, and good magneto-optical mode overlap. With achievable further improvements and optimization, efficient microwave-optical conversion and magnon cooling devices become a realistic possibility. I. INTRODUCTION crocavity [20]. These are typically hemispherical resonators where a reflection-coated microlens is positioned in close Magnetic-field tunable ferromagnetic modes can be easily proximity to a mirror surface. Devices can be fiber-based strongly coupled to microwave resonators [1–3]. Further cou- [21, 22], or fabricated on planar surfaces [23], and have previ- pling to optical photons offers the prospect of useful transduc- ously been used to obtain large coupling rates to single atoms tion of microwave quantum signals to telecoms optical wave- [24], N-V centers [25], single organic dye molecules [26], and lengths [4]. For this reason, the interaction of magnons and excitons in 2D materials [27]. The advantage of this structure optical photons has been explored recently in the whispering is that any transferable material can be easily embedded [28], and the modes are tunable by the position of the lens. Optical gallery modes (WGM) of yttrium iron garnet (YIG) spheres 3 [5–7]. However, despite the high Q-factor of the magnetic and mode volumes as small as 1fL (1 µm ) have been achieved, optical modes [8], the optomagnonic coupling rates achieved with Q-factors in excess of 10,000 [29]. in mm-scale YIG spheres have been limited to 1Hz. If the In this article, we demonstrate a viable route to low mode coupling rate can be increased significantly, in turn∼ raising the volume, high coupling rate magneto-optical cavities with conversion efficiency, this would open a wide range of tech- mode volumes limited by the optical wavelength. We embed nological opportunities [9], as well as the ability to coherently single crystal YIG layers in an open microcavity, and show modify the magnetization dynamics, for example cooling or a two orders of magnitude increase in the coupling rate over dynamical driving the magnon mode [10, 11]. whispering gallery mode devices. With further reduction in The low coupling rate for optical whispering gallery modes mode volume, it is expected that the strong-coupling limited is due to the poor mode overlap and the large volume of mag- can be reached. This work, therefore, shows a path towards netic material involved. To overcome the poor overlap, it may efficient microwave-optical conversion, and optical magnon be possible to exploit magnon whispering gallery modes in cooling. YIG spheres, with almost ideal overlap with the optical WGM [12]. A simpler strategy is to explore more compact struc- tures, as very recently shown in rib waveguide devices [13]. II. COUPLING RATE In that case, the mm-long structure confines both the magnons and photons, yielding excellent overlap inside the structure, We first briefly review the enhanced scattering process in enabling a coupling rate of 17Hz. cavity optomagnonics. Magnetic Brillouin light scattering The estimated maximum coupling rate for a YIG optical is an inelastic process where a photon is scattered from an resonator is 0.1 MHz [14], based on a mode volume of the 3 input mode aˆ into an output mode aˆ , with absorption or order of the≈ resonant wavelength cubed λ . There are sev- i o emission of a magnon in mode mˆ . Brillouin light scatter- arXiv:2009.04162v1 [cond-mat.mes-hall] 9 Sep 2020 eral candidate wavelength-scale optical resonators [15], which ing is most efficient between orthogonally polarized opti- could get close to this maximum coupling rate. The choice cal modes, as this compensates the angular momentum lost of resonator, however, must take into account the significant or gained to the magnon mode, conserving angular momen- challenges of micro-patterning YIG [16]. We note that, while tum. To enhance the BLS significantly, we require two op- sub-wavelength mode confinement is possible with plasmonic tical resonances, enhancing both the input and output optical devices [17–19], this typically comes with high optical losses fields. These should be orthogonally polarized, and with fre- in the metal components. quency separation matching the magnon frequency. This is A simple optical resonator design, with wavelength scale the triple resonance condition, which has been observed pre- mode volumes combined with large Q-factors, is an open mi- viously in whispering gallery mode resonators [7], and in a recent waveguide device [13]. The interaction Hamiltonian that governs the scattering is of ∗ [email protected] † † the form Hint = G(ˆai aˆomˆ +ˆaiaˆomˆ ), with interaction strength 2 quantified by the coupling rate, a) c 4gµB ηmagηopt G = iθf . (1) − nr Ms r Vopt The numerical constant µB is the Bohr magneton and c the speed of light. The factors affecting this rate can be separated ~1¤ m in two parts. Firstly, the materials parameters of the embed- DBR magnet material substrate ded magnetic material: the Faraday coefficient θf , refractive b)i) ii) GGG (7 m) YIG/GGG layer index n, gyromagnetic ratio g and saturation magnetization YIG (2¢ m) BCB (~1£ m) Ms. These parameters can be optimized by materials devel- Au antenna opment, finding new materials and improving the quality of DBR those available. Secondly, the geometry of the optical cavity Au antenna affects the coupling rate through the volumes of the optical sapphire substrate 2 modes Vi Vo = Vopt = ui,o(r) , where ui,o(r) is the iii) DBR ≈ | | u r 2 mode function with normalizationR max ( i,o( ) )=1. The YIG/GGG | | c) lens array overlap is contained in the fill-factors ηmag = Vint/Vmag and lens array ηopt = Vint/Vopt, which are the proportion of the magnetic and optical modes volumes that contribute to the DBRs Vmag Vopt Au antenna coupling through the triple-mode overlap, 50¡ m crack ∗ Vint = drum(r) [u (r) uo(r)]. (2) Z · i × Figure 1. (a) Schematic of the magneto-optical cavity design. The open microcavity consists of two parts: a concave lens milled into a Here, the mode function um is also normalized such that 2 substrate and coated with a DBR, and a planar mirror with magnetic max ( um(r) )=1. This expression includes the effect of | | layer. Left: Cross section of design to show relative dimensions of the mode polarization. To maximize the geometric factors we the lens and beam waist. Right: 3D representation of the device would like a low optical mode volume resonator, with excel- structure. (b)Fabrication of magneto-optical microcavity. (i) Flat lent overlap with the magnon mode, and orthogonal polariza- side of open microcavity. A gold microwave antenna is patterned on tion of all three modes. the DBR surface before the YIG/GGG layer is bonded. (ii) Cross In this paper, we focus exclusively on the minimization of section of flat mirror, showing two-layer BCB bonding polymer. (iii) the optical mode volume. The design is such that lateral pat- Cross-section section of open microcavity, showing microlens array. terning of the continuous YIG layer to confine the magnon (c) Optical image through cavity structure, showing lens array and mode can incorporated at a later stage. microwave antenna. III. DESIGN A schematic of our proposed device is shown in Fig. 1(a). single-crystal YIG from a lattice matched GGG growth sub- The mirrors forming the open microcavities are purchased strate. We later bond this layer to the mirror surface with a from Oxford HiQ [30]. They consist of one planar surface spin-on polymer. and one microlens array. Both surfaces have a high qual- ity reflective coating consisting of 22 layers of SiO2 and The advantage of the open microcavity design is that the Ta2O5, deposited by sputtering. This distributed Bragg reflec- polarization splitting is minimized due to the cylindrical sym- tor (DBR) has a reflectivity of 99.8% at its design wavelength metry. In principle, a minor asymmetry can tune the splitting of 1300nm. The microlens array contains 16 lenses with four to match the magnon frequency, given the precise control of different radii of curvature, from 100 µm down to 20 µm, fab- lens profile that has been demonstrated [31]. For an optical ricated by focused-ion-beam milling [31]. The lens array is resonator with an asymmetrical cross-section, the splitting is situated on a raised pedestal to allow alignment of the two typically a fixed fraction of the free spectral range. There- mirrors. fore, as the mode volume shrinks, the frequency separation To embed a high quality, single crystal YIG layer in the mi- can become too large. This can be seen in the whispering crocavity, we avoid deposition techniques such as pulsed laser gallery mode resonators, where a 1mm diameter YIG sphere deposition and sputtering, because the non-lattice matched was chosen to match the splitting to the magnon frequency DBR substrate would lead to poly-crystalline YIG growth [7]. It is not possible to decrease the size of the sphere, be- [32].
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