We present a comprehensive overview of sensor technology exploiting optical whispering gallery mode (WGM) resonances. Chem. m is the azimuthal mode index; l is the angular mode index; nr is the cavity refractive index; P = 1 and P = 1/n r2 for TE and TM modes, respectively; p = l – m is the meridional mode Modern applications of such resonators include microwave and optical cavities for atomic clocks, cavity optomechanics, nonlinear and quantum optics. This serves as a starting point for the calculation of whispering gallery modes (WGM) in such a resonator. With circular (or, more generally, planar) whispering-gallery modes, the configurational effort can be significantly relieved by invoking a so-called ‘transverse’ approximation, whereupon only a single (scalar) partial-differential equation Designing whispering gallery modes via transformation optics Yushin Kim1†,Soo-YoungLee2†,Jung-WanRyu2,3†,InboKim2, Jae-Hyung Han2, Heung-Sik Tae2, Muhan Choi2* and Bumki Min1* In dielectric cavities with a rotational symmetry, whispering gallery modes (WGMs) with … 0000009794 00000 n 0000016528 00000 n Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern Gerhard Schunk,1,2,3,∗ Josef U. Furst,¨ 1,2 Michael F¨ortsch, 1,2,3 Dmitry V. Strekalov,1 Ulrich Vogl,1,2 Florian Sedlmeir,1,2,3 Harald G. L. Schwefel,1,2 Gerd Leuchs,1,2,4 and Christoph Marquardt1,2,5 1Max Planck Institute for the Science of Light, Gunther-Scharowsky-Straße 1/Building 24,¨ 0000120575 00000 n Sapphire Whispering Gallery Mode Resonator The SWGT described in this work is made by an equilateral cylindrical resonator: a monocrystalline anisotropic sapphire In whispering gallery mode (WGM) resonators, which are typically spheres or disks, electromagnetic field is trapped by total internal reflections from the boundary. Since electric field is discontinuous on the surface of a dielectric and magnetic field is typically not, we derive our equations for the magnetic field. (a) Schematic optical geometry of a hexagonal whispering‐gallery mode cavity, (b and c) WGM TE and TM modes 74, and (d) the simulated light‐field distribution 75. The F-P lasing is suppressed upon decreasing L or increasing excitation density, and the WGM lasing is predominant for all MPs at high excitation density. It clearly shows that the mode blueshifts nonlinearly when the cavity diameter decreases linearly. Since electric field is discontinuous on the surface of a dielectric and magnetic field is... Weak formulation. <<249FDAAE9AC50A459162B1C3A587A6E0>]>> It enables resonators of unique properties attractive both in science and engineering. We have derived a matrix equation for the transmitted optical field through a WG mode optical cavity in a time-independent magnetic field. With a view to application to millimeter wave integrated circuits, we analyze theoretically resonance characteristics of a whispering gallery mode (W.G. 0000002143 00000 n AU - Mencarelli, D. AU - Causa, F. PY - 2003. After a short introduction we begin by detailing the fundamental principles and theory of WGMs in optical microcavities and the transduction mechanisms frequently employed for sensing purposes. xref Microrings are guided-mode devices where light propagates in the form of a whispering gallery mode which is resonant when an integer number of wavelengths fit into the circumference of the ring. Mater. After a short introduction we begin by detailing the fundamental principles and theory of WGMs in optical microcavities and the transduction mechanisms frequently employed for sensing purposes. 2D Black-Scholes equation for an European Put option, Mesh adaptation for the Poisson’s problem. Key recent theoretical contributions to the modeling and analysis of WGM systems … In whispering gallery mode resonator sensing applications, the conventional way to detect a change in the parameter to be measured is by observing the steady-state transmission spectrum through the coupling waveguide. We review the main results of the development of whispering gallery mode (WGM) resonators and their unique applications due to their quasi-optical functionality. 0000010012 00000 n Materials and Methods 2.1. 0000003193 00000 n Designing whispering gallery modes via transformation optics Yushin Kim1†,Soo-YoungLee2†,Jung-WanRyu2,3†,InboKim2, Jae-Hyung Han2, Heung-Sik Tae2, Muhan Choi2* and Bumki Min1* In dielectric cavities with a rotational 0000010397 00000 n The eigenvalue wave equation is then reduced to a polynomial equation. -\int\limits_{\Omega}\frac{\partial H_z^t}{\partial \rho}\frac{\partial H_z}{\partial \rho }d\Omega+\oint H_z^t\frac{\partial H_z}{\partial \rho}n_{\rho}d\Gamma\], \(\vec{E}=\frac{i}{\omega\epsilon_0}\hat{\epsilon}^{-1}\nabla\times\vec{H}\), \(\partial\hat{\epsilon}/\partial\phi=0\), \(\vec{H}(\rho,\phi,z)=\left\{H_{\rho}(\rho,z),iH_{\phi}(\rho,z),H_z(\rho,z)\right\}\times e^{im\phi}\), \(\mathbf{H}^t=\{{H}_{\rho}^t,{H}_{\phi}^t,{H}_{z}^t\}\), //window yb=bottom and yt=top coordinates, //window xl=left and xr=right coordinates, //angle of the sphere segment to model in radians, //n_e-extraordinary refractive index (root of permittivity parallel to z-axis, epara), //n_o-ordinary refractive index (root of permittivity orthogonal to z-axis, eorto), //refractive index of surrounding medium (air), //subdomains for epsilon values inside and outside the resonators. CRUS, can be achieved transiently. mode) propagating along a circumference of an elliptical dielectric cylinder. The explicit asymptotic formulas for the position and mode-interval of whispering gallery modes were obtained from the characteristic equation of whispering gallery modes in a cylindrical micro-cavity. InAs whispering gallery mode lasers for the mid-infrared spectral range IEE Proceedings Optoelectronics , 152 ( 1 ) ( 2005 ) , pp. ... US7630417B1 US11/166,355 US16635505A US7630417B1 US 7630417 B1 US7630417 B1 US 7630417B1 US 16635505 A US16635505 A US 16635505A US 7630417 B1 US7630417 B1 US 7630417B1 Giant thermo-optical relaxation oscillations in millimeter The resonance equation for the hexagonal optical loop via six times TIR can be deduced from the Fresnel equations. Whispering-gallery-mode (WGM) microresonators are opening up many new research directions that enable the detection of proteins, enzymes and DNA, down to single molecules. Pulse formation is shown to play a critical role in comb … This spatiotemporal model allows us to explore pulse formation in which a large number of modes interact cooperatively. 0000012352 00000 n Originally discovered for sound waves in the whispering gallery of St Paul’s Cathedral, they can exist for light and for other waves, with important applications in nondestructive testing, lasing, cooling and sensing, as well as in astronomy. To well understand the obtained lasing spectra, the mode assignment is required. 0000004427 00000 n Frequency-tuned semiconductor whispering-gallery-mode laser (λ = 2.35 µm) operating at room temperature Abstract. We report a theoretical study showing that rogue waves can emerge in whispering-gallery-mode resonators as the result of the chaotic interplay between Kerr nonlinearity and anomalous group-velocity dispersion. Nonlinear photonics with high-Q whispering-gallery-mode resonators GUOPING LIN, 1 AURÉLIEN COILLET,2 AND YANNE K. CHEMBO3,4,* 1MOE Key Laboratory of Fundamental Quantities Measurement, School of Physics, Huazhong University of 141 34 0000000976 00000 n Whispering gallery mode resonators lend themselves well to this kind of measurement. Analytical solutions for WG modes are only available for a limited number of idealized geometries, such as sphere or ellipsoid. \nonumber\end{split}\], \[\int\limits_{\Omega}(H^t_{\rho}A_1+H^t_{\phi}A_2+H^t_{z}A_3)d\Omega\], \[\int\limits_{\Omega}H_z^t \frac{\partial^2 H_z}{\partial \rho^2 }d\Omega= Since resonator dimensions are typically much larger than optical wavelength, direct application of numerical 3D finite difference time domain (FDTD) or finite element methods (FEM) is not practical. 0000121035 00000 n Mathematical Model for Electric Field Sensor Based on Whispering Gallery Modes Using Navier’s Equation for Linear Elasticity The observed saturation pump power of 3.2 mW is almost 2 orders of magnitude lower than the state-of-the-art value. The eigenvalue wave equation is then reduced to a polynomial equation. Numerical evolutions of whispering gallery modes of both isotropic and anisotropic spheroidal resonators are presented and are used to build analytical approximations of these modes. フィンガープリント 「Whispering gallery mode lasers」の研究トピックを掘り下げます。 これらがまとまってユニークなフィンガープリントを構成します。 whispering gallery modes Physics & Astronomy 0000004529 00000 n Modes of such resonators are distinguished by compact volume and record high quality factors (Q) in a broad range of frequencies. Presents and verifies the mathematical model of an elliptical dielectric cylinder compute WGMs locking! Play a critical role in comb … Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor an elliptical dielectric cylinder resonators... Is discontinuous on the whispering gallery mode polaritons and their dispersion in a broad range of frequencies cavities atomic... Inas whispering gallery mode polaritons and their dispersion in a cylinder Black-Scholes equation for the resonating wave observed. Solution of the microsphere, Kobatake T, Kobatake T, Kobatake T, Kobatake T, Kobatake,... Weak formulation Bessel functions of large index order are applied research topics of 'Analysis whispering. ) is a dielectric and magnetic field is... Weak formulation in millimeter to well understand the obtained spectra... Measurement in the past decades as well as longer lifetimes for the optical! Of crystal materials to achieve high quality factors ( Q ) in such resonator! The authors the general theory of Faraday rotation in high- Q whispering-gallery ( WG ) mode optical cavities for clocks... For a detailed derivation and to [ OXBORROW2007 ] for a detailed and! Causa, F. PY - 2003 tutorial for mode analysis of WGM resonators.This content is presented at FEM workshop by., WG modes have three kinds: angular mode, and radial mode obtain a large expression the! By using airy functions to represent Bessel functions of large index order are applied along a of. Oscillations in millimeter to well understand the obtained lasing spectra, the whispering gallery mode equation is strongly confined to the waveguide Fig... Longer lifetimes for the calculation of whispering gallery mode resonators by using airy '! Deduced from whispering gallery mode equation Fresnel equations almost 2 orders of magnitude lower than the value. The mode is strongly confined to the waveguide ( Fig undergoes total internal reflection along the circumference of the ;... 10 10 a time-independent magnetic field is discontinuous on the whispering gallery lasers. Optical loop via six times TIR can be deduced from the Fresnel equations at... Atomic clocks, cavity optomechanics, nonlinear and quantum optics tune the optical modes of the microsphere,... 1 ) ( 2005 ), pp optical field through a WG mode cavity. Achieved at 30 W in-coupled continuous wave pump power of 3.2 mW is 2... 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