IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 12, NO. 11, NOVEMBER 2000 1531 High-Resolution Photon-Scanning Tunneling Microscope Measurements of the Whispering Gallery Modes in a Cylindrical Microresonator D. J. W. Klunder, Student Member, IEEE, M. L. M. Balistreri, F. C. Blom, H. J. W. M. Hoekstra, A. Driessen, Senior Member, IEEE, L. Kuipers, and N. F. van Hulst Abstract—A detailed analysis of spatio-spectral photon scan- ning tunneling microscope scans of the light intensity inside a cylin- drical microresonator has been carried out. By comparing the ex- perimental results with theory, it is shown that the inclusion of spectral mode-beat phenomena is crucial for an accurate analysis of the modes present in the microresonator. Index Terms—Cylindrical microresonators, optical waveguides, photon scanning tunneling microscopy, spectral mode-beat phe- nomena, whispering gallery modes. I. INTRODUCTION R ECENTLY, the intensity distribution in a cylindrical micro-resonator (MR) was mapped with a photon-scan- ning tunneling microscope (PSTM) with an unprecedented high spatial and spectral resolution [1], [2] (see also [3]). Not only were the free spectral ranges (FSRs) of the whispering gallery modes (WGMs) found from these measurements, but also spatial and spectral mode-beats were observed [1]. The effects of both polarization conversion and the excitation of counter-propagating modes could be deduced from analyzing the spatial and spectral scans of the intensity inside the MR [1]. Great effort was taken to prove experimentally the consistency of the interpretation of the huge amount of data obtained in the microcavity itself and the input and output ports (e.g., polarization-dependent measurements [4], measuring the power scattered by the microresonator [5], [6]). In this letter, a method will be shown whereby the mode profiles of the WGMs can be analyzed by wavelength-averaging the spatio-spectral scan [1] of the intensity distribution. A comparison between the resulting wavelength-averaged intensity and simulations is made and the effect of spectral mode-beat phenomena in the analysis is illustrated. Manuscript received March 27, 2000; revised July 18, 2000. This work was supported by the “Nederlandse Organizatie voor Wetenschappelijk Onderzoek (NWO)” under the research program of the “Stichting voor Fundamenteel On- derzoek der Materie (FOM).” D. J. W. Klunder, H. J. W. M. Hoekstra, and A. Driessen are with the Light- wave Devices Group, MESA Research Institute and Department of Applied Physics, University of Twente, 7500 AE Enschede, The Netherlands. M. L. M. Balistreri, L. Kuipers, and N. F. van Hulst are with the Applied Optics Group, MESA Research Institute and Department of Applied Physics, University of Twente, 7500 AE Enschede, The Netherlands. F. C. Blom was with the Lightwave Devices Group, MESA Research In- stitute and Department of Applied Physics, University of Twente, 7500 AE En- schede, The Netherlands. He is now with Uniphase Netherlands B.V., Prof. Hol- stlaan 4, Eindhoven, The Netherlands. Publisher Item Identifier S 1041-1135(00)09577-X. Fig. 1. Top view and cross-section (A-A) of the cylindrical MR under study. II. CYLINDRICAL MR Our MR (see Fig. 1) is positioned next to a monomodal straight waveguide, has a radius of m, and is realized in a Si N –SiO layer-stack with an air cladding on a Silicon substrate [5]–[7]. The field inside an MR can be described as a linear com- bination of the WGMs. These WGMs with parameter Pkl are described by their polarization state P (TE/TM), slab order , radial order , and angular propagation constant . The ex- citation of the WGMs occurs by evanescent coupling with the straight waveguide (TE00) mode. III. SPECTRAL MODE-BEAT PHENOMENA We consider the case of only two co-propagating WGMs with a common origin (e.g., at the coupling between the MR and the straight waveguide). It can be shown that the intensity distribu- tion as a function of the wavelength, for a fixed angle of ob- servation , is a superposition of the radial intensity profiles of the WGMs and an intensity modulation due to the spectral mode-beat between them. The radial distribution of this modula- tion is proportional with the product of the fields of the WGMs. As the accumulated phaseshifts will vary more rapidly as a func- tion of wavelength further away from the common origin, it follows that the spectral mode-beat periods vary inversely pro- portionally with the angle of observation. The description of other spectral mode-beat phenomena (e.g., spectral mode-beat between counter-propagating modes) is completely analogous. IV. WAVELENGTH-AVERAGED INTENSITY By repeatedly scanning in the radial direction with the fiber tip of a PSTM, while varying the wavelength, a spatio-spectral map (see also [8]) of the intensity distribution in the MR is ob- tained (see Fig. 2). In Fig. 2, a number of horizontal bands cor- 1041–1135/00$10.00 © 2000 IEEE