88 IEEE JOURNAL ON SELECTED TOPICS ON QUANTUM ELECTRONICS, VOL. 8, NO. 1, JANUARY/FEBRUARY 2002 Thermal Noise and Radiation Pressure in MEMS Fabry–Pérot Tunable Filters and Lasers Rodney S. Tucker, Fellow, IEEE, Douglas M. Baney, Senior Member, IEEE, Wayne V. Sorin, Fellow, IEEE, and Curt A. Flory, Member, IEEE Abstract—In this paper, we examine thermal noise and radia- tion-pressure effects in MEMS tunable Fabry–Pérot etalons. We show that thermal noise causes a jitter in the center wavelength in very high finesse etalons. In turn, the jitter causes an effective increase in the time-averaged filter bandwidth. Radiation pressure is of little consequence in conventional Fabry–Pérot etalons, but it can give rise to nonlinearities and hysteresis in the tuning response of high-finesse MEMS filters. We develop models of noise and optical nonlinearities and compare the models with a series of measurements on commercial tunable high-finesse MEMS Fabry–Pérot etalons. Index Terms—Fabry–Pérot etalons, MEMS, radiation pressure, thermal noise, tunable optical filters, tunable lasers. I. INTRODUCTION M ICROELECTROMECHANICAL (MEMS) Systems Fabry–Pérot tunable etalons [1]–[4] find a wide range of applications in telecommunications and optical signal pro- cessing. MEMS filters are capable of achieving broad tuning range together with very high finesse and wide free spectral range. When integrated with an active lasing medium, tunable laser characteristics can be realized [5]–[7]. MEMS-tun- able vertical-cavity surface-emitting lasers (VCSELs) are outstanding candidates for applications in optical networks requiring frequency-agile optical transmitters. It has been known for some time that mechanical thermal noise can have significant influence on the performance of MEMS devices and miniature sensors. See, for example, [8]–[10]. In conventional Fabry–Pérot etalons, thermal effects are not significant. However, in high-finesse devices, as the size and mass of the etalon mirrors and their support structures decrease mechanical thermal effects can become important. In this paper, we show how thermal noise causes random perturbations to the position of the mirrors in high-finesse MEMS Fabry–Pérot tunable filters. These perturbations give rise to random fluctuations of the center frequency of the filter. If the amplitude of these fluctuations is significant compared to the Fabry–Pérot filter bandwidth, the noise may adversely Manuscript received July 13, 2001; revised November 30, 2001. R. S. Tucker was with Agilent Technologies, Agilent Laboratories, Palo Alto, CA 94304-1392 USA. He is now with the ARC Special Research Centre for Ultra-Broadband Information Networks, Department of Electrical and Electronic Engineering, University of Melbourne, Vic 3010, Australia. D. M. Baney and C. A. Flory are with Agilent Technologies, Agilent Labo- ratories, Palo Alto, CA 94304-1392 USA. W. V. Sorin was with Agilent Technologies, Agilent Laboratories, Palo Alto, CA 94304-1392 USA. He is now with Novera Optics, Inc., San Jose, CA 95131 USA. Publisher Item Identifier S 1077-260X(02)02230-X. affect the filter performance. In MEMS lasers, thermal noise can influence the laser linewidth through the same mechanism. Another nonideal characteristic exhibited by MEMS Fabry–Pérot etalons is radiation-pressure-induced nonlineari- ties. Radiation pressure effects in etalons have been previously considered in the context of sensor devices and squeezed light, often at cryogenic temperatures [12]–[15]. We show in this paper that these nonlinearities may be significant even at room temperature, and can give rise to filter tuning responses that are dependent on the optical input power level. In some circumstances, the tuning responses show hysteresis effects. In MEMS lasers, the radiation-pressure-induced nonlinearities may affect the low-frequency chirp characteristics of the device. Radiation-pressure-induced nonlinearities are caused by small displacements of one or both of the etalon mirrors in response to changing optical power levels in the cavity. These effects are more significant in high-finesse etalons, where the stored optical power level can reach high levels. In this paper, we examine thermal noise effects and radia- tion-induced-nonlinearities in MEMS Fabry–Pérot etalons. A simple dynamic model is given in Section II, Section III presents an analysis of the thermal noise effects in MEMS Fabry–Pérot etalons and shows how thermal noise causes an effective in- crease in the filter bandwidth. Section IV examines the effects of radiation pressure on the dynamics of MEMS Fabry–Pérot etalons and shows how radiation pressure causes nonlinearities and hysteresis in the filter tuning response. We show that the effects of thermal noise and radiation pressure can become sig- nificant in high-finesse etalons. We develop models of the noise and optical nonlinearities and compare the models with a series of measurements on commercial tuneable high-finesse MEMS Fabry–Pérot etalons. II. DYNAMICS OF MEMS FABRY–PÉROT ETALONS We begin with a simple dynamic model of a MEMS Fabry–Pérot etalon. The structure of the etalon is illustrated schematically in Fig. 1. A movable mirror is supported by an elastic structure that keeps the movable mirror parallel to a fixed mirror on the device substrate. A tuning voltage is applied between the movable mirror support and the substrate. The separation between the movable mirror and the fixed mirror is controlled by electrostatic attraction between the movable structure and the substrate. Our analysis is based on a simple dynamic model of the etalon. The model is shown in Fig. 2. The movable mirror has mass , and its displacement from the equilibrium position 1077-260X/02$17.00 © 2002 IEEE