Laser Phase and Frequency Stabilization Using an Optical Resonator

We describe a new and highly effective optical frequency discriminator and laser stabilization system based on signals reflected from a stable Fabry-Perot reference interferometer. High sensitivity for detection of resonance information is achieved by optical heterodyne detection with sidebands produced by rf phase modulation. Physical, optical, and electronic aspects of this discriminator/laser frequency stabilization system are considered in detail. We show that a high-speed domain exists in which the system responds to the phase (rather than frequency) change of the laser; thus with suitable design the servo loop bandwidth is not limited by the cavity response time. We report diagnostic experiments in which a dye laser and gas laser were independently locked to one stable cavity. Because of the precautions employed, the observed sub-100 Hz beat line width shows that the lasers were this stable. Applications of this system of laser stabilization include precision laser spectroscopy and interferometric gravity-wave detectors. PACS: 06, 07.60, 07.65 The adoption of high-finesse Fabry Perot cavities for a prototype gravitational wave detector [1] requires the development of very high precision short term stabilizing techniques for an argon-ion laser. Similarly, there is considerable incentive to improve the frequency stabilization of dye lasers for spectroscopic applications. Optical resonators [2-4] have been used to provide frequency discriminator functions for servo control of both types of laser [-3, 5-81 and form the basis for at least three commercially-available frequency-stabilized dye laser systems. In this paper we describe an improved rf sideband type of optical discriminator capable of high precision, low-noise * Staff Member, Quantum Physics Division, National Bureau of Standards ** Present address : Colorado School of Mines, Golden, Colorado performance and having a response time not limited by the optical resonator. We illustrate the technique with several experiments including demonstration of sub100 Hz laser line widths. Development of Techniques Before considering the uItimate performance capability of frequency-stabilized lasers, we first discuss some practical problems and review the technical progress which has been made previously. In view of the very rapid time scale of fluctuations associated with the dye laser's free-flowing jet and with plasma movement in the ion laser, it is understandable that efforts to improve their frequency-stabilization performance have centered on developing faster transducers and 98 R.W.P. Drever et al. electronic systems. Miniaturization of the PZT transducer and laser mirror can provide ~200kHz servo bandwidth and ~40kHz residual laser frequency noise [9]. Use of an intracavity electro-optic modulator crystal allows increased servo bandwidths (> 1 MHz) and can provide a laser linewidth of a few kHz [6-8], still limited somewhat by the highfrequency surface roughness of the jet stream or by fast argon-plasma noise. Intermediate servo precision can be conveniently obtained with an acousto-optic frequency shifter located outside the laser resonator [10]. However, two basic difficulties remain with the fast optical-frequency discriminator system. For one, to eliminate conversion of laser intensity noise into frequency noise while preserving a bipolar error signal, it is customary to compare an independent sample of the laser intensity with the cavity transmission signal tuned near its half-maximum tuning point [3]. Unfortunately problems of matching photodetectors make it difficult to achieve good long-term stability with such a fringe-side servo, no matter how well the cavity itself is stabilized by a reference laser and frequency offset lock system. Further we may expect that the same laser medium fluctuations that produce frequency noise also will produce changes in the laser spot's shape and thus influence the mode-matched cavity transmission in a correlated and deleterious way. We find, in fact, that spatial filtering improves the system's performance in spite of the loss of control light. A second problem area relates to optimal choice of the reference cavity and servo loop bandwidths. To better suppress the intrinsic laser noise by feedback action, we need to increase the servo gain. Closed-loop stability requirements then dictate a proportional increase in the servo loop bandwidth. However, as shown by [8] with the conventional "fringe-side" servo, transient response errors make it useless to employ a servo control bandwidth substantially greater than the cavity discriminator linewidth. Thus, we have dilemma that the high bandwidth required to control the laser's intrinsic noise effectively requires use of a wider cavity response which then brings increased measurement noise in view of the associated lower discriminator slope. A fundamental advantage of the new locking system to be described is that it locks the laser to the cavity maximum transmission point where the transient response overshoot problem does not exist [4, 8]. It is useful to understand these considerations quantitatively. Performance Limitation The fundamental performance limit of any optical frequency control system is set by the photoelectron shot noise, since this noise in the photocurrent cannot be distinguished from a signal current due to a real frequency variation. Indeed when the servo gain and bandwidth are high, as they will be to suppress the laser's intrinsic noise, this noise will be imposed onto the laser frequency to produce the appropriate servo null. It is easy to calculate the frequency variations associated with this inescapable shot noise limit [8]. For measurements with an averaging time of z, the frequency fluctuations 3v(z), due to measurement shot noise are