Phase measurement by using a forced delay-line oscillator and its application for an acoustic fiber sensor

We demonstrate, theoretically and experimentally, a new method to measure small changes in the cavity length of oscillators. The method is based on the high sensitivity of the phase of forced delay-line oscillators to changes in their cavity length. The oscillator phase is directly detected by mixing the oscillator output with the injected signal. We describe a comprehensive theoretical model for studying the signal and the noise at the output of a general forced delay-line oscillator with an instantaneous gain saturation and an amplitude-to-phase conversion. The results indicate that the magnitude and the bandwidth of the oscillator response to a small perturbation can be controlled by adjusting the injection ratio and the injected frequency. For signals with a frequency that is smaller than the device bandwidth, the oscillator noise is dominated by the noise of the injected signal. This noise is highly suppressed by mixing the oscillator output with the injected signal. Hence, the device sensitivity at frequencies below its bandwidth is limited only by the internal noise that is added in a single roundtrip in the oscillator cavity. We demonstrate the use of a forced oscillator as an acoustic fiber sensor in an optoelectronic oscillator. A good agreement is obtained between theory and experiments. The magnitude of the output signal can be controlled by adjusting the injection ratio while the noise power at low frequencies is not enhanced as in sensors that are based on a free-running oscillator.