Analysis of the Drever-Pound-Hall technique for the simultaneous detection of the detuning of more cavities on a single channel

The Drever-Pound-Hall technique is a powerful tool to stabilize the laser frequency or to lock a cavity to a laser by controlling its length in the order of fraction of wavelength 1-3 . It had been widely applied as method to interrogate fiber optical cavity based sensors, as strain sensors or refractive index sensors, since it allows to reach very high sensitivity, especially in dynamic range, only theoretically limited by the laser shot noise 4-7 . In this paper we present a detailed analysis on the possibility to use the DPH technique for the simultaneous detection of detuning of two or more cavities each lying on a different output branch of a splitter, by interrogating them using only the single input channel of the splitter. More precisely, starting from a reflection configuration of the present technique, where the error signal to control the cavity length is extracted by the signal reflected by the cavity, we analyze all the possible configurations to simultaneously interrogate and discriminate the different cavities, using the same input channel to have not overlap and interference between the signals reflected by each of them. The interest of this kind of analysis resides in the possibility to design very compact and less invading sensors that requires bidirectional detection of the involved physical quantity or, the simultaneous and independent control of several parameters (like, for example, bidirectional strain sensors, that simultaneously detect the strain along two orthogonal directions, or magnetic field sensor able to determine the intensity of the field along perpendicular directions, or, refractive index sensor temperature calibrated 8 ). Using a single interrogation/detection channel the sensor can be placed far away from the interrogation/detection apparatus and connected to the latest only by means of a single optical fiber, instead to have more signal detection channels.