## Amplified ladder networks for time division multiplexing of fiber-optic sensors

##### Abstract

Large systems of fiber-optic sensors are suitable for a wide range of applications ranging from seismic surveying to health monitoring of concrete structures. Time division multiplexing of fiber-optic sensors in ladder network topologies have been demonstrated for networks containing up to 64 sensors. The power budget limits the number of sensors due to the splitting of the interrogating signal pulse energy between the sensors.
This thesis is concerned with application of Erbim-Doped Fiber Amplifiers in fiber-optic sensor networks. Erbium-Doped Fiber Amplifiers (EDFAs) are used as in-line amplifiers, booster amplifier and preamplifiers in a few variants of the ladder network topology. The role of the in-line amplifiers is to compensate for the power lost due to component losses and power coupling out of the fiber buses. Simple models for signal and amplified spontaneous emission received from the considered ladder network topologies are developed. The models are verified experimentally for one topology. Simulations are performed for networks containing identical components. Chapter 4 contain Monte Carlo simulations of networks where component parameters are distributed over some vendor specified range.
A 10-branch amplified ladder networks has been demonstrated by another group. The same gruop has published theoretical work on the optimization of the optical noise figure of ladder network topologies.
In Chapter 2 simulations show that the use of two amplifiers per sensor branch may improve the carrier to noise ratio (CN R) for a 100 sensor passive network by using as little as 40 dB gain per bus. Hundreds of sensors can be multiplexed on a pair of fibers with 1 or 3 μrad/√Hz phase resolution. Further improvement is achieved by partitioning of the ladder network in an outer amplified network having passive subnetworks consisting of two or more sensors in the branches. Less pump power is wasted in component losses because fewer amplifier-coupler stages are required in this modular topology.
The discussion in Chapter 2 shows that the maximum number of sensors in amplified ladder networks is limited by the ability to provide pump power to long chains of EDFAs rather than by the signal power budget which is the case for passive networks. The performance of ladder networks are optimized by determining the optimum coupling coefficients of the amplified buses and by determining the optimum number of sensors in the passive subnetworks. The maximum subnetwork size is limited by the thermal and electronics noise as well as the power lost in the tree couplers.
Remote interrogation of amplified ladder networks is limited to fiber downlead lengths shorter than ∼ 68 km due to the pump power limitations imposed by stimulated Raman scattering. The signal power is limited by stimulated Brillouin scattering (SBS) in the input bus downlead and the return bus uplead. The performance of remotely interrogated amplified networks is maximized at combinations of the coupling coefficients and the network partitioning where the critical powers of the uplead and downlead SBS are equal. The power limit imposed by SBS reduces the optimum subnetwork size and prevents the use of high coupling coefficients. The application of remotely interrogated sensor networks to seismic surveying is briefly discussed. Use of modular networks require only four pump power distribution fibers and two signal fibers, while BALT/AFCATs require up to several tens of pump distribution fibers. For 10 km downlead lengths, it is shown that 165 and 415 sensors can be multiplexed in modular network topology with a phase resolution of 1 and 3 μrad/√Hz, respectively. The optimum number of sensors per subnetwork is 3 and 5 for a phase resolution of 1 and 3 μrad/√Hz, respectively. When the link lengths are increased to 30 km, the maximum number of sensors decreases to 66 and 225 for a phase resolution of 1 and 3 μrad/√Hz, respectively. The optimum number of sensors per subnetwork is 3 and 5.
In Chapter 3, the mathematical model is verified experimentally by the use of two cascaded recirculating rings. It is shown that the signal propagation and ASE build-up in the two recirculating loops are equal to that of an amplified forward coupled array topology provided that the input signal is corrected for the coupling loss occurring when coupling the signal into and out of the rings. The experiment confirms the validity of the model, and demonstrates that the gain of the amplifiers in the return bus is reduced due to saturation from high signal duty cycle and accumulated ASE. The saturation is negligible for the amplifiers in the input bus and in the return bus amplifiers far from the receiver. The return bus amplifiers close to the receiver may need a different design to avoid problems related to the gain saturation. The high number of components in the rings brings the total loss up. This prevents simulations of networks having low gain and low coupling coefficients because the experiment required ∼ 15 dB gain to obtain transparent circulation in the rings.
In Chapter 4, Monte Carlo simulations of modular networks show that the uniformity of the coupling coefficient of the couplers in the amplified buses must be kept low (¿ 0.4 dB) in order to avoid a wide distribution (> 5 dB) of CN R-values if amplifier cascades above 20 stages are to be used. It is demonstrated that the nonuniformity of telecommunications grade tree couplers are a minor problem for the width of the distribution of CN R-values. The CN R-value determined by substituting mean parameter values into expressions developed for identical parameters overestimates the CN R by approximately 0.5 dB.