Fiber loop ringdown (FLRD) has been widely used for the measurement of loss owing to the advantages of small size, light weight, immunity to electromagnetic interference, etc [1], [2]. Different from optical time domain reflectometry, which is limited by the dead zone, FLRD is especially suitable for the accurate measurement of loss in short fiber [3]. Besides, the application of FLRD for measuring temperature [4], strain [5], curvature [6], refractive index [7] and other parameters [8], [9] are implemented by transforming these parameters to loss. The simultaneous sensing of temperature and loss has great potential in practical engineering applications, such as building structural health monitoring, disaster warning [10]. To improve the multiplexing capability, combining multiple magnitude-based FLRDs has been proposed [10], [11], while the cost and complexity of the systems will increase. Compared with the conventional FLRDs technique [12], [13], [14], the phase-shift (PS) FLRD has advantages of low cost, stability and insensitivity to the fluctuations of the light source [15], [16]. PS FLRD is an absorption spectroscopic technique that is inspired by the cavity ring-down spectroscopic (CRDS) technique. Different from CRDS, the length of fiber loop in FLRD is usually tens of meters [17], [18]. Hence, the relationship between the phase shift and the modulating frequency in CRDS is not suitable for FLRD, where the inappropriate setup of frequency and length will decrease the sensitivity of PS FLRD. Additionally, it is challenging for the PS FLRD to implement the multiplexing according to the current conclusion of CRDS.

Recently, optical carrier-based microwave interferometry (OCMI) has attracted a great deal of attentions, which utilizes optical fibers as delay lines for signal processing [19], [20]. The key device in a microwave photonics filter is the optical delay-line module [21], [22], such as recirculating delay lines (RDLs), whose frequency response spectra of magnitude and phase are determined by the adjustment of the coupler, the propagation loss of the loop and the insertion loss of the coupler [23], [24], [25]. By recording the response magnitude and phase spectra of RDLs to simply reconstruct the time-domain signal, microwave-assisted FLRD [26] is proposed to perform loss sensing, which ignores the characteristic of the magnitude and phase spectra. To improve the sensitivity of OCMI, many schemes have been proposed and demonstrated [27], [28], [29]. By tuning the loss of the interference arm and the radio frequency, the phase-shift-amplified OCMI with high sensitivity to the change of optical path and a tunable dynamic range can be achieved. However, the tunable sensitivity is realized by adjusting the intensity ratio of two interference arms, which means the sensitivity is susceptible to the impact from fiber link loss. Moreover, there are few researches on measurement by recording the phase spectra of RDLs. Inspired by optical carrier-based microwave interferometry, the relationship of the loop length, modulating frequency and phase shift in RDL-based FLRD is numerically investigated. Due to the over-emphasis on sensitivity improvement, the insensitive work points are often overlooked in previous works. On the contrary, the insensitive points provide not only anti-crosstalk property for multi-parameters measurements, but also the potential for system multiplexing.

In this paper, to the best of our knowledge, we firstly propose and demonstrate a FLRD-based OCMI with the phase-shift-amplified technique for measuring the loss and temperature of fiber loop simultaneously. The principle of PS FLRD is modified by numerical investigations and verified experimentally. The tunable sensitivity of loss is achieved flexibly by adjusting the RF, and the crosstalk resistance at insensitive points is demonstrated by implementing frequency-shift-based temperature sensing. By selecting proper RF, the sensitivity of system is enhanced significantly, compared with the previous research [17]. Based on the unique characteristics of insensitive points, we theoretically validate the multiplexing method of phase demodulation. Therefore, the conventional PS FLRD system, which is based on lock-in amplifier (LIA), can be multiplexed by switching RF. Rather than the fixed radio frequency, the vector network analyzer (VNA) sweeps the frequency of modulated signal to validate the proposed theory. The loss of the ring loop leads to the phase change at most RF, but the phase of each insensitive point is almost constant. The temperature sensing is carried out by demodulating the frequency shift of the loss insensitive point, where the optical path of the ring is affected by the variation of temperature. Hence, the loss and temperature of the ring loop are demodulated from the phase change at low RF and the frequency shift at high RF, respectively. The measurements of two parameters are independent and the tunable sensitivity of loss is achieved by sweeping the RF. The impact of the loop length and the characteristic of insensitive points ignored by the previous researches are numerically calculated and experimentally demonstrated. Based on the insensitive points, the proposed scheme provides a potential avenue to improve FLRD multiplexing capability by switching the RF.