All-optical Stern-Gerlach effect in the time domain.

The Stern-Gerlach experiment, a seminal quantum physics experiment, demonstrated the intriguing phenomenon of particle spin quantization, leading to applications in matter-wave interferometry and weak-value measurements. Over the years, several optical experiments have exhibited similar behavior to the Stern-Gerlach experiment, revealing splitting in both spatial and angular domains. Here we show, theoretically and experimentally, that the Stern-Gerlach effect can be extended into the time and frequency domains. By harnessing Kerr nonlinearity in optical fibers, we couple signal and idler pulses using two pump pulses, resulting in the emergence of two distinct eigenstates whereby the signal and idler are either in phase or out of phase. This nonlinear coupling emulates a synthetic magnetization, and by varying it linearly in time, one eigenstate deflects towards a higher frequency, while the other deflects towards a lower frequency. This effect can be utilized to realize an all-optical, phase-sensitive frequency beam splitter, establishing a new paradigm for classical and quantum data processing of frequency-bin superposition states.

Toward multimode-fiber shape sensing.

We demonstrate machine-learning assisted dynamic tracking of the shape of a multimode fiber whose spatial configuration is manipulated by the movement of three linear stages. The data source used for the analysis is the coherent speckle pattern of light that has made a round trip in the fiber.

Ultrahigh scan-rate quasi-distributed acoustic sensing system using array match interrogation.

Inspired by compressed sensing techniques, a method for significantly enhancing the maximum allowable scan rate in quasi-distributed acoustic sensing (Q-DAS) is described and studied. Matching the scan parameters to the interrogated array facilitates orders of magnitude improvement in the scan rate and a corresponding increase in the maximum slew rate (SR) of differential phase variations which can be measured without ambiguity. The method is termed array matched interrogation (AMI). To improve the method's SNR, maximum number of sensing sections and maximum range, the interrogation pulse can be replaced by a perfect periodic autocorrelation (PPA) code. This version of the method is referred to as coded array matched interrogation (C-AMI). The implementation of C-AMI is not trivial and requires special design rules which are derived and tested experimentally. The design rules ensure that the 'folding' of the returning peaks of the Q-DAS array into a scan period, which is much shorter than the fiber's roundtrip time, will not lead to overlaps. The method demonstrated a scan rate of 20 times higher than the common limit and measurement of unprecedented slew-rate of 10.5 ×106 rad/s.

Two-wavelength phase-sensitive OTDR sensor using perfect periodic correlation codes for measurement range enhancement, noise reduction and fading compensation.

We demonstrate a two-wavelength differential-phase-measuring OTDR sensor that uses perfect periodic correlation phase codes to enhance the measurement performance. The two-wavelength technique extends the measurement range of OTDR sensors by synthesizing a virtual longer-wavelength measurement from two simultaneous measurements of phase using different lasers. This increases the range free from phase unwrapping errors. However, we find that the application of this technique greatly increases the relative measurement noise. To compensate for this issue, we introduce the use of optical pulse compression using perfect periodic correlation phase codes to increase the measurement signal-to-noise ratio and also to facilitate the simultaneous compensation of Rayleigh and polarization fading. In addition, we apply a method to further reduce the relative noise that is added to the two-wavelength measurement by using the synthetic wavelength measurement to unwrap the differential phase measured with a single wavelength. All this is highlighted in a 1-km sensing link in which up to 20-cm spatial resolution and 12.6 pϵ/Hz strain sensitivity are demonstrated as well as a 67-fold enhancement in measurement range compared with the use of the conventional single-wavelength method.

Visual data detection through side-scattering in a multimode optical fiber.

Light propagation in optical fibers is accompanied by random omnidirectional scattering. The small fraction of coherent guided light that escapes outside the cladding of the fiber forms a speckle pattern. Here, visual information imaged into the input facet of a multimode fiber with a transparent buffer is retrieved, using a convolutional neural network, from the side-scattered light at several locations along the fiber. This demonstration can promote the development of distributed optical imaging systems and optical links interfaced via the sides of the fiber.

Fiber-optic distributed seismic sensing data generator and its application for training classification nets.

Distributed acoustic sensing (DAS) is a powerful tool thanks to its ease of use, high spatial and temporal resolution, and sensitivity. Growing demand for long-distance distributed seismic sensing (DSeiS) measurements, in conjunction with the development of efficient algorithms for data processing, has led to an increased interest in the technology from industry and academia. Machine-learning-based data processing, however, necessitates tedious in situ calibration experiments that require significant effort and resources. In this Letter, a geophysics-driven approach for generating synthetic DSeiS data is described, analyzed, and tested. The generated synthetic data are used to train DSeiS classification algorithms. The approach is validated by training an artificial neural-network-based classifier using synthetic data and testing its performance on experimental DSeiS records. Accuracy is greatly improved thanks to the incorporation of a geophysical model when generating training data.

Use of distributed acoustic sensing for Doppler tracking of moving sources.

Distributed acoustic sensing (DAS) via fiber-optic reflectometry techniques is finding more and more applications in recent years. In many of these applications, the position of detected acoustic or seismic sources is defined with a single longitudinal coordinate which specifies the distance between the detection point in the fiber to the DAS interrogator. In this paper we describe a DAS system which is intended to operate in a fluid (air or water) and to detect and localize moving objects, with three spatial coordinates, using the acoustic waves they generate or reflect and their Doppler shifts. The new method uses optical frequency domain reflectometry (OFDR) and lumped Rayleigh reflectors (LRR's) to ensure sufficiently high sensitivity for operation in fluid media. The new method was used to track a narrowband (CW) signal source.

Sinusoidal frequency scan OFDR with fast processing algorithm for distributed acoustic sensing.

Recently it was shown that sinusoidal frequency scan optical frequency domain reflectometry (SFS-OFDR) can achieve remarkable performance in applications of distributed acoustic sensing (DAS). The main advantage of SFS-OFDR is the simplicity with which highly accurate sinusoidal frequency scans can be generated (in comparison with linear frequency scans). One drawback of SFS-OFDR has been the computationally intensive algorithm it required for processing of the measured backscatter data. The complexity of this algorithm was O(N2) where N is the number of backscatter samples. In this work a fast processing algorithm for SFS-OFDR, with computational complexity O (N log N), is derived and its performance and limitations are studied in details. The new algorithm facilitated highly sensitive DAS operation over a sensing fiber of 64km, with 6.5m resolution and scan rate of 400Hz. The high sensitivity of the system was demonstrated in a field trial where it successfully detected human footsteps near the end of the fiber with excellent SNR.

Lumped Rayleigh reflectors.

Distributed acoustic sensing (DAS) via optical fibers makes use of Rayleigh backscattering for the detection of acoustic waves that interact with the fiber along its entire length. The random nature of Rayleigh backscattering leads to nonuniform performance along the fiber and, occasionally, to complete signal fading. In addition, distance-dependent signal-to-noise (SNR) degradation is always present due to propagation loss. In contrast, using arrays of discrete reflectors [such as weak fiber Bragg gratings (FBGs) with equal center wavelengths] offers deterministic performance which can be designed to be uniform along the fiber. Here we describe an approach for implementing Rayleigh-based discrete reflectors that can offer enhanced detection performance in selected regions. It is based on enclosing sections of the fiber in acoustically insulated boxes to create lumped Rayleigh reflectors. Besides diminishing the randomness in detection sensitivity, the method enables increasing the detection SNR far beyond the typical value for Rayleigh-based DAS and obtaining sensitivities comparable with discrete reflectors. The proposed method was successfully tested via both simulation and experiment.

On the sensitivity of distributed acoustic sensing.

In distributed acoustic sensing (DAS) an optical fiber is transformed into an array of thousands of "virtual microphones." Most current DAS methodologies are based on coherent interference of Rayleigh backscattered light and thus are prone to signal fading. Hence, the sensitivities of the "microphones" fluctuate randomly along the fiber. Therefore, specifying the sensitivity of DAS without considering its random nature is incomplete and of limited value. In this Letter, the statistical properties of DAS SNR and DAS sensitivity are studied in detail for the first time, to the best of our knowledge. It is shown that the mean dynamic DAS SNR is proportional to the SNR obtained in a single measurement of the fiber's "static" backscatter profile and, in turn, to the energy of the interrogation pulse. Finally, the minimum input signal, which produces a specified mean DAS SNR, is proposed as a new figure of merit for the characterization of system performances and for comparison between the sensitivities of different DAS modalities.

Distributed acoustic and vibration sensing via optical fractional Fourier transform reflectometry.

Distributed acoustic sensing has been traditionally implemented using optical reflectometry. Here we describe an alternative to the common interrogation approaches. According to the new method the frequency of the source is varied sinusoidally with time. For a sufficiently high scan frequency there is a position along the fiber, z(0), for which the roundtrip time is half the scan period. Back-reflections from this point will generate a linear chirp at the receiver output. The Fractional Fourier Transform (FrFT) is used to analyze the receiver output and yields the reflection profile at z(0) and its vicinity. The method, which enables high spatial resolution at long distances with high scan rates, is demonstrated by detecting deliberate perturbations in the Rayleigh backscatter profile at the end of a 20km fiber with a scanning frequency of ~2.5kHz. The spatial resolution at this range and scan-rate is characterized by a measurement of the backscatter profile from a FBG's-array and is found to be ~2.8m.

High resolution DAS via sinusoidal frequency scan OFDR (SFS-OFDR).

There are many advantages to using direct frequency modulation for OFDR based DAS. However, achieving sufficiently linear scan via direct frequency modulation is challenging and poses limits on the scan parameters. A novel method for analyzing sinusoidal frequency modulated light is presented and demonstrated for both static and dynamic sensing. SFS-OFDR projects the measured signal onto appropriate sinusoidal phase terms to obtain spatial information. Thus, by using SFS-OFDR on sinusoidal modulated light it is possible to make use of the many advantages offered by direct frequency modulation without the limitations posed by the linearity requirement.

Multiplexing of fiber-optic ultrasound sensors via swept frequency interferometry.

The use of fiber-optic sensors for ultrasound (US) detection has many advantages over conventional piezoelectric detectors. However, the issue of multiplexing remains a major challenge. Here, a novel approach for multiplexing fiber-optic based US sensors using swept frequency interferometry is introduced. Light from a coherent swept source propagates in an all-fiber interferometric network made of a reference arm and a parallel connection of N sensing arms. Each sensing arm comprises a short polyimide coated sensing section (~4cm), which is exposed to the US excitation, preceded by a delay of different length. When the instantaneous frequency of the laser is linearly swept, the receiver output contains N harmonic beat components which correspond to the various optical paths. Exposing the sensing sections to US excitation introduces phase modulation of the harmonic components. The US-induced signals can be separated in the frequency domain and be extracted from their carriers by common demodulation techniques. The method was demonstrated by multiplexing 4 sensing fibers and detecting microsecond US pulses which were generated by a 2.25MHz ultrasound transducer. The pulses were successfully measured by all sensing fibers without noticeable cross-talk.

Optical frequency domain reflectometry at maximum update rate using I/Q detection.

We introduce a new optical frequency domain reflectometry (OFDR) system and processing method that utilize negative beat frequencies for the first time. The new approach enables efficient use of the available system bandwidth and facilitates distributed sensing with the maximum allowable update rate for a given fiber length. This is achieved by using a coherent optical-communications-type receiver that detects both the in-phase (I) and quadrature (Q) components of the backscatter field. The I and Q components are digitally combined to produce a complex backscatter signal whose Fourier transform is not necessarily symmetric. Judicious processing of the complex backscatter signal maps the reflection profile of one half of the sensing fiber to positive beat-frequencies and the profile of the other half to negative beat-frequencies. The new approach was tested via comprehensive computer simulations and experiment.

Dynamic optical frequency domain reflectometry.

We describe a dynamic Optical Frequency Domain Reflectometry (OFDR) system which enables real time, long range, acoustic sensing at high sampling rate. The system is based on a fast scanning laser and coherent detection scheme. Distributed sensing is obtained by probing the Rayleigh backscattered light. The system was tested by interrogation of a 10 km communication type single mode fiber and successfully detected localized impulse and sinusoidal excitations.

OFDR with double interrogation for dynamic quasi-distributed sensing.

A method for phase sensitive quasi-distributed vibration and acoustical sensing is presented. The method is based on double optical frequency domain reflectometry interrogation of a sensing fiber with an array of discrete weak reflectors. Two replicas of the interrogation signal are launched into the sensing fiber. The time delay between the replicas is equal to the roundtrip time between two consecutive reflectors. Each peak in the spectrum of the returning signal is made from a coherent addition of the reflections of two consecutive reflectors. Its magnitude is highly sensitive to the optical phase in the fiber segment between the reflectors. The system was used to detect and locate the fall of a paperclip from height of 40 cm onto a sandbox where a 15 cm segment of the fiber was buried. In a different experiment the system successfully detected and located minute vibrations at 440 Hz that were induced by touching the fiber with a tuning fork.

Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points.

The spatial resolution of OFDR is normally degraded by the laser phase noise, deviations from linear frequency scan and acoustic noise in the fibers. A method for mitigating these degradation mechanisms, without using an auxiliary interferometer, via inline auxiliary points, is presented and demonstrated experimentally. Auxiliary points are points that are a priori known to have (spatial) impulse reflectivities. Their responses are used for compensating the phase deviations that degrade the response of points that are further away from the source.

Dual-pump push-pull polarization control using stimulated Brillouin scattering.

Stimulated Brillouin scattering (SBS) amplification of probe signals is highly polarization dependent. Maximum and minimum gain values are associated with a pair of orthogonal states of polarization (SOP), which are related to the pump SOP. Since the maximum gain is much higher than the minimum, the SOP of the output probe is pulled towards that of the maximum amplification. Polarization pulling is restricted, however, by pump depletion. In this work, a new method is proposed, analyzed and demonstrated for enhanced SBS polarization pulling, using two orthogonal pumps. Here, one pump amplifies one polarization component of the probe wave, and at the same time the other pump attenuates the corresponding orthogonal component, resulting in a push-pull effect. In the undepleted regime and for equal total power, the same degree of pulling is achieved as in the single pump case, but at a significantly less signal gain. Thus, the dual pump technique can provide high pulling efficiency for stronger input signals, deferring the onset of depletion.

High spatial resolution distributed sensing in optical fibers by Brillouin gain-profile tracing.

A novel BOTDA technique for distributed sensing of the Brillouin frequency in optical fibers with cm-order spatial resolution is proposed. The technique is based upon a simple modulation scheme, requiring only a single long pump pulse for acoustic excitation, and no subsequent interrogating pulse. Instead, the desired spatial mapping of the Brillouin response is extracted by taking the derivative of the probe signal. As a result, the spatial resolution is limited by the fall-time of the pump modulation, and the phenomena of secondary "echo" signals, typically appearing in BOTDA sensing methods based upon pre-excitation, is mitigated. Experimental demonstration of the detection of a Brillouin frequency variation significantly smaller than the natural Brillouin linewidth, with a 2cm spatial resolution, is presented.

Photoacoustic Doppler measurement of flow using tone burst excitation.

In this paper a novel technique for flow measurement which is based on the photoacoustic (PA) Doppler effect is described. A significant feature of the proposed approach is that it can be implemented using tone burst optical excitation thus enabling simultaneous measurement of both velocity and position. The technique, which is based on external modulation and heterodyne detection, was experimentally demonstrated by measurement of the flow of a suspension of carbon particles in a silicon tube and successfully determined the particles mean velocity up to values of 130 mm/sec, which is about 10 times higher than previously reported PA Doppler set-ups. In the theoretical part a rigorous derivation of the PA response of a flowing medium is described and some important simplifying approximations are highlighted.