Strong Feedback Regime Research Articles

Hysteresis Behavior of External Cavity Quantum Cascade Lasers in the Strong Feedback Regime

Hysteresis Behavior of External Cavity Quantum Cascade Lasers in the Strong Feedback Regime

Self-Mixing Interferometer for Acoustic Measurements through Vibrometric Calibration.

The Self-Mixing Interformeter (SMI) is a self-aligned optical interferometer which has been used for acoustic wave sensing in air through the acousto-optic effect. This paper presents how to use a SMI for the measurement of Sound Pressure Level (SPL) in acoustic waveguides. To achieve this, the SMI is first calibrated in situ as a vibrometer. The optical feedback parameters C and α in the strong feedback regime (C≥4.6) are estimated from the SMI vibrometric signals and by the solving of non-linear equations governing the SMI behaviour. The calibration method is validated on synthetic SMI signals simulated from SMI governing equations for C ranging from 5 to 20 and α ranging from 4 to 10. Knowing C and α, the SMI is then used as an acoustic pressure sensor. The SPLs obtained using the SMI are compared with a reference microphone, and a maximal deviation of 2.2 dB is obtained for plane waves of amplitudes ranging from 20 to 860 Pa and frequencies from 614 to 17,900 Hz. The SPL measurements are carried out for C values ranging from 7.1 to 21.5.

Photonic reservoir computing using a self-injection locked semiconductor laser under narrowband optical feedback.

Photonic time-delay reservoir computing (TDRC) using a self-injection locked semiconductor laser under optical feedback from a narrowband apodized fiber Bragg grating (AFBG) is proposed and numerically demonstrated. The narrowband AFBG suppresses the laser's relaxation oscillation and provides self-injection locking in both the weak and strong feedback regimes. By contrast, conventional optical feedback provides locking only in the weak feedback regime. The TDRC based on self-injection locking is first evaluated by the computational ability and memory capacity, then benchmarked by the time series prediction and channel equalization. Good computing performances can be achieved using both the weak and strong feedback regimes. Interestingly, the strong feedback regime broadens the usable feedback strength range and improves robustness to feedback phase variations in the benchmark tests.

Amelioration of accuracy of displacement measurement in strong feedback regime based on region decision: Enlargement of measurement range of self-mixing displacement sensor

Increasing the measurable distance and the displacement measurement limit of a self-mixing displacement sensor poses one of the most important problems to improve the sensor’s performance. In order to solve the problem, there has to be found the estimation method of the optical feedback factor for a strong feedback regime. The hardship of the estimation in this regime is brought about by a strong speckle noise and the restriction of normalization methods presented hitherto. In the paper we have found an approach to improving the accuracy of the self-mixing sensor, which can work even for long range and large displacement, by deciding the region of the optical feedback factor based on the ratio of fringe height and using it and fringe counting method.

Augmentation-Assisted Robust Fringe Detection on Unseen Experimental Signals Applied to Optical Feedback Interferometry Using a Deep Network

Commercialization and industrial deployment of optical feedback interferometry or self-mixing interferometry (SMI) based displacement instruments is held back due to inaccurate fringe detection under different optical feedback or speckle induced by operating conditions. In this work, we propose using deep neural 2D networks, which have renowned generalization performance on unseen data. Nonetheless, training deep neural networks requires very large data which in our application would imply acquiring large datasets of experimental signals by operating such interferometers under as many operating conditions as possible. To circumvent this time- and resource-consuming process, we propose a novel data augmentation scheme which increases the amount of training data needed by a deep network for fringe detection/classification in SMI signals. Interestingly, this has enabled the trained deep network to acquire excellent generalization capability where it has learnt to detect SMI fringes belonging to weak-, and very strong-optical feedback regime, even when it was only trained on moderate-, and strong-feedback regime signals. Consequently, our trained model has shown robust performance for simulated weak-, moderate-, and strong-optical feedback regime SMI signals affected by additive noise. Various experimental SMI signals, acquired under different sensor- and optical-conditions, have also been successfully processed. We also implemented an established fringe detection method for comparison. Our work presents very good generalization capability as compared to this established method. Our novel augmentation scheme is generic and can be applied for other interferometric signals. We have released our dataset and implementation, with the hope that this will assist community in accelerating the commercialization of optical feedback interferometry leveraging the full potential of deep learning.

Fast and highly accurate phase unwrapping algorithm for displacement retrieval using self-mixing interferometry sensor

Self-Mixing interferometry (SMI) has been widely used for displacement, vibration and velocity measurement applications. Many phase unwrapping methods are proposed for high precision measurement. However, most of these methods are compute-intensive and non-real-time in nature due to time-consuming iterative processing, which hinders the development of real-time SMI based sensor for sensing applications. On the other hand, available computationally lighter real-time methods have a very low measurement precision, limiting them to applications not demanding high accuracy measurement. Thus, in this work, a much simpler and highly accurate modified phase unwrapping method (MPUM) is proposed. MPUM is based on two steps processing. The first step of the algorithm is rough phase retrieval, where the wrapped rough phase of the normalized SMI signal is directly unwrapped using a simple threshold-based approach. In second step, this rough unwrapped phase is cleaned to extract desired target displacement by applying a simple phase localization technique. The proposed method is not only simpler and computationally lighter compared to previously proposed methods, but also improves measurement resolution. Furthermore, the proposed method can work for all three (Weak, moderate and strong) feedback regime signals. MPUM was tested for a variety of simulated and experimental SMI signals, and results were compared with already proposed conventional phase unwrapping methods. MPUM has a measurement precision of around 10.7 nm (λ0/73), compared to conventional phase unwrapping methods having precision ranging from λ0/10 to λ0/40. MPUM is 66.8% faster than PUM and improved displacement measurement by 67.2% compared to PUM. Such a high precision and computationally much simpler method will be a critical step for the development of an embedded real-time system for autonomous measurements using an SMI sensor.

Amelioration of Accuracy of Displacement Measurement in Strong Feedback Regime with Collective Fringe Loss: Enlargement of Measurement Range of Self-Mixing Displacement Sensor

Amelioration of Accuracy of Displacement Measurement in Strong Feedback Regime with Collective Fringe Loss: Enlargement of Measurement Range of Self-Mixing Displacement Sensor

Improvement of precision of self-mixing displacement sensor based on region tracking for large displacement

Although it appears that there have been made enough researches as regards the estimation the optical feedback factor C of a self-mixing interferometer, any method of the C estimation cannot ensure its reliability if the operation of the self-mixing displacement sensor covers the strong feedback regime with fringe loss due to large displacement of a target. That is the main reason why the precision of the sensor degenerates for the measurement of large displacement. In the paper we propose a novel C estimation method called region tracking for the C value, which is indispensable for the measurement of long-range displacement, and demonstrate its fidelity experimentally. The experimental results in the paper were given when the target distance was about 60 cm and the target displacement 25 mm. The displacement reconstruction based on the proposed region tracking method ensures a better precision than a half wavelength, depending on the method of displacement retrieval. The approach presented will make a great contribution to further improvement of the accuracy of the self-mixing displacement sensor for large displacement.

Variable Optical Feedback-Based Behavioral Model of a Self-Mixing Laser Sensor

In this paper, a unified behavioral model of laser feedback based self-mixing interferometry (SMI) is proposed which is able to accurately model the SMI sensor signals encountered under experimental variable optical feedback conditions. The model provides correct SMI signals whether feedback is varied in a continuous or discrete manner, while spanning all major feedback regimes (such as weak-, moderate-, and strong-feedback regime) used for sensing applications. As a result, the proposed model allows the simulation of SMI signals in the presence of speckle which is of upmost importance to develop future efficient algorithms to reconstruct target displacements. The optical speckle usually occurs when the target of comparable surface roughness to the laser wavelength is moving as it induces variation of the optical feedback factor. The proposed model is shown to be able to address such cases and in particular to be able to reproduce very similar SMI signals to those acquired in the presence of speckle. It is thus anticipated that the proposed model would facilitate the design and testing of novel SMI algorithms and systems dedicated to the processing of variable optical feedback based SMI signals for metric sensing applications.

On Two Fourier Transform-Based Methods for Estimation of Displacement and Parameters of Self-Mixing Interferometry Over Major Optical Feedback Regimes

Using a self-mixing laser interferometric sensor, the aim of this paper is to propose two new and distinct Fourier transform based methods for estimation of optical coupling factor and linewidth enhancement factor, as well as displacement of a target over all feedback regimes by processing the feedback phase. First algorithm deals only with band-limited smooth displacements, while second method deals with rather more general, smooth displacements. Under noiseless simulations over diverse target motion conditions and optical feedback regimes, these algorithms (first and second) have shown picometric displacement sensing precision of 1.1264 pm and 1.0996 pm respectively, for laser wavelength of 785 nm. The performance of proposed methods has also been quantified in case of additive noise. During experimental verification, by using a reference sensor with 2 nm resolution, their precision was measured to be 36.2142 nm and 34.4388 nm respectively, for weak-, moderate-, and strong-optical feedback regime signals. Importantly, for strong feedback regime, these methods have shown better performance than two previously reported methods.

Deformation Method of Self-Mixing Laser Sensor’s Feedback Phase for Estimation of Optical Feedback Coupling Factor and Displacement

This paper, while focusing on post-perturbed phase processing of optical feedback based self-mixing laser displacement sensor, rigorously derives a general strategy to achieve the particular task of retrieving displacement from perturbed (feedback based) phase based on a proposition, which has been proved separately. From this, a new algorithm has been derived for estimation of optical feedback coupling factor and corresponding displacement over weak-, moderate-, and strong-optical feedback regimes, by using the concept of deformation. This method can work on all displacements so long as these are sufficiently smooth, i.e, have enough continuous derivatives. The algorithm’s steps are shown to be mathematically consistent. Furthermore, its performance has also been verified, and compared with a previous method, by using simulated and experimental signals for an SM sensor with emission wavelength of 785 nm. Displacement measurement precision has also been quantified by using a commercial transducer with 2 nm resolution showing that the proposed method provides comparable displacement precision even for fringe-loss affected, strong-feedback regime signals.

High Resolution Laser Self-Mixing Displacement Sensor Under Large Variation in Optical Feedback and Speckle

Self-Mixing interferometry (SMI) signal characteristics are highly dependent on both the operating optical regime and target surface. In this paper, a method is proposed to overcome some identified limitations of the even power scalable algorithm (EPSA), such as the required operating regime to be weak feedback. In addition, by using the up-sampling techniques, the number of stages involved in the even-power scalable algorithm can be drastically increased without any data acquisition bandwidth modification. Here, 10 successive stages have been successfully implemented to achieve a theoretical resolution of ${\lambda } _{\sf 0}/ {\sf 2}^{\sf 13}$ . It is further shown that the proposed method can handle and process weak, moderate and strong feedback regime as well as speckle affected SMI signals more efficiently. Lastly, FPGA based hardware emulation of EPSA is also done for later embedded implementation of this high-resolution algorithm. FPGA synthesis results show that the designed system can measure maximum target velocity up to 1.18 m/s while consuming total power of 1.4W.

High-speed joint estimation of for strong feedback regime with fringe loss

A self-mixing (SM) displacement sensor is very simple and economic in hardware. In order to improve the resolution of the displacement measurement, the optical feedback factor C must be estimated for the phase unwrapping method (PUM). In particular, when the SM sensor operates in a wide range of the C value including the strong feedback regime with fringe loss, the C estimation is necessary even for any consecutive samples based unwrapping (CSU) method or fringe counting method, which does not intrinsically require the C estimation. It is because each fringe of self-mixing signals (SMSs) in such a case does not correspond to the half of the emission wavelength of the laser. The paper proposes a method of the high speed joint estimation of the optical feedback factor and the linewidth enhancement factor in the case of the strong feedback regime with fringe loss, i.e., when C>7.8. Incorporation of the presented approach with those reported by Ri et al. (2020) and Kim (2020) which have presented the immediate C estimation method in a weak regime and a moderate or strong regime without fringe loss, respectively, will give an effective tool to develop a low-cost real-time SM displacement sensor with a better resolution than half-wavelength.

Immediate estimation of feedback factor and linewidth enhancement factor from measured self-mixing signals under moderate or strong regime

The estimation of self-mixing interferometry (SMI) parameters such as optical feedback factor C and linewidth enhancement factor is essential to self-mixing (SM) displacement sensors with sub-wavelength resolution. We propose a new method, which is a very simple and fast method to estimate C and when C > 1 based on an analysis of self-mixing signals (SMSs) in a laser diode. The proposed method is extremely simple, because it takes advantage of analytic relations which enable one to obtain C and from the simple algebraic operations of the data from SMSs. The simplicity of the method is a great help to developing a compact and low-cost self-mixing (SM) displacement sensor with sub-wavelength resolution which cannot ensure complex operation such as optimization. And the proposed method is highly effective in developing real-time and fast algorithm for the C estimation. This method is applicable when the sensor operates under a moderate or strong feedback regime. The estimation accuracy of C and are comparable to the results of Yu et al 2004 IEEE Photon. Technol. Lett. 16 990–2; Zabit 2010 PhD Thesis Toulouse; and Fan 2011 MS Thesis University of Wollongong, respectively, and the estimation time of the C parameter is over 30 times faster than Zabit and Fan.

Effect of linewidth enhancement factor on displacement reconstruction and immediate estimation of feedback factor for weak feedback

Metrology based on self-mixing interferometry (SMI) covers a wide range of metrical application such as measurement of distance displacement, vibration, velocity, flow and size of Brownian particles. In general, two SMI parameters namely, optical feedback factor C and linewidth enhancement factor (LEF) α are significant in the above-mentioned measurements. Particularly, the joint estimation of C and α is the key to real-time displacement self-mixing (SM) sensor with sub-wavelength resolution.The application of the approach to the immediate estimation of C and α proposed by Kim et al. (2018) is limited to the moderate and strong feedback regime. The paper presents an approach to the immediate estimation of C for the weak feedback regime, to which the approach by Kim et al. (2018) is impossible to be applied, thus allowing the immediate joint estimation method to be applied to all the regimes. Because the proposed method is incomparably simpler than the previous ones and very efficient in hardware, it will be of great assistance to developing a low-cost real-time SM displacement sensor with sub-wavelength resolution in which complex computation such as optimization are impossible. In addition, the paper discusses the effect of C and α on the accuracy of displacement reconstruction.

Effect of Linewidth Enhancement Factor on Fringe in a Self-Mixing Signal and Improved Estimation of Feedback Factor in Laser Diode

The optical output power of a laser diode is modulated by the self-mixing effect when the optical beam is back-reflected or back-scattered into the laser cavity by a target. The optical feedback factor C is the most important one that defines the feature of the self-mixing signals (SMSs). And the estimation of C is indispensable for the displacement reconstruction by the phase unwrapping method because it is impossible to reconstruct the displacement with sub-wavelength resolution, provided the exact value of C is unknown. Unfortunately, C is subject to constant change during the measurement and, what is worse; its estimation is usually very time-consuming. This paper studies the feature of a high and low fringe of SMSs in moderate and strong feedback regime and the effect of the feedback factor and the linewidth enhancement factor on the fringes and presents a simple approach to the estimation of C when C > 1.5 based on the behavioral model proposed by Plantier et al. In particular, the novel approach enables fast direct estimation of C because it is based on analytic relations between C and the amplitudes of the high and low peak in SMSs.

Atmospheric oxygen regulation at low Proterozoic levels by incomplete oxidative weathering of sedimentary organic carbon

It is unclear why atmospheric oxygen remained trapped at low levels for more than 1.5 billion years following the Paleoproterozoic Great Oxidation Event. Here, we use models for erosion, weathering and biogeochemical cycling to show that this can be explained by the tectonic recycling of previously accumulated sedimentary organic carbon, combined with the oxygen sensitivity of oxidative weathering. Our results indicate a strong negative feedback regime when atmospheric oxygen concentration is of order pO2∼0.1 PAL (present atmospheric level), but that stability is lost at pO2<0.01 PAL. Within these limits, the carbonate carbon isotope (δ13C) record becomes insensitive to changes in organic carbon burial rate, due to counterbalancing changes in the weathering of isotopically light organic carbon. This can explain the lack of secular trend in the Precambrian δ13C record, and reopens the possibility that increased biological productivity and resultant organic carbon burial drove the Great Oxidation Event.

Instabilities and Bifurcations of a DFB Laser Frequency-Stabilized by a High-Finesse Resonator

Recently reported miniature configurations with semiconductor distributed feedback lasers under resonant feedback are considered theoretically. Limiting instabilities and bifurcations are systematically explored by combining the theory of chirp reduction and a bifurcation analysis. It is shown that the regime of optimal chirp reduction also exhibits the best local stability. It suffers only from undamping of relaxation oscillations in a finite interval of feedback strength. The existence of a separate strong-feedback regime with high stability is consistent with the two experiments available so far. We regard this feature as a generic specificum of miniature configurations not known from large-scale setups. This regime can open new prospects for applications of compact frequency-stabilized semiconductor lasers with extremely low noise and small line width.

A Numerical Analysis for Optimizing the Gratings Length and Coupling Coefficient for High Reflectivity and Low Cavity Loss in Fiber Grating Fabry-Perot Laser Model

The effects of gratings length (kLFG) and amplitude coupling (Co) coefficients on the effective reflectivity (Reff) and the total cavity loss (αtot) of an external cavity laser source (ECLS) based fiber Bragg gratings (FBGs) are numerically analyzed for designing a laser source operating in strong feedback regime (Regime V). In this study, FBG is used as a wavelength selective element to control the properties of the laser output by controlling the fiber gratings reflectivity level. The study is performed by modifying full analytical expressions for the Reff and the αtot based on laser coupled-wave equations. Results show that Reff is strongly dependent on kLg and Co. Also, it is found that αtot has been reduced significantly with increasing Co, especially at high value for kLG (kLFG&gt; 1.5).

Nanoscale Displacement Sensing Based on Nonlinear Frequency Mixing in Quantum Cascade Lasers

We demonstrate a sensor scheme for nanoscale target displacement that relies on a single quantum cascade laser (QCL) subject to optical feedback. The system combines the inherent sensitivity of QCLs to optical reinjection and their ultrastability in the strong feedback regime where nonlinear frequency mixing phenomena are enhanced. An experimental proof of principle in the micrometer wavelength scale is provided. We perform real-time measurements of displacement with λ/100 resolution by inserting a fast-shifting reference etalon in the external cavity. The resulting signal dynamics at the QCL terminals shows a stroboscopic-like effect that relates the sensor resolution with the reference etalon speed. Intrinsic limits to the measurement algorithm and to the reference speed are discussed, disclosing that nanoscale ranges are attainable.