Feedback Regimes of LFI Sensors: Experimental Investigations.

In this article, we revisit the concept of optical feedback regimes in diode lasers and explore each regime experimentally from a somewhat unconventional point of view by relating the feedback regimes to the laser bias current and its optical feedback level. The results enable setting the operating conditions of the diode laser in different applications requiring operation in different feedback regimes. We experimentally explored and theoretically supported this relationship from the standard Lang and Kobayashi rate equation model for a laser diode under optical feedback. All five regimes were explored for two major types of laser diodes: inplane lasers and vertical-cavity surface emitting lasers. For both lasers, we mapped the self-mixing strength vs. drive current and feedback level, observed the differences in the shape of the self-mixing fringes between the two laser architectures and a general simulation, and monitored other parameters of the lasers with changing optical feedback.

Self-Pulsations in Terahertz Quantum Cascade Lasers under Strong Optical Feedback: The Effect of Multiple Reflections in the External Cavity.

We have recently reported the self-pulsation phenomenon under strong optical feedback in terahertz (THz) quantum cascade lasers (QCLs). One important issue, however, we left open: the effect of multiple round trips in the external cavity on the laser response to feedback. Our current analysis also casts additional light on the phenomenon of self-pulsations. Using only one external cavity round trip (ECRT) in the model has been the common approach following the seminal paper by Lang-Kobayashi in 1980. However, the conditions under which the Lang-Kobayashi model, in its original single-ECRT formulation, is applicable has been rarely explored. In this work, we investigate the self-pulsation phenomenon under multiple ECRTs. We found that the self-pulsation waveform changes when considering more than one ECRT. This we attribute to the combined effect of the extended external cavity length and the frequency modulation of the pulsation frequency by the optical feedback. Our findings add to the understanding of the optical feedback dynamics under multiple ECRTs and provide a pathway for selecting the appropriate numerical model to study the optical feedback dynamics in THz QCLs and semiconductor lasers in general.

Terahertz quantum cascade laser under optical feedback: effects of laser self-pulsations on self-mixing signals.

In this article, we explore the interplay between the self-pulsations (SPs) and self-mixing (SM) signals generated in terahertz (THz) quantum cascade lasers (QCLs) under optical feedback. We find that optical feedback dynamics in a THz QCL, namely, SPs, modulate the conventional SM interference fringes in a laser feedback interferometry system. The phenomenon of fringe loss in the SM signal - well known in interband diode lasers - was also observed along with pronounced SPs. With an increasing optical feedback strength, SM interference fringes transition from regular fringes at weak feedback (C ≤ 1) to fringes modulated by SPs under moderate feedback (1 < C ≤ 4.6), and then [under strong feedback (C > 4.6)] to a SM waveform with reduced number of fringes modulated by SP, until eventually (under even greater feedback) all the fringes are lost and only SPs are left visible. The transition route described above was identified in simulation when the SM fringes are created either by a moving target or a current modulation of the THz QCL. This SM signal transition route was successfully validated experimentally in a pulsed mode THz QCL with SM fringes created by current modulation during the pulse. The effects of SP dynamics in laser feedback interferometric system investigated in this work not only provides a further understanding of nonlinear dynamics in a THz QCL but also helps to understand the SM waveforms generated in a THz QCLs when they are used for various sensing and imaging applications.

Laser feedback interferometry in multi-mode terahertz quantum cascade lasers.

The typical modal characteristics arising during laser feedback interferometry (LFI) in multi-mode terahertz (THz) quantum cascade lasers (QCLs) are investigated in this work. To this end, a set of multi-mode reduced rate equations with gain saturation for a general Fabry-Pérot multi-mode THz QCL under optical feedback is developed. Depending on gain bandwidth of the laser and optical feedback level, three different operating regimes are identified, namely a single-mode regime, a multi-mode regime, and a tuneable-mode regime. When the laser operates in the single-mode and multi-mode regimes, the self-mixing signal amplitude (peak to peak value of the self-mixing fringes) is proportional to the feedback coupling rate at each mode frequency. However, this rule no longer holds when the laser enters into the tuneable-mode regime, in which the feedback level becomes sufficiently strong (the boundary value of the feedback level depends on the gain bandwidth). The mapping of the identified feedback regimes of the multi-mode THz QCL in the space of the gain bandwidth and feedback level is investigated. In addition, the dependence of the aforementioned mapping of these three regimes on the linewidth enhancement factor of the laser is also explored, which provides a systematic picture of the potential of LFI in multi-mode THz QCLs for spectroscopic sensing applications.

Coherent imaging using laser feedback interferometry with pulsed-mode terahertz quantum cascade lasers.

We report a coherent terahertz (THz) imaging system that utilises a quantum cascade laser (QCL) operating in pulsed-mode as both the source and detector. The realisation of a short-pulsed THz QCL feedback interferometer permits both high peak powers and improved thermal efficiency, which enables the cryogen-free operation of the system. In this work, we demonstrated pulsed-mode swept-frequency laser feedback interferometry experimentally. Our interferometric detection scheme not only permits the simultaneous creation of both amplitude and phase images, but inherently suppresses unwanted background radiation. We demonstrate that the proposed system utilising microsecond pulses has the potential to achieve 0.25 mega-pixel per second acquisition rates, paving the pathway to video frame rate THz imaging.

Microparticle discrimination using laser feedback interferometry.

In this work, we present a method to discriminate between different microparticle sizes in mixed flowing media based on laser feedback interferometry, which could ultimately form the basis for a small, low-cost, real-time microembolus detector. We experimentally evaluated the performance of the system using microparticle phantoms, and the system achieved approximately 45% positive predictive value and better than 98% negative predictive value in the detection and classification of abnormally large particles.

Polarization-sensitive laser feedback interferometry for specular reflection removal.

Specular reflection from the surface of targets or prepared specimens represents a significant problem in optical microscopy and related optical imaging techniques as usually the surface reflection does not contribute to the desired signal. Solutions exist for many of these imaging techniques; however, remedial techniques for imaging based on laser feedback interferometry (LFI) are absent. We propose a reflection cancellation technique based on crossed-polarization filtering that is tailored for a typical LFI configuration. The technique is validated with three experimental designs, and a significant improvement of about 40 dB in the ratio of the diffuse and specular LFI signal is observed. Applications of this principle extend from specular reflection removal to characterization of target materials in industrial to biomedical domains.

Multi-spectral terahertz sensing: proposal for a coupled-cavity quantum cascade laser based optical feedback interferometer.

We propose a laser feedback interferometer operating at multiple terahertz (THz) frequency bands by using a pulsed coupled-cavity THz quantum cascade laser (QCL) under optical feedback. A theoretical model that contains multi-mode reduced rate equations and thermal equations is presented, which captures the interplay between electro-optical, thermal, and feedback effects. By using the self-heating effect in both active and passive cavities, self-mixing signal responses at three different THz frequency bands are predicted. A multi-spectral laser feedback interferometry system based on such a coupled-cavity THz QCL will permit ultra-high-speed sensing and spectroscopic applications including material identification.

Origin of terminal voltage variations due to self-mixing in terahertz frequency quantum cascade lasers.

We explain the origin of voltage variations due to self-mixing in a terahertz (THz) frequency quantum cascade laser (QCL) using an extended density matrix (DM) approach. Our DM model allows calculation of both the current-voltage (I-V) and optical power characteristics of the QCL under optical feedback by changing the cavity loss, to which the gain of the active region is clamped. The variation of intra-cavity field strength necessary to achieve gain clamping, and the corresponding change in bias required to maintain a constant current density through the heterostructure is then calculated. Strong enhancement of the self-mixing voltage signal due to non-linearity of the (I-V) characteristics is predicted and confirmed experimentally in an exemplar 2.6 THz bound-to-continuum QCL.

Model for a pulsed terahertz quantum cascade laser under optical feedback.

Optical feedback effects in lasers may be useful or problematic, depending on the type of application. When semiconductor lasers are operated using pulsed-mode excitation, their behavior under optical feedback depends on the electronic and thermal characteristics of the laser, as well as the nature of the external cavity. Predicting the behavior of a laser under both optical feedback and pulsed operation therefore requires a detailed model that includes laser-specific thermal and electronic characteristics. In this paper we introduce such a model for an exemplar bound-to-continuum terahertz frequency quantum cascade laser (QCL), illustrating its use in a selection of pulsed operation scenarios. Our results demonstrate significant interplay between electro-optical, thermal, and feedback phenomena, and that this interplay is key to understanding QCL behavior in pulsed applications. Further, our results suggest that for many types of QCL in interferometric applications, thermal modulation via low duty cycle pulsed operation would be an alternative to commonly used adiabatic modulation.

Concurrent Reflectance Confocal Microscopy and Laser Doppler Flowmetry to Improve Skin Cancer Imaging: A Monte Carlo Model and Experimental Validation.

Optical interrogation of suspicious skin lesions is standard care in the management of skin cancer worldwide. Morphological and functional markers of malignancy are often combined to improve expert human diagnostic power. We propose the evaluation of the combination of two independent optical biomarkers of skin tumours concurrently. The morphological modality of reflectance confocal microscopy (RCM) is combined with the functional modality of laser Doppler flowmetry, which is capable of quantifying tissue perfusion. To realize the idea, we propose laser feedback interferometry as an implementation of RCM, which is able to detect the Doppler signal in addition to the confocal reflectance signal. Based on the proposed technique, we study numerical models of skin tissue incorporating two optical biomarkers of malignancy: (i) abnormal red blood cell velocities and concentrations and (ii) anomalous optical properties manifested through tissue confocal reflectance, using Monte Carlo simulation. We also conduct a laboratory experiment on a microfluidic channel containing a dynamic turbid medium, to validate the efficacy of the technique. We quantify the performance of the technique by examining a signal to background ratio (SBR) in both the numerical and experimental models, and it is shown that both simulated and experimental SBRs improve consistently using this technique. This work indicates the feasibility of an optical instrument, which may have a role in enhanced imaging of skin malignancies.

Laser Feedback Interferometry as a Tool for Analysis of Granular Materials at Terahertz Frequencies: Towards Imaging and Identification of Plastic Explosives.

We propose a self-consistent method for the analysis of granular materials at terahertz (THz) frequencies using a quantum cascade laser. The method is designed for signals acquired from a laser feedback interferometer, and applied to non-contact reflection-mode sensing. Our technique is demonstrated using three plastic explosives, achieving good agreement with reference measurements obtained by THz time-domain spectroscopy in transmission geometry. The technique described in this study is readily scalable: replacing a single laser with a small laser array, with individual lasers operating at different frequencies will enable unambiguous identification of select materials. This paves the way towards non-contact, reflection-mode analysis and identification of granular materials at THz frequencies using quantum cascade lasers.

Multiple signal classification for self-mixing flowmetry.

For the first time to our knowledge, we apply the multiple signal classification (MUSIC) algorithm to signals obtained from a self-mixing flow sensor. We find that MUSIC accurately extracts the fluid velocity and exhibits a markedly better signal-to-noise ratio (SNR) than the commonly used fast Fourier transform (FFT) method. We compare the performance of the MUSIC and FFT methods for three decades of scatterer concentration and fluid velocities from 0.5 to 50 mm/s. MUSIC provided better linearity than the FFT and was able to accurately function over a wider range of algorithm parameters. MUSIC exhibited excellent linearity and SNR even at low scatterer concentration, at which the FFT's SNR decreased to impractical levels. This makes MUSIC a particularly attractive method for flow measurement systems with a low density of scatterers such as microfluidic and nanofluidic systems and blood flow in capillaries.

Effect of the optical system on the Doppler spectrum in laser-feedback interferometry.

We present a comprehensive analysis of factors influencing the morphology of the Doppler spectrum obtained from a laser-feedback interferometer. We explore the effect of optical system parameters on three spectral characteristics: central Doppler frequency, broadening, and signal-to-noise ratio. We perform four sets of experiments and replicate the results using a Monte Carlo simulation calibrated to the backscattering profile of the target. We classify the optical system parameters as having a strong or weak influence on the Doppler spectrum. The calibrated Monte Carlo approach accurately reproduces experimental results, and allows one to investigate the detailed contribution of system parameters to the Doppler spectrum, which are difficult to isolate in experiment.

Effect of injection current and temperature on signal strength in a laser diode optical feedback interferometer.

We present a simple analytical model that describes the injection current and temperature dependence of optical feedback interferometry signal strength for a single-mode laser diode. The model is derived from the Lang and Kobayashi rate equations, and is developed both for signals acquired from the monitoring photodiode (proportional to the variations in optical power) and for those obtained by amplification of the corresponding variations in laser voltage. The model shows that both the photodiode and the voltage signal strengths are dependent on the laser slope efficiency, which itself is a function of the injection current and the temperature. Moreover, the model predicts that the photodiode and voltage signal strengths depend differently on injection current and temperature. This important model prediction was proven experimentally for a near-infrared distributed feedback laser by measuring both types of signals over a wide range of injection currents and temperatures. Therefore, this simple model provides important insight into the radically different biasing strategies required to achieve optimal sensor sensitivity for both interferometric signal acquisition schemes.

Methodology for materials analysis using swept-frequency feedback interferometry with terahertz frequency quantum cascade lasers.

Recently, we demonstrated an interferometric materials analysis scheme at terahertz frequencies based on the self-mixing effect in terahertz quantum cascade lasers. Here, we examine the impact of variations in laser operating parameters, target characteristics, laser-target system properties, and the quality calibration standards on our scheme. We show that our coherent scheme is intrinsically most sensitive to fluctuations in interferometric phase, arising primarily from variations in external cavity length. Moreover we demonstrate that the smallest experimental uncertainties in the determination of extinction coefficients are expected for lossy materials.

Imaging of acoustic fields using optical feedback interferometry.

This study introduces optical feedback interferometry as a simple and effective technique for the two-dimensional visualisation of acoustic fields. We present imaging results for several pressure distributions including those for progressive waves, standing waves, as well as the diffraction and interference patterns of the acoustic waves. The proposed solution has the distinct advantage of extreme optical simplicity and robustness thus opening the way to a low cost acoustic field imaging system based on mass produced laser diodes.

Self-mixing sensing system based on uncooled vertical-cavity surface-emitting laser array: linking multichannel operation and enhanced performance.

We compare the performance of a self-mixing (SM) sensing system based on an uncooled monolithic array of 24×1 vertical-cavity surface-emitting lasers (VCSELs) in two modes of operation: single active channel and the concurrent multichannel operation. We find that the signal-to-noise ratio of individual SM sensors in a VCSEL array is markedly improved by multichannel operation, as a consequence of the increased operational temperature of the sensors. The performance improvement can be further increased by manufacturing VCSEL arrays with smaller pitch. This has the potential to produce an imaging system with high spatial and temporal resolutions that can be operated without temperature stabilization.

On the nature of Acket's characteristic parameter C in semiconductor lasers.

Quasi-static interferometric signals in lasers under feedback arise from slowly varying perturbations of the intracavity electric field resulting from the reinjection of a portion of the emitted field into the cavity. Such interferometric signals are well described by the steady-state solution to the Lang-Kobayashi rate equation model. We give an exact series expansion for this steady-state solution that shows precisely how Acket's characteristic parameter C and Henry's linewidth enhancement factor α influence such signals. We show how the series coefficients can be extracted easily and explain how to determine C and α directly from them. Moreover, we draw a precise analogy between self-mixing and FM signals, showing that C plays exactly the same role in self-mixing as the modulation index does in FM.

Solving self-mixing equations for arbitrary feedback levels: a concise algorithm.

Self-mixing laser sensors show promise for a wide range of sensing applications, including displacement, velocimetry, and fluid flow measurements. Several techniques have been developed to simulate self-mixing signals; however, a complete and succinct process for synthesizing self-mixing signals has so far been absent in the open literature. This article provides a systematic numerical approach for the analysis of self-mixing sensors using the steady-state solution to the Lang and Kobayashi model. Examples are given to show how this method can be used to synthesize self-mixing signals for arbitrary feedback levels and for displacement, distance, and velocity measurement. We examine these applications with a deterministic stimulus and discuss the velocity measurement of a rough surface, which necessitates the inclusion of a random stimulus.