Thomas Taimre

Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing

This tutorial presents a guided tour of laser feedback interferometry, from its origin and early development through its implementation to a slew of sensing applications, including displacement, distance, velocity, flow, refractive index, and laser linewidth measurement. Along the way, we provide a step-by-step derivation of the basic rate equations for a laser experiencing optical feedback starting from the standard Lang and Kobayashi model and detail their subsequent reduction in steady state to the excess-phase equation. We construct a simple framework for interferometric sensing applications built around the laser under optical feedback and illustrate how this results in a series of straightforward models for many signals arising in laser feedback interferometry. Finally, we indicate promising directions for future work that harnesses the self-mixing effect for sensing applications.

Terahertz imaging using quantum cascade lasers—a review of systems and applications

The terahertz (THz) frequency quantum cascade laser (QCL) is a compact source of THz radiation offering high power, high spectral purity and moderate tunability. As such, these sources are particularly suited to the application of THz frequency imaging across a range of disciplines, and have motivated significant research interest in this area over the past decade. In this paper we review the technological approaches to THz QCL-based imaging and the key advancements within this field. We discuss in detail a number of imaging approaches targeted to application areas including multiple-frequency transmission and diffuse reflection imaging for the spectral mapping of targets; as well as coherent approaches based on the self-mixing phenomenon in THz QCLs for long-range imaging, three-dimensional imaging, materials analysis, and high-resolution inverse synthetic aperture radar imaging.

Swept-frequency feedback interferometry using terahertz frequency QCLs: a method for imaging and materials analysis

The terahertz (THz) frequency quantum cascade laser (QCL) is a compact source of high-power radiation with a narrow intrinsic linewidth. As such, THz QCLs are extremely promising sources for applications including high-resolution spectroscopy, heterodyne detection, and coherent imaging. We exploit the remarkable phase-stability of THz QCLs to create a coherent swept-frequency delayed self-homodyning method for both imaging and materials analysis, using laser feedback interferometry. Using our scheme we obtain amplitude-like and phase-like images with minimal signal processing. We determine the physical relationship between the operating parameters of the laser under feedback and the complex refractive index of the target and demonstrate that this coherent detection method enables extraction of complex refractive indices with high accuracy. This establishes an ultimately compact and easy-to-implement THz imaging and materials analysis system, in which the local oscillator, mixer, and detector are all combined into a single laser.

Generalized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization

The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper, we investigate how these methods can be eXtended to provide a general non-parametric cross-entropy framework based on φ-divergence distance measures. We show how the χ 2 distance, in particular, yields a viable alternative to the Kullback—Leibler distance. The theory is illustrated with various eXamples from density estimation, rare-event simulation and continuous multi-eXtremal optimization.

Coherent three-dimensional terahertz imaging through self-mixing in a quantum cascade laser

We demonstrate coherent terahertz (THz) frequency imaging using the self-mixing effect in a quantum cascade laser (QCL). Self-mixing voltage waveforms are acquired at each pixel of a two-dimensional image of etched GaAs structures and fitted to a three-mirror laser model, enabling extraction of the amplitude and phase parameters of the reflected field. From the phase, we reconstruct the depth of the sample surface, and we show that the amplitude can be related to the sample reflectance. Our approach is experimentally simple and compact, and does not require frequency stabilization of the THz QCL.

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 Ackets characteristic parameter C and Henrys 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.

Efficient prediction of terahertz quantum cascade laser dynamics from steady-state simulations

Terahertz-frequency quantum cascade lasers (THz QCLs) based on bound-to-continuum active regions are difficult to model owing to their large number of quantum states. We present a computationally efficient reduced rate equation (RE) model that reproduces the experimentally observed variation of THz power with respect to drive current and heat-sink temperature. We also present dynamic (time-domain) simulations under a range of drive currents and predict an increase in modulation bandwidth as the current approaches the peak of the light–current curve, as observed experimentally in mid-infrared QCLs. We account for temperature and bias dependence of the carrier lifetimes, gain, and injection efficiency, calculated from a full rate equation model. The temperature dependence of the simulated threshold current, emitted power, and cut-off current are thus all reproduced accurately with only one fitting parameter, the interface roughness, in the full REs. We propose that the model could therefore be used for rapid dynamical simulation of QCL designs.

Approach to frequency estimation in self-mixing interferometry: multiple signal classification

Based on the nature of self-mixing signals, we propose the use of the multiple signal classification (MUSIC) algorithm in place of the fast Fourier transform (FFT) for processing signals obtained from self-mixing interferometry (SMI). We apply this algorithm to two representative SMI measurement techniques: range finding and velocimetry. Applying MUSIC to SMI range finding, we find its signal-to-noise ratio performance to be significantly better than that of the FFT, allowing for more robust, longer-range measurement systems. We further demonstrate that MUSIC enables a fundamental change in how SMI Doppler velocity measurement is approached, letting one discard the complex fitting procedure and allowing for a real-time frequency estimation process.

Demonstration of the self-mixing effect in interband cascade lasers

In this Letter, we demonstrate the self-mixing effect in an interband cascade laser. We show that a viable self-mixing signal can be acquired through the variation in voltage across the laser terminals, thereby removing the need for an external detector. Using this interferometric technique, we have measured the displacement of a remote target, and also demonstrated high resolution imaging of a target. The proposed scheme represents a highly sensitive, compact, and self-aligned sensing technique with potential for materials analysis in the mid-infrared.

Terahertz inverse synthetic aperture radar imaging using self-mixing interferometry with a quantum cascade laser

We propose a terahertz (THz)-frequency synthetic aperture radar imaging technique based on self-mixing (SM) interferometry, using a quantum cascade laser. A signal processing method is employed which extracts and exploits the radar-related information contained in the SM signals, enabling the creation of THz images with improved spatial resolution. We demonstrate this by imaging a standard resolution test target, achieving resolution beyond the diffraction limit.