Karl Bertling

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.

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.

Displacement and distance measurement using the change in junction voltage across a laser diode due to the self-mixing effect

The conventional self-mixing sensing systems employ a detection scheme utilizing the photocurrent from an integrated photodiode. This work reports on an alternative way of implementing a Vertical-Cavity Surface-Emitting Laser (VCSEL) based self-mixing sensor using the laser junction voltage as the source of the self-mixing signal. We show that the same information can be obtained with only minor changes to the extraction circuitry leading to potential cost saving with reductions in component costs and complexity. The theoretical linkage between voltage and photocurrent within the self-mixing model is presented. Experiments using both photo current and voltage detection were carried out and the results obtained show good agreement with the theory. Similar error trends for both detection regimes were observed.

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.

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.

Self-mixing laser Doppler flow sensor: an optofluidic implementation.

We present the miniaturization of self-mixing interferometry (SMI) into a microfluidic circuit using an optical fiber, forming an optofluidic device that can be used as a component in lab on a chip systems. We characterize the performance of the device as a fluid velocity (and hence flow) sensor, showing it to produce good accuracy and correlation with theory over a range of velocities from 0.5 to 60  mm/s and almost four decades of scatterer concentration. SMI in an optofluidic system has the advantage that only a single path to the optical inspection point is needed, as the laser source is also the receiver of light. In addition, the same system that is used for measuring fluid velocity can be used to measure other quantities such as particle size. The configuration presented is inherently easy to optically align due to the self-aligned property of SMI and divergent nature of light exiting the embedded optical fiber, providing for low-cost manufacturing.