Three-dimensional terahertz imaging using swept-frequency feedback interferometry with a quantum cascade laser

Terahertz microscopy using laser feedback interferometry based on a generalised phase-stepping algorithm

In this paper we report an improved method of coherent sensing through the use of a generalized phase-stepping algorithm to extract magnitude and phase information from interferometric fringes acquired by laser feedback interferometry (LFI). Our approach allows for significantly reduced optical sampling and acquisition times whilst also avoiding the need for fitting to complex models of lasers under optical feedback in post-processing. We investigate theoretically the applicability of this method under different levels of optical feedback, different laser parameters, and for different sampling conditions. We furthermore validate its use experimentally for LFI-based sensing using a terahertz (THz)-frequency laser in both far-field and near-field sensing configurations. Finally we demonstrate our approach for two-dimensional nanoscale imaging of the out-of-plane field supported by individual micro-resonators at THz frequencies. Our results show that fully coherent sensing can be achieved reliably with as little as 4 sampling points per imaging pixel, opening up opportunities for fast coherent sensing not only at THz frequencies but across the visible and infra-red spectrum.

Imaging elastic waves in solids: how to use laser feedback interferometry to visualize them

The use of ultrasonic elastic waves is a well established technique for non-destructive testing of materials and structures, in particular to exploit the interaction of waves with structural features to detect and characterize defects. Optical methods offer the advantage of visualising the distribution of elastic waves in a non-contact manner without disturbing the elastic wave. In this work we propose a laser feedback interferometry (LFI) based system as a cost effective, non-contact, alternative to a well established laser Doppler vibrometer technique. We demonstrate the visualization of the elastic waves, using an example of an elastic wave propagating through a prismatic acrylic rod. We show that the ultra-compact and simple implementation of LFI enables accurate visualization of the elastic waves in solids, and opens the pathway to a range of new opportunities in ultrasonic non-destructive testing and evaluation.

THz microscope for three-dimensional imaging with superconducting Josephson junctions

Superconducting Josephson junctions have a wide range of applications ranging from quantum computing to voltage standards, and they may also be employed as versatile sensors for high-frequency radiation and magnetic fields. In this work, we present a unique measurement setup utilizing a single Josephson junction on a cantilever for high-resolution spatial measurements of spectroscopically resolved THz and microwave field distributions. This THz microscope can be utilized to measure power and frequency of electromagnetic radiation from ∼1 GHz to 5 THz. It may also be used to measure static magnetic fields and provide topological scans of samples. The samples can be both actively radiating or passively irradiated at either room temperature or cryogenic temperatures. We review the measurement setup of the THz microscope and describe the evaluation of its measurement data to achieve three-dimensional visualizations of the field distributions. The diverse capabilities of this unique tool are demonstrated by its different measurement modes with measurements of field distributions at 20 GHz and 1.4 THz, spectroscopically resolved THz measurements, and magnetic field measurements.

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.

Secondary envelope extraction based on multiple Hilbert transforms for laser self-mixing micro-vibration measurement

This paper presents a method that can be applied to weak feedback and full-range moderate feedback in the field of self-mixing interference measurement, and the target motion displacement can be obtained by multiple Hilbert transforms of the signal after the secondary envelope extraction. Simulations and experiments of multiple micro-vibration measurements were performed with different optical feedback factors, and the results were consistent with theoretical analysis. This method effectively eliminates the impact of the self-mixing interference signal with fringe shift on micro-vibration reconstruction.

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.

Gas spectroscopy with integrated frequency monitoring through self-mixing in a terahertz quantum-cascade laser

We demonstrate a gas spectroscopy technique, using self-mixing in a 3.4 terahertz quantum-cascade laser (QCL). All previous QCL spectroscopy techniques have required additional terahertz instrumentation (detectors, mixers, or spectrometers) for system pre-calibration or spectral analysis. By contrast, our system self-calibrates the laser frequency (i.e., with no external instrumentation) to a precision of 630 MHz (0.02%) by analyzing QCL voltage perturbations in response to optical feedback within a 0-800 mm round-trip delay line. We demonstrate methanol spectroscopy by introducing a gas cell into the feedback path and show that a limiting absorption coefficient of ∼1×10^-4  cm^-1 is resolvable.

Confocal laser feedback tomography for skin cancer detection

Tomographic imaging of soft tissue such as skin has a potential role in cancer detection. The penetration of infrared wavelengths makes a confocal approach based on laser feedback interferometry feasible. We present a compact system using a semiconductor laser as both transmitter and receiver. Numerical and physical models based on the known optical properties of keratinocyte cancers were developed. We validated the technique on three phantoms containing macro-structural changes in optical properties. Experimental results were in agreement with numerical simulations and structural changes were evident which would permit discrimination of healthy tissue and tumour. Furthermore, cancer type discrimination was also able to be visualized using this imaging technique.

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.

Analytical stability boundaries for quantum cascade lasers subject to optical feedback

We consider nonlinear rate equations appropriate for a quantum cascade laser subject to optical feedback. We analyze the conditions for a Hopf bifurcation in the limit of large values of the delay. We obtain a simple expression for the critical feedback rate that highlights the effects of key parameters such as the linewidth enhancement factor and the pump. All our asymptotic approximations are validated numerically by using a path continuation technique that allows us to follow Hopf bifurcation points in parameter space.

Study of QCL Laser Sources for the Realization of Advanced Sensors

We study the nonlinear dynamics of a quantum cascade laser (QCL) with a strong reinjection provided by the feedback from two external targets in a double cavity configuration. The nonlinear coupling of interferometric signals from the two targets allows us to propose a displacement sensor with nanometric resolution. The system exploits the ultra-stability of QCLs in self-mixing configuration to access the intrinsic nonlinearity of the laser, described by the Lang–Kobayashi model, and it relies on a stroboscopic-like effect in the voltage signal registered at the QCL terminals that relates the “slow” target motion to the “fast” target one.