1. Introduction

Near-field nanoscopy at terahertz (THz) frequencies (0.1-10 THz, 3mm-3µm wavelength) has been growing intensely in the past 20 years, making the field incredibly broad [1]. It enables studies of object within a very large span of scales, from the wavelength scale (300 µm) to the nanometer scale; it had to be adapted to a broad range of instrumentations, promoting the development of a broad range of near-field probes (aperture-limited probes as fiber or hollow tips, or metal or silicon tips for which the resolution is wavelength independent) that can be used for imaging [1]. These developments offered unexpected opportunities. While it may be logical to have one instrument that fits all purposes, there is no universal THz near-field solution that is capable to address all the applications. The diversity of the field has been beneficial so far to the development and the understanding of the capabilities and limitation of the different near-field approaches. Presently, there is indeed choice which method to use for a given application, hence endorsing near-field THz nanoscopy as an universal tool for mapping waveguide and resonators-modes [2], metasurfaces [3] and bio-tissues [4] (over mm² areas) or nanowires [5], quantum dots [6], and photoexcited electromagnetic modes as plamons [7,8], plasmon-polaritons [9], excitons [10], or phonon polaritons [11,12] (over nanometer scales).

So far, THz scattering scanning near-field optical microscopy (s-SNOM) has been performed using broadband sources, such as those used in time domain TDS systems, that show a performance drop at frequencies > 1.8 THz [13], and only allow slow data acquisition rates (14 sec/pixel) [13], gas lasers [14], or bulky (not table-top) and high-cost free electron lasers [15], or, alternatively, sub-THz electronic sources, [16] or THz quantum cascade lasers (QCLs) emitting only one discrete frequency in a phase-sensitive detectorless configuration [17–19]. The main disadvantages of broadband THz sources are their cumbersome setups, which require an external laser to generate ultrashort pump pulses, their limited ( µW) output-powers and the need of sensitive THz detectors, whilst electronic sources and gas lasers only operate on specific modes, and are usually neither compact nor high power. In contrast, when THz QCLs are used for THz nanoscopy, they are powerful, do not require a separate detector, and can be eventually operated in a multi-frequency configuration, either with a few random emitted modes [19], or in a frequency comb configuration, with a sequence of multiple phase locked modes [20]. The right choice of an appropriate method in THz microscopy is critical.

Here, I discuss the potential of a series of near-field nanoimaging approaches that, while exploiting the same core building block (a detectorless QCL-based nanoscope) [17], rely on different physical mechanism for imaging reconstruction and I highlight their potential for mapping bi-dimensional (2D) and one-dimensional nanomaterials and devices.

2. Detectorless near-field nanoscopy

The core operational mechanism of QCL-based THz s-SNOM is self-mixing interferometry (SMI) [21,22]. The basic concept of self-mixing was discovered soon after laser invention. The reinjection of a small part (10⁻⁴-10⁻²) of the emitted field produces coherent nonlinear interference in the laser cavity and is enough to significantly perturb the laser. This is typically annoying, so the benefits are counterintuitive: all laser parameters (voltage, threshold current, emitted power, laser linewidth) are perturbed. However, this also makes a laser source capable of sensing its external environment. The process is also inherently fast (>GHz acquisition rates) since the maximum response speed to optical feedback is determined by the frequency of the relaxation oscillations in the laser, and sensitive (noise-equivalent-powers < 10 pW/Hz^1/2). In THz-QCLs, indeed, the lifetime of the upper laser state is limited by elastic and inelastic scattering mechanisms to 5–10 ps [23], enabling, in principle, response frequencies of the order of 100 GHz. Coherent superposition of re-injected THz field with the QCL intracavity field produces a perturbation of the laser voltage ΔV that depends on both the amplitude and the phase of the THz field scattered by the tip, hence allowing to reconstruct the near field maps [17–19].

The simple architecture of SMI can be described in a three-cavity model employing the Lang-Kobayashi (LK) theory [24,25], in which two coupled differential equations describe the evolution of the excited state population N(t) and the optical field E(t). SMI arises from this term which changes the field amplitude and phase and contains the target reflectivity R and the external cavity length. The LK equations read [24]:

2.1 Mapping 2D nanomaterials

Nanoscopy in the SMI configuration can allow to probe modal characteristics and photoexcited modes, at multiple wavelengths, with a resolution set by the tip radius (30-250 µm). This can be done by mounting on the same chip a set of single-mode THz QCLs operating at different wavelengths (λ)/frequencies in the 1.5-5.0 THz range, with a polarization parallel to the tip. In order to sample the SM fringes and retrieve the phase shift experienced by the field in the scattering process, the length L of the external cavity, formed by the tip and output laser facet, can be varied up to distances >2λ = 4πc/ω₀ with a delay line built on a linear translation stage with a sub-µm spatial resolution (Fig. 1(a)). 2D materials can be scanned along a line orthogonal to the substrate-material edge. The amplitude of the self-mixing signal at high demodulation orders n ≥ 3, as a function of the distance between the tip and the output laser facet L, and of the position on the sample, labeled as x, can be extrapolated by analyzing the self-mixing fringes at each x with sinusoidal fit functions, together with the phase ϕ_n along the scan trajectory. With this approach it is also possible to image signal intensity modulations in regions on flat topography, which can provide signature of interference of propagating modes launched by the tip and reflected at the flake edges [26]. This approach has been recently applied to map topological insulators as Bi₂Se_2.2Te_0.8 and Bi₂Se₃ of different thicknesses (20-120 nm) allowing to identify hyperbolic plasmon–phonon-polaritons modes at THz frequencies, and massive bulk plasmons associated to band bending induced 2D electron gas, respectively [26].

 

Fig. 1. a. Schematic of a QCL based detectorless near field optical microscope; b-c. Scanning electron microscope image of a near-field probe with a 20 µm aperture and an embedded heterostructure of hBN/single layer graphene (SLG). d. Schematics of a THz near-field probe with an embedded 2D material transistor, front- and back- illuminated in an interferometric near field set-up. e. Schematics of photocurrent THz nanoscopy on a semiconductor nanowire. f-g. Near-field photovoltage map in a nanowire (f) [5] and graphene (g) field effect transistor (FET) collected at zero source-drain bias and at gate voltage V_G = 7 V(f) or at different V_G (g). The V_G-dependent acoustic plasmon propagating in the graphene FET is marked by dashed blue lines.

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3. Hyperspectral nanoscopy based on QCL frequency combs

A hyperspectral, detectorless, s-SNOM imaging system at frequencies in the 2-5 THz range, can be built by employing a high power (∼10 mW) excitation source based on a frequency comb-emitting THz QCL [27]. By coupling the THz QCL FC to the tip of the s-SNOM, the intermode FC beatnote can be modulated in intensity, position and linewidth through optical feedback and used to drive the laser in a stable comb regime; the FC itself can be, in turn, used as a detector of the field backscattered by the nanoscope tip. Such coherent, detectorless FC nanoscope can provide nanoscale (40-100 nm) resolution at multiple THz frequencies over a continuous spectral bandwidth (2-5 THz), with fast acquisition rates (<ms/pixel) and pW/Hz^1/2 noise equivalent powers, simultaneously, solving the present hand-user limitations of commercial THz TDS s-SNOM apparatus. The combined nanoscale spatial resolution and phase-sensitive homodyne detection achievable with this technique prospects extensive opportunities in the 3-10 THz frequency range, for example for probing bio-samples over the nm scale or reconstructing the dispersion of photoexcited modes bio-samples.

4. Synthetic holography

Optical holography [28] is an imaging technique where the light scattered from an illuminated object is superposed with a reference wave. The resulting interference pattern—the hologram—encodes the complex optical field scattered from an object within a single image.

Synthetic optical holography (SOH) is a recently introduced holographic modality of quantitative phase imaging in s-SNOM [29]. While the sample is rapidly scanned in position, the reference mirror of the interferometer is slowly translated to modulate the phase of the reference field. An intriguing perspective is to take advantage of SMI to implement the same acquisition strategy in a compact detectorless configuration. Instead of measuring near field maps at fixed L, the optical path length, or the phase, at each pixel, can be varied while the s-SNOM is scanning the sample, hence reconstructing a hologram.

This technique can be an extremely powerful tool for measuring, in one shot, the dispersion characteristics of 2D nanomaterials, employing a coherent multiwavelength source as a QCL FC. It is also appealing for mapping the confined electromagnetic resonant modes in micro-resonators over larger scales (µm²) still with nanoscale resolution or for imaging propagation of confined modes in the split gap of a resonators/metamaterials embedding a 2D material.

5. Aperture type near field nanoscopy

s-SNOM exploit an atomic force microscope (AFM) tip to induce strongly concentrated THz fields at the tip apex. A fraction of the concentrated field is scattered, and the scattered wave carries information about the dielectric constant ε underneath the tip in its amplitude and phase, therefore enabling spatial resolution determined by the tip apex size rather than the wavelength. However, the scattering efficiency of the AFM tip is prohibitively low in the THz frequency range. Conversely, the original near-field microscopy concept [30], relies on detecting light through a sub-wavelength aperture in a metallic screen. The spatial resolution of this method is determined by the aperture size (a), and it is usually adopted to probe structural characteristics over millimeter size samples.

The transmitted field also contains evanescent waves, which are localized in the near-field zone of the aperture [31]. These evanescent waves represent the major component of the transmitted field for deeply sub-wavelength apertures (<λ/100) [32]. However, being localized at the aperture, they remain almost undetected in most near-field imaging systems. A recently developed approach to overcome the issue is encoded in a novel near-field THz probe concept, where the evanescent THz field is converted into a detectable electrical signal at the nanoscale [33]. A THz nanodetector based on thin flake of bi-dimensional nanomaterials can be integrated into the evanescent field region of a sub-wavelength aperture to enable efficient detection of the transmitted wave (Fig. 1(b),(c)). To access the phase information from a detector, that, by design, is an inherently incoherent detector, one can propose a scheme (Fig. 1(d)), where the aperture probe is also back illuminated from the top side (Fig. 1(d)). This approach also allows to boost the sensitivity as we can use coherent gain and amplify even the weakest signal.

6. Photocurrent nanoscopy

Nanoscale-resolved THz photocurrent near-field microscopy is a technique in which near field signals associated with light-induced effects (as propagating modes or photocurrents) are detected thermoelectrically rather than optically [34]. This technique allows on-chip detection and simplifies imaging, as more sophisticated s-SNOM detection schemes can be avoided.

This technique, still making use of a thermally stable [35] THz QCL to photoexcite the sample, can be employed to investigate local photocurrents induced by illumination in one-dimensional (1D) nanostructures such as nanowires [5] (Fig. 1(e)), allowing reconstructing the different spatial distribution of the current profiles thought the photocurrent distribution (with nanoscale resolution) along the nanowire axis (Fig. 1(f)). This can be unambiguously identify the nature of the photoresponse (thermoelectric, bolometric, plasmonic) [36], hence allowing to engineer the detection speed, which, in a thermally driven THz photo-response, is limited by the efficiency of the energy transfer between incoming photons and the photo-detecting system. The same concept can be easily extended to 2D nanomaterials-based photodetectors, which actually outperform, in the THz, the performance of commercial detectors [37]. It can also be adopted to capture THz acoustic plasmons in graphene [5] (Fig. 1(f)), and offer potential challenges to trace deeply sub-wavelength THz plasmon polaritons (λ_p ≈ λ₀/100), with dispersion tunable by electrostatic control of the carrier density. This is highly appealing in 2D anisotropic materials, since the in-plane anisotropy of the dielectric response can result into anisotropic polariton propagation. This could be innovatively exploited for inducing directional subwavelength light confinement.