Graphene-enabled coherent terahertz wave detection and thickness determination

Abstract

Coherent detection and interferometry in the terahertz (THz) regime are key capabilities that enable applications ranging from astronomy to non-destructive testing. Phase-sensitive THz detection is currently achieved using nonlinear crystals or external interferometers and photomixers. However, the former approach requires femtosecond pulsed radiation, and all approaches suffer from a large footprint and sensitive alignment. Here, we demonstrate a graphene-enabled, on-chip, integrated THz detector-interferometer with optical cavity and antenna, exhibiting high sensitivity to the phase of incident THz light. We exploit this by determining the thickness of thin films placed in front of the detector-interferometer, obtaining a strongly sub-wavelength thickness accuracy of $\sim$5 $μ$m, while we predict that an accuracy of 10 nm is within reach. This is relevant for a range of industrial application domains, including automotive, construction, and health. The detector-interferometer moreover exhibits a record-high external responsivity - without any normalization to a diffraction-limited spot size - of 73 mA/W and a noise-equivalent power of 79 pW$~\rm{Hz}^{-1/2}$. This performance is due to enhanced absorption at the cavity mode around 89 GHz, in agreement with multi-physics simulations. These results pave the way to exploiting coherent wave detection in the THz regime with utility in spectroscopy, next-generation wireless communication, and beyond.

Figures (11)

• Figure 1: Schematic of the integrated graphene-based THz detector-interferometer. The device contains hBN-encapsulated graphene underneath a dipolar antenna. The photo-active region is the graphene channel below the gap of the dipolar antenna. This channel has side contacts (not shown) that enable us to measure photocurrent. The antenna and the metallic back mirror form an optical cavity, where incident (THz) light can travel back and forth and interfere. The THz cavity consists mostly of silicon.
• Figure 1: Interference pattern observed when scanning the detector position.a,b, Photocurrent measured while moving the detector along the travel direction of the light for incident radiation at 89 GHz (a) and 160 GHz (b), together with the Fourier transforms of these interference patterns (c,d). The Fourier transforms are performed to determine the periodicity of the signals and give main peaks at 1.79 mm and 0.98 mm for 89 and 160 GHz, respectively. This is close to half of the wavelength of the incident light, which is 1.69 mm and 0.94 mm, respectively. The fact that we observe oscillations for both frequencies shows that the occurrence of interference is not limited to the resonance frequency of the internal cavity.
• Figure 2: Spectral and spatial signatures of interference.a, Measured photocurrent as a function of frequency $f$ (wavelength $\lambda_0$), where a main peak occurs at 89 GHz (3.35 mm). The inset presents a zoom of the main peak with a Lorentzian fit (dotted black line). b, Schematic of the relevant internal and external cavities. The photocurrent peak corresponds to the situation where reflections in the internal cavity lead to constructive interference at the graphene location. The thinnest cavity for which this occurs is when $L = \frac{\lambda_{\rm 0}}{4 n_{\rm THz}}$. c, Measured photocurrent at 89 GHz while moving the detector along the light propagation direction $x$. The oscillatory pattern has a maximum (minimum) at position $x_\text{max}$ ($x_\text{min}$), with ${\lvert x_\text{max} - x_\text{min} \rvert} = \lambda_0/4$. d, Schematic of the experimental geometry when moving the detector in the $x$-direction. Maxima (minima) occur when the incident field at the graphene position has a maximum (minimum). e, Measured photocurrent as a function of frequency in the near-infrared (NIR) range, showing periodic oscillations with maxima $f_\text{max}$ and minima $f_\text{min}$. f, Representation of the interference conditions at telecom frequencies, where the frequency spacing is determined by the internal cavity via ${\lvert f_\text{max} - f_\text{min} \rvert} = c/4n_{\rm NIR} L$.
• Figure 2: Time-resolved photocurrent measurements. In order to determine the cooling time of the hot electrons in the graphene THz detector, we perform time-resolved photocurrent measurements with an incident wavelength of 1030 nm. For details on the technique, see \ref{['meth']} and Ref. tielrooij_generation_2015. We observe a pronounced main dip at zero time delay, and secondary periodic dips that are likely related to reflections inside the sub-THz cavity. To extract the cooling time from the time-resolved photocurrent, we describe the photocurrent using a sum of exponential decay functions of the form $I_\text{PTE} \propto (T_e - T_l) \exp \left( -\frac{\tau_\text{delay}}{\tau_\text{cool}}\right)$tielrooij_hot-carrier_2015tielrooij_generation_2015, where $T_e$, $T_l$, $\tau_\text{delay}$, $\tau_\text{cool}$ are the electronic temperature, lattice temperature, the delay time, and the cooling time, respectively. Each dip has two exponentially decaying functions -- to positive and to negative time delays. We obtain a cooling time of 3.4 ps for the main dip around time zero.
• Figure 3: Enhanced responsivity and absorption from experiment and simulation. a, Measured photocurrent $I_\text{PTE}$ at 89 GHz vs. incoming THz power $P_{\rm in}$, giving an external responsivity of 73 mA/W. b, Simulation of the THz absorption vs. frequency for incident THz light that is focused with a numerical aperture of 0.5, as in the experiment. The absorption gives a peak value due to interference in the internal cavity (blue curve), in agreement with the experimental results of Fig. \ref{['fig2']} a. Additional enhancement occurs due to the external cavity (grey curve), which gives rise to a substructure that is shown in the inset. c,d, Maps of the electric field intensity $E_\text{THz}^2$ (c) and absorption density (d) as a function of frequency and lateral position $y$, along the source-drain direction. These maps show strong enhancement inside the gap of the dipolar antenna around the resonance frequency. The dashed lines indicate the gap of the dipolar antenna with width $w_{\rm gap}$.