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Due to the large bandgaps for both LAO and STO, the input photon energies in the experiments are not sufficient for exciting valence electrons to the conduction band. Although there are mid-gap states in STO18, the reported lifetime for STO photoexcited carriers exceeds tens of nanoseconds under the current experimental conditions19, 20, which is not sufficiently fast for generating ultra-broad-bandwidth THz fields or for detecting the generated THz field via photoconductive sampling. However, the corresponding nonlinear optical process (optical rectification) is able to generate a broadband THz field. The experiments are conducted at temperature T = 80 K. Below T = 105 K, bulk STO undergoes a cubic-to-tetragonal transition; however, the STO remains centrosymmetric, with a vanishing second-order susceptibility, which is denoted as $ \chi ^{\left( 2 \right)}$. Even though the breaking of inversion symmetry at the interface of LAO/STO can produce a $ \chi ^{\left( 2 \right)}$ response21, 22, the 2D nature of the interface makes it unlikely for the second-order nonlinear effect to play a dominant role. In contrast, the third-order susceptibility, which is denoted as $ \chi ^{\left( 3 \right)}$, is exceedingly large for bulk STO23. It has been experimentally demonstrated that the ultrafast photoconductive response at the LAO/STO nanojunction is DC electric field tunable and spatially confined to the region of the nanojunction11. These prior results suggest that the third-order nonlinear effect is the leading mechanism for wave mixing. The nanometer-scale dimension (~10 nm) of the nanojunction provides strong confinement of the DC bias field, thereby resulting in an intensity of 5.5 × 105 V/cm for Vdc = −550 mV. In this sense, the third-order nonlinear process can also be viewed as a DC bias field-mediated second-order nonlinear process.
The time-varying optical field, namely, Eopt, from the ultrafast pulses and the quasi-static bias field, namely, Ebias, from the DC bias voltage interact at the LAO/STO nanojunction, thereby resulting in a change in the polarization, which is denoted as P, in STO:
$$ P = \varepsilon _0\left( {\chi ^{(1)}E_{opt} + \chi ^{(3)}E_{bias}^2E_{opt} + \chi ^{(3)}E_{bias}E_{opt}^2 + \chi ^{(3)}E_{opt}^3} \right) $$ (1) where $ \varepsilon _0$ is the vacuum permittivity and $ \chi ^{(1)}$ is the linear susceptibility of STO. Frequency components $ \omega _1$ and $ \omega _2$ in the optical fields mix and the resulting time-varying polarization induces a field, which offsets the applied DC electric field and further mixes with the bias field, the optical field and even with itself to produce a photoinduced voltage change at the difference frequency of $ \omega _1 - \omega _2$ at the LAO/STO nanojunction.
To investigate the underlying physical mechanism, a numerical simulation of the measured time-domain signal has been performed (Fig. 4). The shape of the input pulse is approximated by a Gaussian:
$$ e^{ - \left( {t/t_p} \right)^2}\cos \left( {\omega _ct} \right) $$ (2) Fig. 4 Comparison between the numerical simulation results and the measured time-domain signal.
a Both the beating envelope and the asymmetry in the upper and lower amplitudes of the envelope are reproduced in the simulation plot. b A close-up of the measured and simulated time-domain signals near time delay τ = 0 shows good agreement between the twowhere tp is the pulse width and $ \omega _c$ is the central angular frequency of the pulse. Then, the simulated time-domain signal takes the form:
$$ \Delta V\left( \tau \right)\sim a\left(\vphantom{de^{ - \left( {\frac{\tau }{{t_p}}} \right)^2}} \left[ \cos \left( {\omega _1\tau } \right) + \cos \left( {\omega _2\tau } \right) \right] + b\left[ \cos \left( {2\omega _1\tau } \right)\right.\right. \\ \hskip 6pt \left.+ \cos \left( {2\omega _2\tau } \right) + 4\left( \cos \left[ {\left( {\omega _1 - \omega _2} \right)\tau } \right] + \cos \left[ {\left( {\omega _1 + \omega _2} \right)\tau } \right] \right) \right] \\ \hskip 6pt + \left[ce^{ - \frac{1}{2}\left( {\frac{\tau }{{t_p}}} \right)^2} + 4de^{ - \frac{3}{4}\left( {\frac{\tau }{{t_p}}} \right)^2}\right]\cos \left( {\omega _c\tau } \right) \\ \hskip 6pt \left.+ \, de^{ - \left( {\frac{\tau }{{t_p}}} \right)^2}\left[ 2 + \cos \left( {2\omega _c\tau } \right) \right] \right) $$ (3) Here, a, b, c and d are fit coefficients (see Supplementary Information for a detailed derivation). In this simulation, $ a \cong 4.33 \times 10^{ - 5}$ (V), $ b = 0.018$, $ c = 1.10$, and d = 0.154. The first term represents the linear response of the two selected frequencies at the LAO/STO nanojunction. The second term corresponds to the frequency mixing through the third-order nonlinear effect. The third and fourth terms are the induced linear and third-order nonlinear photoconductive response by the pulse at the nanojunction, respectively. These two terms exist because of the small nonvanishing fundamental pulse background (the baseline of the blue curve in Fig. 2b). In Fig. 4a, we compare the measured time-domain signal at a difference frequency of 20 THz (the yellow curve in Fig. 3a) with the results of the numerical simulation. Both the beating envelope and the asymmetry in the upper and lower amplitude of the envelope are reproduced. The overall decay of the signal amplitude is due to the finite width of the two selected fundamental wavelengths. Fig. 4b shows a magnified view of the measured signal and the simulated response near τ = 0; satisfactory agreement is observed between the two. The unequal amplitudes of the lower and upper envelopes are a result of the nonlinear process that produces the THz response. The fast oscillation with a beating envelope mostly originates from the superposition of the two fundamental frequencies. Discrepancies between the measured signal and the simulated signal are most visible at the node (near τ = 20fs) and are attributed to imperfect alignment of the two beams during the movement of the optical time delay line. This theoretical model also predicts that the fundamental signal amplitude depends linearly on the laser excitation power, while the THz amplitude depends on the square of the laser power (see Supplementary Information for more details); these predictions are also supported by experimental results (Figure S1). In addition to the main nonresonant DC bias field-mediated nonlinear wave mixing process, other responses could contribute to the measured signal. For example, the photoexcited free carriers from the mid-gap states could introduce near-resonant structure into the response. Nonetheless, the good agreement between the simulation results (fit to Eq. (3)) and the experimental data demonstrates that these responses are unlikely to play a dominant role.
Compared to other ultra-broad-bandwidth THz sources, such as free-electron lasers24 and nonlinear crystals, such as GaSe crystals25, the LAO/STO nanojunctions are easy to fabricate and reconfigurable and do not rely on phase matching due to the extremely small dimensions of the device. Here, the bandwidth of the THz emission is not restricted by the material; it is limited only by the spectral bandwidth of the ultrafast pulses. Moreover, the LAO/STO nanojunctions naturally yield a high spatial resolution. By simply drop-casting the target nanoscale objects onto the LAO/STO surface and creating a nanojunction in the vicinity of a single particle or molecule, individual nanoscale objects can be addressed independently, thereby offering insights that would otherwise be inaccessible via averaging over the ensemble. Spatial mapping of arbitrary substrates is also possible by scanning an LAO/STO nanojunction device in close proximity to the sample (or the other way around). Variations on the sample surface lead to modifications in the interaction among various fields at the nanojunction, which can be reflected by the measured photoinduced voltage change, with a spatial resolution that is determined by the nanojunction size. However, the extremely small size of the nanojunction results in a small amplitude of the THz emission. THz fields that are generated at LAO/STO nanojunctions are mostly in the near-field regime, which is a regime that is home to many interesting short-range interactions. In this work, we only control the amplitude of the input ultrafast pulse. Full use of the dual-mask SLM, via which both amplitude and phase modulation can be realized, can enable the realization of THz waveforms of arbitrary shape for future applications.
In conclusion, we have demonstrated over-100-THz-bandwidth selective difference frequency generation at LAO/STO nanojunctions that spans the entire far-infrared to mid-infrared regime via femtosecond optical pulse shaping. The ultrabroad tunability, combined with an exceptional spatial precision of 10 nm, is highly promising for exploring the fundamental physics of single nanoscale objects such as quantum dots, nanoparticles or individual molecules. The low optical excitation power imposes minimal heating or other adverse effects on the analyte. The LAO/STO nanojunction serves as both a generator and a detector of THz emission11. By writing two similar nanojunctions adjacent to each other, the second nanojunction can be used to detect the THz field that is generated from the first nanojunction, without the implication of beating signals. In this way, it is possible to realize both generation and detection of tunable ultra-broad-bandwidth THz fields in a micrometer-scale area. Numerous nanoelectronic devices have already been realized at the LAO/STO interface, such as photodetectors17 and field-effect transistors26. Combining the versatility of the LAO/STO nanodevices with tunable THz functionality opens a new pathway toward the realization of integrated lab-on-chip optoelectronic devices.