Giant near-field nonlinear electrophotonic effects in an angstrom-scale plasmonic junction

Domain: physics
Published: 2026-01-24
Editorial outcome: minor_revision

Abstract
Plasmons facilitate a strong confinement and enhancement of near-field light, offering exciting opportunities to enhance nonlinear optical responses at the nanoscale. However, despite significant advancements, the electrically tunable range of the nonlinear optical responses at nanometer-scale plasmonic structures remains limited to a few percents per volt. Here, we transcend the limitation of the nanometer regime by expanding the concept of electro-photonics into angstrom-scale platform, enabling high-performance modulation of near-field nonlinear optical responses inaccessible in prior architectures. We demonstrate ~2000% enhancement in second-harmonic generation (SHG) within 1 V of voltage application by utilizing an angstrom-scale plasmonic gap between a metallic tip and a flat metal substrate in a scanning tunneling microscope. Extending this near-field SHG scheme to sum-frequency generation that is accompanied by large frequency upconversion, we also found that such giant electrical modulation of plasmon-enhanced nonlinear optical phenomena is effective over mid-infrared to visible broad wavelength range. Our results and concepts lay the foundation for developing near-field-based angstrom-scale nonlinear electrophotonics with significant modulation depth at low driving voltage.

Introduction
An ultimate goal in photonics is to design photonic phenomena with desired functions by intentionally controlling light–matter interactions. While the photonic functionalities are fundamentally determined and limited by the intrinsic material properties such as permittivity and conductivity, much effort has been devoted to tune and exploit those functionalities. In particular, tailoring nonlinear optical effects is of paramount importance with the growing demand for diverse photonic functionalities, such as light frequency conversion1, all-optical switching2, optical imaging3, and spectroscopic analysis of materials4,5. Since the nonlinear optical processes depend superlinearly on the incident electric field, integrating with plasmons that intensely confine and enhance light within nanometric volumes should dramatically augment near-field nonlinear optical phenomena at the nanoscale beyond the diffraction limit. This concept underpins a fascinating research field of nonlinear plasmonics6–10, encompassing various applications such as enhanced up/down conversion of optical frequency11–13, plasmonic sensing of local environments14–17, and nonlinear optical imaging of nanomaterials18–25. These plasmonic functionalities are fundamentally governed by the intrinsic optical properties of constituent materials and the static geometry of the plasmonic structures, such as size, shape, material composition, and surrounding environment26–31. Although these static structural properties are typically difficult to adjust at their post-fabrication stage, designing active plasmonic systems that respond to external stimuli, such as light, heat, mechanical force, or electric field, provides a route toward active modulation of both linear32–39 and nonlinear40–46 plasmonic responses. Since such tunable plasmonic platforms are essential for advanced nanophotonic applications47,48, approaches that allow more flexible and efficient active control of plasmonic responses are highly desirable.

One promising strategy for active control of plasmonic responses is to directly exploit the metallic nature of plasmonic systems. Metal plasmonic structures can serve not only as light-enhancing media in a near-field optical scheme but also as electrodes that can facilitate various electrical perturbations49–53. These dual optical and electrical functionalities provide an interesting platform for electrical modulation of plasmonic nonlinear optical processes, which are critical for on-chip integrated optoelectronics, including tunable nanolasers54–56 and optical modulators57,58. By applying the voltage across plasmonic gap structures, an electrostatic field is generated within these gaps, which can affect the plasmonic nonlinear optical properties inside the gaps. Although several studies have successfully reported the possibility of the plasmonic gap-based modulation40–44, most have focused on relatively wide (sub-100 nm) gap structures, as fabricating and maintaining angstrom-scale narrow gaps remains a significant technical challenge. Consequently, while valuable progress has been made, the reported modulation depths have typically been limited to less than a 10% signal increase per volt40–44. Therefore, a practical level of electric modulation reaching 1000% signal increase has typically required as high as ~100 V of voltage application, preventing the application from being used in a realistic device.

In this study, we expand the platform of electrophotonics from the sub-100 nm into the angstrom regime, unveiling the potential of an angstrom-scale plasmonic junction as a groundbreaking platform for electrophotonic control of near-field nonlinear optical effects. As a first experimental realization of such angstrom-scale electrophotonics, we leverage a voltage-applicable and precisely position-controllable plasmonic gold tip integrated with a scanning tunneling microscope (STM). This system achieves giant electrical modulation of plasmonic nonlinear optical responses, demonstrating a ~2000% signal enhancement with a minimal voltage sweep of 1 V. Our work represents the first experimental realization of this near-field nonlinear electrophotonic effect in second-harmonic generation (SHG) excited by femtosecond near-infrared (IR) laser pulses. Moreover, by temporally and spatially superimposing the near- and mid-IR laser pulses, we extend this effect to the sum-frequency generation (SFG) process that is accompanied by large frequency upconversion from mid-IR to the visible region. Showing broadband operability of the gigantic near-field nonlinear electrophotonic effects, our work shows great potential for advancing functionalities in angstrom-scale electrophotonic systems.

Results
Angstrom-scale platform of nonlinear plasmonics
SHG is a second-order nonlinear optical process in which two photons with identical frequencies interact with a material and are converted into a single photon with doubled frequency of the original photons (Fig. 1a). The possibility of electric modulation of the near-field SHG signals from angstrom-scale plasmonic gap was explored in the experimental setup illustrated in Fig. 1c. For our first demonstration, we adopted a recently constructed experimental platform based on an angstrom-scale gap that consisted of an electrochemically etched Au tip59 (Fig. 1b) and an atomically flat Au(111) substrate equipped in an ultra-high vacuum STM unit (<1×10−7 Pa)60–63. In this system, we can control the distance of the plasmonic gap between the tip apex and the substrate at the angstrom scale by precisely regulating the tunneling current (Supplementary Notes 3 and 4). Prior to the SHG experiments, the tip underwent Ar+ sputtering for 3 h to clean the tip apex64. This sputtering enabled reproducible nonlinear optical experiments presented below, as well as clear STM imaging.

In the gap, ~6 Å-thick self-assembled monolayer (SAM) of 4-methylbenzenthiol (MBT) was formed on the Au substrate as a model ultrathin dielectric layer with well-defined homogenous structure65 (see Supplementary Fig. 1 for the STM image of an MBT SAM). To induce the tip-enhanced SHG (TE-SHG) process, we exposed the gap to near-IR excitation pulses (1500 nm, 280 fs, FWHM: 19 nm) with p-polarization at a high repetition rate (50 MHz). In general, when the optical structure is considerably smaller than the optical wavelength, the phase-matching condition breaks down, resulting in a dipole-like radiation pattern of the output signal66. Thus, we collected TE-SHG emissions separately in forward- and backward-scattering directions (see the “Methods“ section for details). As reported in our recent study60, the TE-SHG output exhibits long-time stability and quadratic dependence on the excitation intensity, provided the excitation power is maintained sufficiently low (≤0.7 mW). Therefore, to ensure minimal signal fluctuations, the excitation intensity in all TE-SHG measurements presented in the subsequent sections was set to 0.5 mW (10 pJ/pulse). Indeed, employing this intensity allowed us to obtain clear STM images even under light irradiation (Supplementary Fig. 11), ensuring that the optical damaging effect induced by the laser pulse is sufficiently suppressed60.

Near-field SHG and its giant electric modulation
When the substrate was retracted from the tip by ~30 nm, thereby deactivating the plasmonic excitation, no backward-scattered SHG signal was detected (gray curve in Fig. 2a). Owing to the phase-matching condition of far-field nonlinear optical processes, normal far-field SHG signal from the flat Au(111) substrate without plasmonic excitation was detected only in the forward-scattering direction (Supplementary Fig. 7). Although tip plasmons of the tip apex alone could be excited even in the 30 nm-retracted condition, their contribution can be safely disregarded because the backward-scattered signal emission is absent despite identical power and integration time for the measurements of forward- and backward-scattered signals (Supplementary Note 5). The minimal contribution from the tip plasmon was further corroborated by our numerical simulation, revealing that the plasmonic enhancement caused by a tip alone is more than one order of magnitude smaller than that in an angstrom-scale gap (Supplementary Fig. 18).

Then, the tip-substrate distance (d), defined as the metal-to-metal separation between the tip apex and the substrate surface, was reduced from ~30 nm to ~5 Å under the sample bias of 0.1 V. In this condition, not only did the intensity of the forward-scattered SHG signal increase (light blue curve in Supplementary Fig. 7), but also the backward-scattered SHG signal newly appeared (light blue curve in Fig. 2a). In this case, since the movement of the piezoelectric stage is quite small (~30 nm) compared to the optical wavelength of light, the signal collection efficiency should remain unchanged even after the formation of the angstrom-scale junction. Moreover, while the tip apex is expected to slightly indent into the SAM layer at a tip–substrate distance of ~5 Å, the potential influence of such contact, including chemical enhancement effects67, should be negligibly small because the terminal methyl group of MBT molecules is chemically inert (Supplementary Note 3). Therefore, the signal increase in the forward-scattering geometry (light blue curve in Supplementary Fig. 7) and the appearance of the backward-scattered signal (light blue curve in Fig. 2a) are obviously due to the near-field enhancement activated within the angstrom-scale tip-substrate gap, and thus the observed signals correspond to TE-SHG emission. Note that the technical basis for detecting such tip-enhanced nonlinear optical signals separately from far-field signals has already been established and reported in our recent publications60–63.

While we also detected TE-SHG from the bare Au(111) surface without molecular adsorption (Supplementary Fig. 13), the observed intensity was much lower than that observed for the Au substrate coated with MBT SAM. We consider that the TE-SHG signal observed in the absence of the SAM is attributed to the nonlinear optical response of the surface electrons of the Au tip and substrate. Since the electric field enhancement at the central region of the gap is expected to be much stronger than that near the top surfaces of the Au substrate and Au tip68, the SAM film placed within the gap region can produce significantly stronger TE-SHG emission than the surface electrons of the Au tip and substrate. Therefore, the main source of TE-SHG signals at 0.1 V shown in Fig. 2a and Supplementary Fig. 7 is the vibrationally non-resonant χ(2) response of the MBT SAM, which is amplified through the field enhancement effect caused by the tip–substrate gap (Supplementary Note 10). In this case, the observed spectral shape of TE-SHG reflects that of the near-IR excitation pulses (Supplementary Fig. 2).

As also shown in Fig. 2a and Supplementary Fig. 7, we found that the TE-SHG intensity markedly increased when the sample bias (V) was increased from 0.1 to 0.75 V, with the tunneling current setpoint maintained constant (500 pA). This voltage increase at a constant tunneling current (500 pA) extended the tip–sample distance from ~5 to ~7 Å (Fig. 2b). Based on conventional classical electrodynamic simulations, the near-field enhancement strength is expected to decrease by several tens of percent during this ~2 Å tip–substrate distance elongation69–74. However, at the gap distances of <1 nm, the influences of quantum mechanical phenomena, such as electron spill-out from the metal surface and the overlap of electronic wavefunctions across the gap, begin to quench plasmon excitations and suppress the increase in field enhancement68,71,72,75–78. Particularly, substantially short tip–substrate distance of <4 Å leads to a regime where such quantum plasmonic quenching becomes dominant, resulting in a steep decrease in the electric field enhancement factors68,71,72,75–78. In contrast, the 4–7 Å regime represents a crossover region just before this steep decline. Thus, in this distance range, the quantum suppression effects and the classically expected enhancement nearly cancel each other, making the overall field enhancement effectively independent of the tip–substrate distance68,71,72,75–78. Therefore, the near-field enhancement strength should remain essentially unaffected during the distance elongation from 5 to 7 Å. Despite such constant field enhancement, the TE-SHG intensity significantly increased with the applied voltage (Fig. 2a). Importantly, this distance expansion occurred when the bias voltage was raised from 0.1 to 0.75 V at a constant tunneling current (500 pA). With this voltage increase, the electrostatic field below the tip apex (V/d) increased from 2×108 to 1×109 Vm−1. Therefore, both the TE-SHG intensity and the electrostatic field increased concurrently, indicating the presence of substantial electrostatic field-induced effects that boost the overall TE-SHG intensity.

To gain more quantitative insights into the field-effect modulation of the TE-SHG intensity, we fixed the tip–substrate distance at d~7 Å and monitored the voltage dependent variation in the TE-SHG intensity (Fig. 3). At this tip–substrate distance, the classically predicted near-field enhancement and the quantum plasmonic quenching effects arrive at an early optimal balance, resulting in almost maximum near-field enhancement values68,71,72,75–78. Moreover, as long as the tip–substrate distance is kept constant, variations in the STM bias voltage on the order of 1 V essentially do not affect the near-field-enhancement factor within the gap79. Therefore, fixing the tip–substrate distance at ~7 Å can be regarded as the optimal condition under which the field enhancement can be maintained at its nearly maximum value regardless of the applied bias voltage. This enables us to exclusively examine the influence of electrostatic fields on the TE-SHG process, while eliminating the contributions of variations in the near-field enhancement. Note that the constant tip–substrate distance of 7 Å was kept by adjusting the tunneling current setpoint in the range of 40–1750 pA synchronously with the voltage sweep (Supplementary Note 4). During the voltage sweep, the excitation intensity of the incident laser was maintained low and constant at 0.5 mW. Despite such fixed tip–substrate distance and excitation power, the TE-SHG intensity significantly grew up when increasing the sample bias voltage from 0.1 to 1 V (Fig. 3). Importantly, such a significant TE-SHG signal modulation was also observed when we swept the bias voltage inversely from −0.1 to −1 V, exhibiting a quadratic dependence on the applied voltage (Fig. 3). More remarkably, the experimentally obtained relative modulation in the TE-SHG signal intensity (ΔITESHG(V)=ITESHG(V=0)) reached ~2000% at V=±1 V (the blue open circles in Fig. 3), indicating the achievement of ~2000% V−1 giant modulation depth. The stability and reproducibility of these results were confirmed through repeated measurements as described in detail in Supplementary Notes 6 and 12.

It should be noted that while the quantum plasmonic effects in an angstrom-scale junction have been discussed primarily by referring to previous studies68,71,72,75–78 as qualitative support, the presence of such quantum plasmonic effects can also be ensured from our experimental observations. As shown in Supplementary Fig. 14, voltage-controlled quadratic modulation of TE-SHG, similar to that shown in Fig. 3, was also observed under the constant tunneling current conditions, where the tip–substrate distance varies in the range of 4–6 Å during the voltage-dependent measurement. This clearly demonstrates that the overall field-enhancement strength remains essentially insensitive to the tip–substrate distance within the experimentally varied 4–6 Å distance range. Therefore, the presence of quantum plasmonic effects that cause distance-invariant field-enhancement behavior is supported not only by previous studies68,71,72,75–78 but also by our experimental results (Fig. 3 and Supplementary Fig. 14). Moreover, the agreement of the bias-dependent profiles shown in Fig. 3 and Supplementary Fig. 14 also indicates negligible contributions of tunneling current to the observed variations in the TE-SHG intensity (Fig. 3). Consequently, we can reasonably conclude that the observed electrical modulation behavior is predominantly governed by voltage-induced electrophotonic effects, distinct from variations in the near-field enhancement or contributions from the tunneling current.

Notably, the observed near-field nonlinear electrophotonic effects, characterized by a quadratic response and a large modulation depth of ~2000% V−1, are in stark contrast with previous studies40–44. Over the past decade, electric-field modulations in plasmon-enhanced near-field nonlinear optics have been pioneered with sub-100 nm scale gap structures, within which organic molecules or inorganic insulators were embedded as nonlinear optical media. However, due to the inherent challenges in fabricating angstrom-scale gaps, the sub-100 nm scale structures used in these previous studies exhibited modulation depths of the order of 10% V−1, with a linear response to the applied voltage40–44. In contrast, our angstrom-scale plasmonic gap occupied by a molecular SAM exhibits a quadratic voltage response with a significantly large electrical modulation depth of 2000% V−1. Moreover, we confirmed that the surface electrons of gold also generate TE-SHG signals even without the SAM and exhibits a similar quadratic voltage dependence with an electrical modulation depth of ~1000% V−1 (Supplementary Fig. 13). We consider that the giant TE-SHG modulation observed for the bare Au(111) surface (Supplementary Fig. 13) is likely attributed to the electric field-induced change in the free electron density at the topmost Au surface80. These results underscore that the angstrom-scale plasmonic gap serves as a medium-independent platform for achieving substantial nonlinear optical modulation depths of at least ~1000% V−1 with a modest bias of ≤1 V.

Given that no structural changes were observed in the MBT SAM sample (Supplementary Fig. 12), the contribution of field-induced phase transitions or polarization-switching phenomena81–84 can be considered insignificant. Consequently, the observed gigantic modulation of TE-SHG signals is attributed primarily to electro-optic interactions triggered by the electrostatic field within the plasmonic gap (EDC). Such electro-optic interaction in the second-order SHG output is likely to be induced by the third-order nonlinear effect of molecules, representing the mixed interaction between the incident light Egap(ω) and the electrostatic field EDC, P(3)(2ω)=ε0χ(3)(2ω;0,ω,ω)EDCEgap(ω)Egap(ω). In this case, the total TE-SHG signal intensity (ITESHG) includes contributions not only from the second-order nonlinear polarization (P(2)(2ω)=ε0χ(2)(2ω;ω,ω)Egap(ω)Egap(ω)) but also from the electrically tunable third-order nonlinear polarization (P(3)(2ω)), as follows:

ITESHG / |χ(2)+χ(3)EDC|2Igap2, (1)

where Igap denotes the intensity of the tip-enhanced electric field of the incident excitation pulses (Igap / |Egap(ω)|2); and χ(2) and χ(3) are second- and third-order nonlinear optical susceptibility, respectively, of the medium sensing the enhanced-electric field in the angstrom-scale gap. Note that our recent work demonstrated that, when the tip apex size is on the order of several tens of nanometers as in the present study (Fig. 1b), the generated nonlinear polarizations are predominantly dipolar in nature, with negligible contributions from quadrupolar or higher-order multipolar components (Supplementary Note 14)63. Moreover, since such relatively large tip apex can support only dipolar plasmonic mode (Supplementary Fig. 21)74, TE-SHG signal radiation observed in Figs. 2 and 3 should be mediated by dipolar plasmons (Supplementary Notes 13 and 14).

The incorporation of the field-induced χ(3)EDC term in Eq. (1) is referred to as the electric-field-induced second-harmonic (EFISH) effect. Notably, during the bias-dependent TE-SHG measurements (Fig. 3), the excitation intensity was fixed at 0.5 mW, and the field enhancement strength within the gap was kept constant by maintaining a fixed tip–substrate distance (~7 Å). Under these controlled conditions, Igap in Eq. (1) can be regarded as constant. Therefore, the observed bias-dependent TE-SHG intensity (Fig. 3) is predominantly governed by the EFISH effect arising from the χ(3)EDC term in an angstrom-scale plasmonic gap structure, with sufficient stability and reproducibility (Supplementary Notes 6 and 12). Note that, as detailed in Supplementary Note 14, among the multiple tensor elements of χ(2) and χ(3), only χ(2)ZZZ and χ(3)ZZZZ components dominantly contribute to the generation of TE-SHG signals (Supplementary Note 14).

By expanding the right-hand side of Eq. (1), we obtain a voltage-independent term (ITESHG(V=0)=|χ(2)|2Igap2) and voltage-dependent terms (ΔITESHG(V)=[|χ(3)|2EDC2 + 2Re(χ(3)χ(2)*)EDC]Igap2). When the contribution from χ(3)EDC is significantly smaller than that from χ(2), the voltage-dependent component is dominated by the linear EDC term40–44,85,86, resulting in the modest electrical modulation depth on the order of at most 10% V−1. In contrast, when the χ(3)EDC term far exceeds the χ(2) term, the voltage-dependent component becomes dominated by the quadratic EDC term, leading to significantly enhanced modulation depth exceeding 1000% V−1. Previous studies employing sub-100-nm plasmonic gap structures generated relatively modest electric fields (~107 Vm−1), resulting in linear voltage dependence with modest modulation depths (~10% V−1)40–44,85,86. In this case, a high bias on the order of 100 V is required to achieve a modulation depth of ~1000%. In contrast, our approach leveraged an angstrom-scale plasmonic gap (d<10 Å), facilitating a much more intense electrostatic field (~109 Vm−1) even under a moderate voltage application (~1 V), within a range that does not damage metal electrodes or molecules87–89. This resulted in a dominant contribution from the χ(3)EDC term, achieving a significantly larger modulation depth on the order of 1000% V−1 with a quadratic voltage dependence. These findings highlight a pronounced near-field nonlinear electrophotonic effect unique to angstrom-scale gap structures.

Notably, the optical near field Egap and the electrostatic field EDC inherently exhibit non-uniform spatial distributions due to the curved geometry of the tip apex (Supplementary Figs. 20 and 22), thereby giving rise to position-dependent nonlinear polarizations within the nanoscale region beneath the tip apex. In such conditions, the TE-SHG electric fields emitted from these individual nonlinear polarizations depend on their absolute spatial position, and the experimentally observed TE-SHG intensity and its electrophotonic modulation arise from the coherent sum of these position-dependent contributions. Specifically, as described in Supplementary Note 15, the overall TE-SHG intensity (ITESHG), including the contributions from both the bias-independent second-order signal and the EDC-induced third-order signal, is given by the total intensity of SHG fields emitted from N molecules within the gap:

ITESHG / N2 |<χ(2) Lgap(rn)Kgap,Z(rn)2> + <χ(3) Lgap(rn)Kgap,Z(rn)2> EDC|2 Igap2, (2)

where <...> denotes spatial averaging over molecules present within the gap region; rn is the position of nth molecule; d(rn) represents the position-dependent tip–substrate distance determined by the curvature radius of the tip apex; Kgap,Z(rn) is an enhancement factor of Z-directed field; Lgap(rn) is efficiency of radiation from a nonlinear polarization located at the position rn; and Igap0 is incident field intensity. To simplify this formulation, we introduce an effective tip–substrate distance deff, which satisfies the relation

<Lgap(rn)Kgap,Z(rn)2> / deff = <Lgap(rn)Kgap,Z(rn)2> : (3)

Substituting this expression into Eq. (2) yields

ITESHG / N2 |<χ(2) + χ(3) (V/deff)>|2 |<Lgap(rn)Kgap,Z(rn)2>|2 Igap02 : (4)

By defining V/deff term as EDC,eff and omitting N2 and |<Lgap(rn)Kgap,Z(rn)2>|2 Igap02 terms for simplicity, we arrive at the simplified expression of EFISH similar to that given in Eq. (1). Notably, deff defined in Eq. (3) represents an effective spatial average of the tip–substrate distance within the gap, weighted by the near-field intensity distribution and the curvature of the tip apex. Thus, the expression of EDC,eff = V/deff effectively incorporates the influences of spatial field inhomogeneity. Moreover, even in the presence of such spatial inhomogeneity, the effective electrostatic field EDC,eff remains linearly proportional to the bias voltage V. Consequently, the overall TE-SHG intensity still exhibits a quadratic dependence on V, and thus the experimentally observed parabolic voltage dependence of TE-SHG intensity (Fig. 3) is a physically valid behavior.

Based on Eq. (4), the bias-dependent modulation of TE-SHG intensity is expressed as

ΔITESHG(V) / ITESHG(V=0) = |χ(3)|2/|χ(2)|2 (V/deff)2 + 2Re(χ(3)χ(2)*)/|χ(2)|2 (V/deff) (5)

The fitting analysis of the bias-dependent intensity change shown in Fig. 3 using this equation yielded the coefficients of V2 and V in Eq. (5) as |χ(3)|2/deff2|χ(2)|2 = (21.1±0.7) V−2 and 2Re(χ(3)χ(2)*)/deff|χ(2)|2 = (−3.9±0.6) V−1, respectively. Moreover, for a tip apex curvature radius of ~50 nm (Fig. 1b) and an actual tip–substrate distance d of ~7 Å, deff is determined to be 9.7 Å (Supplementary Notes 14 and 15). Based on these estimations, the relative values of χ(2) and χ(3) were derived as |χ(3)|2/|χ(2)|2 = (19.9±0.7) nm2/V2 and 2Re(χ(3)χ(2)*)/|χ(2)|2 = (−3.8±0.6) nm/V. From these relative values, we can also estimate the threshold field (EDC,0), at which χ(2) and χ(3)EDC effects equally contribute to the nonlinear optical generation (|χ(3)EDC| = |χ(2)|), to be 2.2×108 Vm−1. Using the effective gap distance value of deff = 9.7 Å, the corresponding applied voltage is estimated to be ±0.21 V. Thus, when applied voltage exceeds this value, the contributions from χ(3)EDC become dominant over that from χ(2).

It should be noted that although sub-angstrom (~0.5 Å) fluctuations in the actual distance d, which should induce variations in EDC, are inevitably present under our ambient experimental conditions (Supplementary Fig. 11d), their influence was not incorporated into the fitting analysis. This is because our numerical analysis to examine the distance-sensitivity of EFISH effects revealed that sub-angstrom variations in the gap distance have only a minor influence on the measured electrophotonic modulation (Supplementary Fig. 24). Furthermore, since the measured TE-SHG intensity is an ensemble average over the tip apex area, the fluctuations in EDC would be effectively averaged out and would not manifest in the measured modulation curves. For these reasons, the fluctuations in EDC were not explicitly taken into account in our fitting analysis.

Extension to tip-enhanced sum-frequency generation
Nonlinear optical processes generally involve multiphoton interaction and are often accompanied by drastic frequency conversion between the incoming and outgoing light. We recently demonstrated that such multicolored input and output light with separated frequencies can be simultaneously enhanced in a tip–substrate gap structure, thereby enabling the efficient plasmonic enhancement of nonlinear optical processes involving significant wavelength conversion60 (Supplementary Note 13). The TE-SHG process discussed thus far exemplifies this phenomenon because it arises from the simultaneous enhancement of both near-IR excitation and visible emission60. While the giant nonlinear electrophotonic modulation has been demonstrated for this near-IR-to-visible TE-SHG process (Fig. 3), extending this modulation to other nonlinear optical processes involving even more pronounced wavelength conversion would further substantiate the broadband applicability of the observed nonlinear electrophotonic effects. In this context, we next focus on the voltage dependence of a tip-enhanced SFG (TE-SFG) process61–63, another representative second-order nonlinear optical process characterized by a large frequency upconversion from the mid-IR input into near-IR or even visible output (Fig. 4a).

For the demonstration of voltage-dependent TE-SFG measurements in the angstrom-scale plasmonic junctions (Fig. 4b), we used spatially and temporally overlapped mid-IR (ω1: 3280 nm, 300 fs, FWHM: 60 nm, 20 mW) and near-IR (ω2: 1033 nm, 1 ps, FWHM: 1 nm, 0.5 mW) pulses as the excitation light with a repetition frequency of 50 MHz, both detuned from molecular resonance. Moreover, while the STM chamber was maintained at ultra-high vacuum conditions in the TE-SHG measurements, we exposed the chamber to the air atmosphere prior to the TE-SFG experiments in order to verify the operability of nonlinear electrophotonic modulation in open air under ambient conditions. Then, as shown in Fig. 4c, the vibrationally non-resonant TE-SFG signals were clearly observed in the visible region around 785 nm. The observed spectral shape and band width predominantly reflect those of the incident mid-IR excitation pulse (Supplementary Fig. 3). Similar to the results of TE-SHG experiments in Fig. 2a, the TE-SFG intensity also increased with the sample bias voltage at constant current of 250 pA (Fig. 4c). While the tip–substrate distance varied from 6.7 to 8.2 Å in this experiment, the distance dependence of the electric field enhancement strength should be negligibly small due to the quantum plasmonic quenching effects68,71,72,75–78. Therefore, by analogy with the case of the bias-dependent TE-SHG (Fig. 2a), the observed TE-SFG intensity modulation shown in Fig. 4c can also be attributed to bias-induced effects.

Then, we investigated the impact of bias voltage while maintaining an almost constant tip–substrate distance (d~7 Å). As shown in Fig. 4d, the intensity of the TE-SFG signals drastically increased with increasing the applied voltage in both positive (0.1→0.75 V) and negative (−0.1→−0.75 V) directions. Consistent with the results of electrically controlled TE-SHG experiments (Fig. 3), the experimentally obtained ΔITESFG(V) (the blue open circles in Fig. 4e) exhibited a quadratic dependence on the applied voltage, with the value at V = ±0.75 V exceeding 2000% of the TE-SFG intensity at V = 0 V (ITESFG(V=0)). Similar bias dependences were also obtained using other Au tips (Supplementary Fig. 15), ensuring the reproducibility of our experiments. These findings demonstrate that the giant electric-field-induced modulation mechanism of plasmonic nonlinear optical effects is also highly effective for TE-SFG (ITESFG / |χ(3)EDC + χ(2)|2 I(ω1)I(ω2) / |χ(3)EDC|2I(ω1)I(ω2)) and operates over a broadband wavelength range, encompassing the mid-IR, near-IR, and visible regions. This broad-wavelength applicability is in stark contrast to the previously reported electronic resonance-assisted EFISH study90, where the range of excitation wavelength that can be used to detect the large EFISH effect was significantly restricted. Note that the slight difference in the minima of the TE-SHG (Fig. 3) and TE-SFG (Fig. 4e) curves may arise from minor variations in the atomic-scale shape of the Au tips and the resultant difference in the electrostatic field distribution within the gap.

Remarkably, the achievement of more than 2000% V−1 modulation of TE-SFG signals in an angstrom-scale plasmonic gap (Fig. 4e) was realized under room temperature and ambient pressure conditions, rather than low temperature and ultra-high vacuum environments. Even under these ambient conditions, the stability of the signals under light irradiation (Supplementary Note 6) and the reproducibility of the results with different STM tips (Supplementary Fig. 15) were thoroughly verified. In addition, the possibility of the dielectric breakdown caused by an intense electrostatic field within the gap (~109 Vm−1) can also be reasonably ruled out in our ambient experimental conditions, because of the rare electron–gas collision within our angstrom-scale gap (Supplementary Note 9). This allows us to safely disregard any intense-field-induced modification of the tip or substrate, even under ambient experimental conditions. Furthermore, the near-field tip-enhancement scheme constructed under room temperature achieves markedly higher SHG and SFG conversion efficiencies than conventional far-field excitation, despite the much smaller number of molecules involved in the signal generation process in the near-field scheme (Supplementary Note 7). These findings highlight the promising potential of the observed nonlinear electroplasmonic phenomena and pave the way for the development of photonic devices that combine substantial modulation depth, operation under ambient conditions, and higher conversion efficiency.

Finally, it should be noted that our near-field-based giant electrical modulation depth on the order of 2000% V−1 compares favorably with, and even exceeds, the recently reported record-high values (>1000% V−1) for practical applications in the field of far-field-based electrophotonics81–84,90. In far-field schemes, the electric field across macroscopic electrodes is typically much weaker than that in near-field schemes. Such weaker electrostatic fields alone are generally insufficient to induce giant electro-optic interactions. Consequently, the record-high values in far-field approaches have been achieved primarily through some medium-design strategies. One of such approaches is to minimize the contribution of χ(2) with respect to χ(3) using centrosymmetric amorphous material films with ~100 nm thickness90. Another important approach is to utilize field-induced phase transition or polarization switching phenomena in specific electroactive nonlinear optical media, such as transition metal dichalcogenides81, superlattice structures82,83, and ferroelectric sheets84. In contrast to these approaches that rely on specialized material designs, our near-field-based giant electrical modulation was achieved using a common SAM of electro-nonactive organic molecules that do not exhibit field-induced polarization switching and drastic phase transition. Furthermore, a similar extent of electric modulation (~1000% V−1) was also observed even in the absence of the SAM (Supplementary Fig. 13). These results demonstrate that, in our near-field-based nonlinear optical modulation scheme, the choice of material is largely noncritical for achieving a modulation depth of at least 1000% V−1. Therefore, the angstrom-scale plasmonic gaps have great potential to serve as an optimal platform for giant nonlinear optical modulation. A promising avenue for further exploration is the use of more electroactive nonlinear optical media, similar to those used in far-field-based approaches81–84, to further improve modulation performance. Such advancements could achieve a practical level of modulation depth (~1000%) even under more modest bias voltages, paving the way for an atomic-scale electrophotonic information-processing technology.

Methods
Preparation of STM tip and sample
Gold tips for STM were prepared by electrochemical etching of gold wires with a diameter of 0.25 mm (Nilaco) in a 2.79 M KCl (FUJIFILM Wako Pure Chemical Corporation) aqueous solution59. After the etching process was completed, the prepared tips were washed with concentrated H2SO4 and ultrapure water and introduced into our STM chamber (USM1400, UNISOKU). Prior to the nonlinear optical measurements, we processed the Au tips with Ar+ sputtering (2×10−3 Pa, 3 kV) for 3 h.

For the substrate to form the angstrom-scale gap structure, a 200 nm-thick gold thin film vapor-deposited on a mica substrate (UNISOKU) was employed. The substrate was first annealed in a butane flame to achieve an atomically flat Au(111) surface (Supplementary Fig. 1a) and cooled down to room temperature. Then, the Au substrate was immersed in 1 mM ethanolic solution of 4-Methylbenzenethiol (MBT) at room temperature for 48 h to form a ~6 Å-thick self-assembled monolayer (SAM) of MBT on its surface (Supplementary Fig. 1b)65. Thereafter, the Au substrate was picked up from the solution, rinsed with pure ethanol, and dried with N2 gas just before being placed into our STM chamber.

Tip-enhanced nonlinear optical measurements
All the nonlinear optical measurements were performed at room temperature. Our optical system is based on an amplified Yb-fiber laser (1033 nm, 280 fs, 40 W, 50 MHz; Monaco-1035-40-40, Coherent). The fundamental output from the laser was divided into two portions by a beamsplitter. The first portion (120 nJ) was used to drive a commercially available optical parametric oscillator (OPO, Levante IR, APE), generating two kinds of wavelength-tunable IR pulses: signal (1.3–2 μm) and idler (2.1–5 μm). The second portion was passed through an air-spaced Fabry–Pérot etalon to narrow down the spectral width. Three kinds of pulses (signal, idler, and narrow-band fundamental wave) were used as excitation sources of TE-SHG and TE-SFG experiments, as described below. See Supplementary Figs. 2 and 3 for the spectra of those pulses.

For TE-SHG experiments, the STM chamber was maintained at ultra-high vacuum conditions with a base pressure of <1×10−7 Pa. The OPO’s signal output centered at 1500 nm was used as an excitation source. The excitation light intensity was attenuated to 0.5 mW (pulse energy: 10 pJ, peak power density: 5×106 W/cm2) by a variable neutral density filter, and then focused onto the apex of the STM tip at an incident angle of 55° using a custom-made CaF2 aspherical lens (NA = 0.34, focal length of 19.3 mm at 1033 nm) installed on the STM head. The incident light was linearly polarized along the axis of the tip (p-polarized). The backward-scattered TE-SHG signal at 750 nm was collimated with the same lens and separated from the incident light path using a custom-made dichroic mirror. The forward-scattered TE-SHG signal was collimated with another lens mounted in the reflection direction, and then the incident light was cut off by using a short-pass filter. Those two kinds of signals were separately input into a bundle fiber branched into two halves without polarization selection and directed into a spectrometer (Kymera 328i, Andor). Within the spectrometer, the signals from both directions were focused on the distinct vertical positions on the same electronically cooled CCD detector (iDus 416, Andor), allowing us to separately measure those two signals at the same time. The spectrometer wavelength was calibrated using an Hg/Ar lamp (SL2, StellarNet). When measuring voltage-dependent TE-SHG signals shown in Fig. 3, the measurements were repeated three times, with the order of the voltage sweeps varied for each measurement (Supplementary Note 6), and the signal accumulation time for each voltage point was 10 s.

For TE-SFG experiments, we extended this optical setup to a two-color excitation scheme, and the STM chamber was maintained at ambient pressure in an air atmosphere. To drive the TE-SFG process, the near-IR fundamental output from the Yb-fiber laser (0.5 mW, pulse energy: 10 pJ, peak power density: 5×106 W/cm2) and the mid-IR idler output (20 mW, pulse energy: 400 pJ, peak power density: 2×106 W/cm2) were spatially and temporally overlapped. The two laser pulses were combined collinearly at a dichroic mirror (reflective for 1033 nm and transparent for 1300–7000 nm) and then focused onto the apex of the STM tip by the same aspherical lens used in TE-SHG measurements. Both excitation pulses were linearly polarized along the axis of the tip (p-polarized). The detection of the signals was performed using the same method as that used for TE-SHG measurements. When measuring voltage-dependent TE-SFG signals shown in Fig. 4d and e, the applied voltages were varied in a random order, and the signal accumulation time for each voltage point was 300 s (Supplementary Note 6).

The relative modulations of TE-SHG/TE-SFG intensities plotted in Figs. 3 and 4e are defined as ΔI(V)/I(V=0), where I(V=0) denotes the TE-SHG/TE-SFG intensity at V=0 V, and ΔI(V)=I(V)−I(V=0) represents the bias-induced intensity change in the nonlinear optical signals. Under our STM-based experimental conditions, however, direct measurement of I(V=0) is technically difficult. This is because a net tunneling current becomes zero at V=0 V, preventing the operation of the feedback loop of STM to maintain an angstrom-scale tip–substrate gap distance. To circumvent this limitation, we approximated I(V=0) as the average TE-SHG/TE-SFG intensities obtained at small positive and negative biases (±0.1 V): I(V=0) ≈ [I(V=+0.1 V)+I(V=−0.1 V)]/2. This approximation is justified because the measured bias dependence of I(V) is well described by a parabolic function, and the intensities at ±0.1 V are much smaller than those at ±1 V. Consequently, the variation of I(V) within the ±0.1 V range is sufficiently small, and the averaged value not only provides a reasonable estimate of the zero-bias limit but also has almost no influence on the quantitative evaluation of the relative modulation depth ΔI(V)/I(V=0). Therefore, this averaged value was adopted as the reference intensity for quantitatively evaluating the relative modulation.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_3": "I reviewed this manuscript before it was transferred to Nature Communications. While this work is along the lines of the previous work on EFISH by Mark Brongersma's, the demonstrated strong modulation would warrant publications in this journal. I am however still puzzled how the device operates at ambient conditions without electric discharges under such strong electric field in the junction. Unfortunately, the authors did not comment on this before they transferred the manuscript to Nature Communications.", "reviewer_4": "Dear Editor,\nThe manuscript by Takahashi et al., “Giant near-field nonlinear electrophotonic effects in an ångström-scale plasmonic junction,” reports voltage-controlled enhancements of tip-enhanced SHG and SFG exceeding ~2000% within a 1 V bias across a ~6 Å Au–Au junction in an STM. By reducing the electrode spacing to the subnanometer scale, the authors generate quasi-static fields approaching 10⁹ V/m and demonstrate that the EFISH contribution (χ(3)·E_DC) dominates the intrinsic χ(2) response—yielding quadratic bias dependence and unprecedented modulation depths. The experiments span UHV and ambient conditions, and cover mid-IR to visible upconversion, highlighting the platform’s broadband potential.\nThe topic is timely and of broad interest to the nonlinear optics, nanophotonics, and scanning-probe communities. While the experiments are carefully executed, I have raised several technical questions and critiques that warrant clarification. In my view, the work has the potential to merit publication in Nature Communications once these points are adequately addressed.\nBelow, I outline the key issues and recommended revisions for the authors' consideration.\n1) Equation (1) forms the core of the authors’ interpretation of the TE-SHG modulation, combining intrinsic second-order nonlinearities with the field-induced EFISH term. While the conceptual framework is sound, the fitting model appears to make several implicit assumptions that would benefit from clarification or further validation. Example:\n> Gap Distance Sensitivity: Since EDC=V/dEDC = V/dEDC=V/d, sub-ångström variations in the tip–sample distance (±0.5–1 Å) could significantly impact the EFISH term. Could the authors please clarify whether this was accounted for in the fitting, or consider a brief sensitivity analysis?\n>Field Enhancement Uniformity: The use of a scalar Egap does not reflect the likely spatial nonuniformity in such confined junctions. Could the authors please clarify whether peak, average, or mode-volume field values were used would help?\nIn summary, the current fitting model is a reasonable starting point, but I encourage the authors to address the above points either through clarifications, sensitivity analysis, or supplemental modeling to ensure the robustness and physical fidelity of their interpretation of the EFISH effect in such highly confined plasmonic junctions. As a suggestion a simple FEM/FDTD simulations showing how Egap and EDCvary with d could strengthen the physical basis of the model and support the claimed >1000%/V modulation.\n2) This comment/suggestion is precisely the kind of control experiment needed to disentangle field-induced optical effects from tunneling-related carrier effects: Based on my understanding from their experimental procedure in STM, “constant current” mode means the system dynamically adjusts the tip height to maintain a fixed tunneling current (e.g., 500 pA) at a given bias. Importantly, this current is carried by tunneling electrons across the gap as stated by the authors. The authors use a constant-current STM configuration where the tip height is dynamically adjusted to maintain a fixed tunneling current (e.g., 500 pA) at a given bias. However, a high tunneling current inherently implies a significant injection of electrons across the plasmonic gap per second. This raises concerns that parasitic processes such as hot-carrier generation, inelastic scattering, impact ionization, photoluminescence, or electroluminescence may contribute to or amplify the observed second-order nonlinear signals (e.g., SHG or SFG).\nThese effects, especially in metal–molecule–metal junctions, could mimic or mask the optical nonlinearities the authors attribute to χ^(2) or χ^(3) processes. Therefore, I strongly encourage the authors to perform control measurements at lower setpoint currents (e.g., 10–50 pA) to test the robustness of their interpretation.\nIf the same bias-dependent modulation of TE-SHG intensity is observed at these reduced tunneling currents (I₁, I₂, I₃…), it would provide strong evidence that the effect is not driven by electron-induced mechanisms, but rather originates from a purely optical field-induced nonlinearity, such as EFISH (χ^(3)·E_DC), as claimed.\n3) I am having also slight concern with the terminology: Definition of “Ångström-Scale” vs. SAM Thickness:\nThe tip–substrate distance is often referred to as “5–7 Å,” but includes a ∼6 Å SAM layer (MBT). Therefore, the actual metal–metal distance may be larger. As a suggestion, I kindly recommend the clarification for the definition of “angstrom-scale gap” defined from metal-to-metal, tip apex to SAM, or through tunneling current equivalent?\n4) Nonlocal and Spill-Out Effects: Nonlocal response and electron spill-out play important roles in plasmonic nanogaps, especially at sub-nanometer dimensions. In Section 9 of the Supplementary Information, the authors acknowledge the possibility of quantum quenching—such as tunneling and nonlocal screening—but argue that these effects are minimal due to a maintained tip–sample distance of ≥5 Å. While this is a plausible assumption, the claim remains qualitative. To strengthen their argument, it would be beneficial for the authors to include either:\n• A reference to prior work that identifies the onset of quantum plasmonic suppression (e.g., electron tunneling or nonlocal damping) at angstrom-scale separations,\n• Or, if possible, a simple simulation or estimate that demonstrates the transition from field-driven χ^(3) modulation to quantum-dominated behavior in their specific geometry.\nSeveral key studies may be relevant here:\n>Esteban R. et al. Bridging quantum and classical plasmonics with a quantum-corrected model. Nat. Commun. 3:825 doi: 10.1038/ncomms1806 (2012).\n>Skjølstrup, E.J., Søndergaard, T. and Pedersen, T.G., 2018. Quantum spill-out in few-nanometer metal gaps: Effect on gap plasmons and reflectance from ultrasharp groove arrays. Physical Review B, 97(11), p.115429.\n>Zhu, W., Esteban, R., Borisov, A. et al. Quantum mechanical effects in plasmonic structures with subnanometre gaps. Nat Commun 7, 11495 (2016). https://doi.org/10.1038/ncomms11495\n5) I am also curious how the choice of crystalline Au influences the nonlinear modulation effects reported here. The authors utilize flame-annealed Au(111), which provides a flat, atomically ordered surface. However, what would they expect if an amorphous gold film or tip were used instead?\nIn particular, it would be helpful to know whether the electron scattering, plasmon damping, or local field enhancement in amorphous gold would significantly reduce the efficiency or stability of the observed TE-SHG and TE-SFG effects. Clarifying this would help evaluate how generalizable the approach is to other material systems and fabrication methods.\n6) While the study offers compelling experimental evidence for giant near-field nonlinear modulation in an ångström-scale plasmonic junction, the theoretical underpinnings remain underdeveloped. I note that in Section 13 of the Supplementary Information, the authors introduce simulations to capture field enhancement and its spectral evolution. However, this section is quite limited in detail.\nTo enhance the clarity and reproducibility of this part of the work, the authors should explicitly state the underlying mechanism behind their numerical method used (FDTD), the dielectric functions employed for gold and MBT, and whether nonlocal or quantum-corrected models were considered. Given the sub-nanometer nature of the gap, such modeling choices are highly consequential.\nMore broadly, the manuscript would benefit significantly from deeper computational or analytical exploration of:\n• The near-field distribution and its evolution under applied bias,\n• The interaction between light and tunneling carriers in such confined geometries,\n• The voltage-dependent transition from χ^(2)- to χ^(3)-dominated nonlinearities,\n• And the gap-size dependence of TE-SHG and TE-SFG efficiencies.\nIn addition, the physical origin of the observed nonlinear peaks remains insufficiently explored. A decomposition of the nonlinear scattering response into electromagnetic modes—such as via quasi-normal mode analysis or pole fitting of the scattering matrix—could provide insights into whether dipolar, quadrupolar, or higher-order gap plasmons are involved.\nIncorporating these theoretical and mechanistic insights would not only support the authors’ experimental claims but also deepen the conceptual impact of this important work.\n7) Additionally, I noticed that Fig. S15 in the current Supplementary Information appears closely related to Fig. 4 from the authors' prior publication (Takahashi et al., J. Phys. Chem. Lett. 2023). However, it is unclear what modeling assumptions have changed between the two—particularly whether the current work accounts for the spacer layer (e.g., MBT) when defining the tip–substrate gap in the simulations. Could the authors clarify whether the SAM thickness was explicitly included in the field enhancement calculations presented in Fig. S15? It would also be helpful to briefly explain how the present modeling differs from the earlier work—both in physical assumptions and numerical parameters.\n8) Page2", "reviewer_35": "Slightly, less critical but still important point is that regarding the very first part of introduction, the Authors stated that “Plasmonic functionalities are determined by the intrinsic optical properties of materials and the static geometry of the plasmonic structures (e.g., size, shape, and surrounding environment), making it difficult to adjust the plasmonic properties after the geometry of the plasmonic nanostructure is fixed.” While I understand the statement but it is misleading the potential readers from the point of when the geometry fixed it is hard to tune/control the optical properties. There are several studies counter actively showing the tunability of the intrinsic optical properties by changing the size and hybridizing the material content while keeping/maintaining the shape of the determined geometry.\nSingle material:\n[1] Campos, A., Troc, N., Cottancin, E. et al. Plasmonic quantum size effects in silver nanoparticles are dominated by interfaces and local environments. Nat. Phys. 15, 275–280 (2019). https://doi.org/10.1038/s41567-018-0345-z\n[2] Ringe, Emilie, et al. \"Plasmon length: a universal parameter to describe size effects in gold nanoparticles.\" The journal of physical chemistry letters 3.11 (2012): 1479-1483.\n[3] Henry, A.I., Bingham, J.M., Ringe, E., Marks, L.D., Schatz, G.C. and Van Duyne, R.P., 2011. Correlated structure and optical property studies of plasmonic nanoparticles. The Journal of Physical Chemistry C, 115(19), pp.9291-9305.\nFor the hybrid/colloidal formation:\n[4] Rossner, Christian, Tobias AF König, and Andreas Fery. \"Plasmonic properties of colloidal assemblies.\" Advanced Optical Materials 9.8 (2021): 2001869.\n[5] Kilic, Ufuk, et al. \"Broadband enhanced chirality with tunable response in hybrid plasmonic helical metamaterials.\" Advanced Functional Materials 31.20 (2021): 2010329.\n[6] Kılıç, U., Mock, A., Feder, R., Sekora, D., Hilfiker, M., Korlacki, R., Schubert, E., Argyropoulos, C. and Schubert, M., 2019. Tunable plasmonic resonances in Si-Au slanted columnar heterostructure thin films. Scientific reports, 9(1), p.71.\nI thereby kindly recommend that the author shines a light on the path of potential readers by showing the efforts being made and are indeed exist some studies available in the literature that some geometries can provide the opportunity still spectrally and amplitude-wise tailor the optical properties.\n9) Lastly, the manuscript’s novelty is enhanced by ambient-pressure operation. However, reviewer 3's concern about dielectric breakdown remains partially open. I think that authors kindly include the gas breakdown discussion in the main text or supplementary (it is currently only in their response letter), perhaps citing the limited gas volume (<10^⁻20 cm³) and impossibility of avalanche ionization as justification.", "reviewer_5": "The manuscript by S.Takahashi et al. presents a study on the tip-enhanced nonlinear optical processes on plasmonic thin films. They experimentally demonstrate the TE-SHG, TE-SFG and so on by utilizing an angstrom-scale plasmonic gap between a metallic tip and a flat metal substrate in a scanning tunneling microscope. They have found that such plasmonic gaps can experience strong near-field enhancement, which leads to a modulation factor up to 2000%/V in the EFISH process. Their results are detailed and well-organized, and may open new avenue for designing angstrom-level photonic devices. However, I still have several questions and comments about this manuscript before recommend it for publication.\nBelow are my specific comments:\n1. The authors have measured the relative value of the second order and third order nonlinear susceptibilities. As a general question in the area of nonlinear optics, what is the SHG conversion efficiency? Is there a solution to improve this efficiency?\n2. The authors have calculated the enhancement spectra of Au tip, but it seems that this resonance is not close to the fundamental wavelength. Is it possible to manipulate the plasmonic resonance of the Au tip to get a larger enhancement factor?\n3. In the TE-SHG measurement, the SHG intensity first increases and then decreases while the gap becomes larger. I suggest the authors discuss more about this phenomenon. Where is the maximum intensity position? Is it related to the coupling effect or the interference of the plasmonic resonances?\n4. P-polarized FWs are used in the measurement. Is it possible to measure the polarization states of the SHG and SFG signals?\n5. Minor comments: a. the illustration of the backward/forward scattering schemes should be added; b. the font size in figures should be optimized."}, "author_response": "Responses to reviewers’ comments\n1\n3 (manuscript number: NCOMMS-25-44074-T). Please find below a detailed response to each comment.\n5 letters and yellow backgrounds, respectively.\n6\n10 along the lines of the previous work on EFISH by Mark Brongersma's, the demonstrated strong\n11 modulation would warrant publications in this journal. I am however still puzzled how the device\n12 operates at ambient conditions without electric discharges under such strong electric field in the\n13 junction. Unfortunately, the authors did not comment on this before they transferred the manuscript to\n15\n18 electrophotonics beyond the nanoscale regime and our demonstration of the giant electrophotonic\n19 effects within an angstrom-scale plasmonic gap. We also appreciate the reviewer’s positive evaluation\n20 that our work would warrant publication in Nature Communications.\n22 strong electric field in our angstrom-scale junction. As replied in our previous response to the\n23 reviewer’s comment 2, such discharges can be reasonably ruled out under our experimental conditions\n24 in terms of (i) an interelectrode electron transfer mechanism and (ii) the number of gas molecules\n25 within the gap:\n26 (i) The angstrom-scale tip–substrate distance employed in our experiments ensures the overlap of\n27 electronic wavefunctions at the tip and substrate surfaces. Under these conditions, the\n28 interelectrode electron transfer occurs predominantly via the electron tunneling process, rather\n29 than ballistic field emission of electrons into the gas phase. This prevents electron–gas collisions\n30 that would otherwise trigger avalanche ionization of gas molecules, resulting in the absence of the\n31 electric discharges.\n32 (ii) Given the number density of gas molecules under the ambient conditions and the volume of\n33 an angstrom-scale tip–substrate gap, at most only a few molecules can be present within the gap.\n35 molecules, rendering electric discharge physically implausible even under ambient experimental\n36 conditions.\n38 gap structure, and any discharge-induced modification of the tip or substrate can be safely disregarded.\n40 we revised the main text and Supplementary Information to provide the discussion regarding the\n41 absence of dielectric breakdown within the nanogap even under ambient conditions. Thank you for\n42 your comment.\n43\n46 by an intense electrostatic field within the gap (~109 V/m) can also be reasonably ruled out in our\n47 ambient experimental conditions, because of the extremely rare electron–gas collision within our\n48 angstrom-scale gap (further details in Supplementary Section 9). This allows us to safely disregard any\n49 intense-field-induced modification of the tip or substrate even under ambient experimental conditions.\n50\n52 modification of the tip and substrate indicates that dielectric breakdown within the gap and associated\n53 breakdown-induced damage to either the sample or the tip can be ruled out, even under the application\n54 of a strong electrostatic field (~109 V/m) across the gap. The impossibility of the dielectric breakdown\n55 can be correctly interpreted by considering the probability of the electron–gas collision within our\n56 angstrom-scale gap. Generally, the dielectric breakdown is induced by field emission of electrons from\n57 an electrode into gas phase, avalanche ionization of gas molecules, and ballistic acceleration of charge\n58 carriers within the interelectrode gap, leading to physical damage of the electrodes14. Thus, the\n59 collision process between electrons and gas molecules plays a key role in the emergence of dielectric\n60 breakdown. However, since the angstrom-scale tip–substrate distance employed in our experiments\n61 ensures the overlap of electronic wavefunctions at the tip and substrate surfaces, the interelectrode\n62 electron transfer occurs predominantly via the tunneling process, rather than ballistic field emission of\n63 electrons into the gas phase. This prevents electron–gas collisions that would otherwise trigger\n64 avalanche ionization of gas molecules, resulting in the absence of the dielectric breakdown. Moreover,\n65 considering the number density of gas molecules under ambient conditions (2.69×1019 cm−3), the\n66 extremely small volume of the angstrom-scale gap (~10−20 cm3) allows for the presence of at most a\n67 few gas molecules within the gap. This is insufficient to sustain the cascade ionization processes,\n68 making gas-phase electric breakdown physically impossible even under ambient experimental\n69 conditions. Therefore, the possibility of electric discharges within our angstrom-scale gap structure\n70 can be clearly ruled out, and any discharge-induced modification of the tip or substrate can be safely\n71 disregarded.\n72\n76 scale plasmonic junction,” reports voltage-controlled enhancements of tip-enhanced SHG and SFG\n77 exceeding ~2000% within a 1 V bias across a ~6 Å Au–Au junction in an STM. By reducing the\n78 electrode spacing to the subnanometer scale, the authors generate quasi-static fields approaching 109\n80 response—yielding quadratic bias dependence and unprecedented modulation depths. The experiments\n81 span UHV and ambient conditions, and cover mid-IR to visible upconversion, highlighting the\n82 platform’s broadband potential.\n84 probe communities. While the experiments are carefully executed, I have raised several technical\n85 questions and critiques that warrant clarification. In my view, the work has the potential to merit\n86 publication in Nature Communications once these points are adequately addressed. Below, I outline\n87 the key issues and recommended revisions for the authors' consideration.\n88\n91 exploration of angstrom-scale nonlinear electrophotonics, extending beyond the conventional\n92 nanoscale regime. We also greatly appreciate the reviewer’s recognition of the timeliness and broad\n93 relevance of our work to the nonlinear optics, nanophotonics, and scanning-probe communities, as\n94 well as the reviewer’s acknowledgment of our careful execution of the experiments. Note that\n95 following the reviewer’s comment, we re-examined the quantitative accuracy of the parameters\n96 presented in this paper and found that the tip–substrate distance ((cid:11)) employed in the bias-dependent\n98 to minor changes in the estimated relative values of (cid:1)((cid:12)) and (cid:1)((cid:13)), it does not affect the main\n99 conclusions or the overall concept of the paper.\n101 replies and associated revisions to our manuscript in the following. We believe that these revisions\n102 will help us more clearly convey the reliability and impact of our achievements to broad readership of\n104\n105\n107 1) Equation (1) forms the core of the authors’ interpretation of the TE-SHG modulation, combining\n108 intrinsic second-order nonlinearities with the field-induced EFISH term. While the conceptual\n109 framework is sound, the fitting model appears to make several implicit assumptions that would benefit\n110 from clarification or further validation. Example:\n111\n112 > Gap Distance Sensitivity: Since (cid:6) = (cid:17)/(cid:11), sub-ångström variations in the tip–sample distance\n(cid:14)(cid:15)\n113 (±0.5–1 Å) could significantly impact the EFISH term. Could the authors please clarify whether this\n114 was accounted for in the fitting, or consider a brief sensitivity analysis?\n115 >Field Enhancement Uniformity: The use of a scalar Egap does not reflect the likely spatial\n116 nonuniformity in such confined junctions. Could the authors please clarify whether peak, average, or\n117 mode-volume field values were used would help?\n119 address the above points either through clarifications, sensitivity analysis, or supplemental modeling\n120 to ensure the robustness and physical fidelity of their interpretation of the EFISH effect in such highly\n121 confined plasmonic junctions. As a suggestion a simple FEM/FDTD simulations showing how Egap\n122 and EDC vary with d could strengthen the physical basis of the model and support the claimed\n123 >1000%/V modulation.\n124\n127 underlying our fitting model based on equation (1) in the main text. In order to ensure the robustness\n128 and physical fidelity of our interpretation of the experimental result, the reviewer recommended that\n129 we address (a) Gap Distance Sensitivity and (b) Field Enhancement Uniformity. In the following,\n130 we provide point-by-point responses to these two issues.\n131\n132 (a) Gap Distance Sensitivity\n134 excitation pulses for TE-SHG, indicating the absence of significant tip–substrate distance variations\n135 that could disturb the STM topography during the TE-SHG measurements. While sub-angstrom\n136 fluctuations of ~0.5–1 Å cannot be entirely excluded, their typical timescale is on the order of\n137 microsecond scale and much shorter than minute-scale signal integration time in our measurements.\n(cid:19)(cid:20)\n139 effectively averaged out and would not manifest in the measured modulation curves. For this reason,\n140 the fluctuations in (cid:6) were not explicitly taken into account in our fitting analysis.\n(cid:19)(cid:20)\n142 clearly convey that sub-angstrom variations in the tip–substrate distance can be disregarded in our\n143 experimental conditions. Thank you for your comment.\n144\n145 (b) Field Enhancement Uniformity\n(cid:21)(cid:22)(cid:23)\n147 nonuniform and extends over the nanoscale region with a radius of ~20 nm (Fig. I). Notably, we also\n148 performed theoretical analysis of the electrostatic field distribution within the gap based on the image\n149 charge method [Rev. Bras. Ensino Fís. 31, 3503 (2009)] and revealed that a comparable degree of\n150 spatial nonuniformity is also present in the electrostatic field across the gap ((cid:6) , Fig. II).\n(cid:19)(cid:20)\n152 spatially uniform, the tip–substrate junction exhibits a position-dependent field distribution due to the\n153 curved geometry of the tip apex. Consequently, both (cid:6) and (cid:6) exhibit spatial variations, giving\n(cid:21)(cid:22)(cid:23) (cid:19)(cid:20)\n154 rise to position-dependent nonlinear polarizations within the nanoscale region beneath the tip apex.\n156 originate from a nanoscale region of a few tens of nanometers directly beneath the tip apex\n157 [arXiv:2509.09179 [physics.optics]], which is quantitatively consistent with theoretically predicted\n158 ~20-nm-scale lateral field enhancement areas (Figs. I and II). Therefore, the values of (cid:6) and (cid:6)\n(cid:21)(cid:22)(cid:23) (cid:19)(cid:20)\n159 in our analysis represent the effective field strengths averaged over this laterally extended ~20 nm\n160 region confined within the tip–substrate gap.\n163 revised the main text to clarify that (cid:6) and (cid:6) in equation (1) represent the spatially averaged\n(cid:21)(cid:22)(cid:23) (cid:19)(cid:20)\n164 field values over ~20-nm field enhancement region within the angstrom-scale tip–substrate gap.\n166\n(cid:25)(cid:26)(cid:27)\n168 (a, b) surface-normal and (c, d) surface-parallel electric field components calculated through the\n170 nm apex radius, and 15000-nm length. The tip–substrate distance was set to be 2 nm. Panels (a) and\n171 (c) show the field in the XZ plane (Y = 0 nm), while panels (b) and (d) show the field in the XY plane\n172 (Z = 0.5 nm). The wavelength of incident light was 3280 nm. The coordinates (X, Y) = (0 nm, 0 nm)\n173 represent the position of minimum tip–substrate distance. (e) One dimensional spatial profiles of (cid:28)\n(cid:21)(cid:22)(cid:23)\n174 along the X-axis (Y = 0 nm and Z = 0.6 nm). Green and red curves represent the surface-normal and\n175 surface-parallel field components, respectively.\n176\n(cid:30)(cid:31)\n178 application across the tip-substrate nanogap. The calculation was performed through the image\n179 charge method [Rev. Bras. Ensino Fís. 31, 3503 (2009)]. The surface-normal (a) and surface-parallel\n180 (b) electrostatic field components are plotted in the XZ plane (Y = 0 nm). In the calculation, the tip was\n181 approximated by a nanosphere with a 50-nm apex radius, and the tip–substrate distance was set to be\n182 1 nm. The coordinates (X, Y) = (0 nm, 0 nm) represent the position of minimum tip–substrate distance.\n183\n186 fluctuations in (cid:11), which should induce variations in (cid:6) , are inevitably present under our ambient\n(cid:19)(cid:20)\n187 experimental conditions (Supplementary Fig. S11d), their influence was not incorporated into the\n188 fitting analysis. This is because the typical timescale of the fluctuations is on the order of microsecond\n189 and thus much shorter than minute-scale signal integration time in our measurements. Consequently,\n190 the influence of the fluctuations in (cid:6) would be effectively averaged out and would not manifest in\n(cid:19)(cid:20)\n191 the measured modulation curves. For this reason, the fluctuations in (cid:6) were not explicitly taken\n(cid:19)(cid:20)\n192 into account in our fitting analysis.\n193\n(cid:21)(cid:22)(cid:23) (cid:19)(cid:20)\n196 averaged field values over the ~20-nm field enhancement region beneath the tip apex (see\n198\n200 spatial distribution of the electric field within the nanogap. Figure S19 displays the surface-normal and\n201 surface-parallel components of the electric field within the tip–substrate gap ((cid:6) ), which were\n(cid:21)(cid:22)(cid:23)\n202 calculated through the FDTD simulation for a tip with a curvature radius of 50 nm. This tip radius is\n203 comparable to the size of the tip apex used in our experiments (Fig. 1b in the main text). Note that the\n204 tip–substrate gap was assumed to be vacuum, and the presence of the SAM layer was not incorporated.\n206 nanoscale region with a radius of ~20 nm. Furthermore, our theoretical analysis of the electrostatic\n207 field distribution within the gap using the image charge method54 revealed that the electrostatic field\n208 across the gap ((cid:6) ) also exhibits a similar spatial distribution (Fig. S20). Importantly, our recent\n(cid:19)(cid:20)\n209 experiments revealed that near-field second-order nonlinear optical signals originate from a nanoscale\n210 region with an area of a few tens of nanometers directly beneath the tip apex10. Since this result is\n211 consistent with theoretically predicted ~20-nm-scale lateral field enhancement areas (Figs. S19 and\n213 generation of near-field second-order nonlinear optical signals.\n214\n215\n217 2) This comment/suggestion is precisely the kind of control experiment needed to disentangle field-\n218 induced optical effects from tunneling-related carrier effects: Based on my understanding from their\n219 experimental procedure in STM, “constant current” mode means the system dynamically adjusts the\n220 tip height to maintain a fixed tunneling current (e.g., 500 pA) at a given bias. Importantly, this current\n221 is carried by tunneling electrons across the gap as stated by the authors. The authors use a constant-\n222 current STM configuration where the tip height is dynamically adjusted to maintain a fixed tunneling\n223 current (e.g., 500 pA) at a given bias. However, a high tunneling current inherently implies a significant\n224 injection of electrons across the plasmonic gap per second. This raises concerns that parasitic processes\n225 such as hot-carrier generation, inelastic scattering, impact ionization, photoluminescence, or\n226 electroluminescence may contribute to or amplify the observed second-order nonlinear signals (e.g.,\n229 nonlinearities the authors attribute to χ^(2) or χ^(3) processes. Therefore, I strongly encourage the\n230 authors to perform control measurements at lower setpoint currents (e.g., 10–50 pA) to test the\n231 robustness of their interpretation.\n233 currents (I₁, I₂, I₃…), it would provide strong evidence that the effect is not driven by electron-induced\n234 mechanisms, but rather originates from a purely optical field-induced nonlinearity, such as EFISH\n235 (χ^(3)·E_DC), as claimed.\n236\n237 4) Nonlocal and Spill-Out Effects: Nonlocal response and electron spill-out play important roles in\n238 plasmonic nanogaps, especially at sub-nanometer dimensions. In Section 9 of the Supplementary\n240 nonlocal screening—but argue that these effects are minimal due to a maintained tip–sample distance\n241 of ≥5 Å. While this is a plausible assumption, the claim remains qualitative. To strengthen their\n242 argument, it would be beneficial for the authors to include either:\n243 • A reference to prior work that identifies the onset of quantum plasmonic suppression (e.g., electron\n244 tunneling or nonlocal damping) at angstrom-scale separations,\n245 • Or, if possible, a simple simulation or estimate that demonstrates the transition from field-driven\n246 (cid:1)((cid:13)) modulation to quantum-dominated behavior in their specific geometry.\n248 >Esteban R. et al. Bridging quantum and classical plasmonics with a quantum-corrected model. Nat.\n250 >Skjølstrup, E.J., Søndergaard, T. and Pedersen, T.G., 2018. Quantum spill-out in few-nanometer\n251 metal gaps: Effect on gap plasmons and reflectance from ultrasharp groove arrays. Physical Review\n253 >Zhu, W., Esteban, R., Borisov, A. et al. Quantum mechanical effects in plasmonic structures with\n254 subnanometre gaps. Nat Commun 7, 11495 (2016). https://doi.org/10.1038/ncomms11495\n255\n258 tip height is dynamically adjusted to maintain a fixed tunneling current at a given bias. As discussed\n259 in the main text and in Supplementary Section 11, the influence of the tunneling current in our\n260 experiments was clearly ruled out through our control experiments performed under a constant\n261 tunneling current setpoint.\n263 not only the applied bias but also the tunneling current setpoint in the range of 40–1750 pA, allowing\n264 us to prevent the variation in the tip-substrate distance and maintain the field enhancement strength\n265 (see Table S1 for the explicit setpoint values). While this experimental scheme may seemingly leave\n266 the possibility of tunneling current contributions in the observed clear quadratic bias dependence and\n267 ~2000%/V modulation of TE-SHG intensity, our control bias-dependent TE-SHG measurements\n268 performed under a “fixed tunneling-current setpoint (500 pA)” also clearly revealed a quadratic\n269 modulation of comparable magnitude (Supplementary Fig. S14b). The consistency of the two results\n270 (Figs. 3 and S14) indicates that giant near-field nonlinear electrophotonic effects occur regardless of\n271 the tunneling current variations, demonstrating that the contributions of tunneling-current–driven\n272 processes, such as hot-carrier generation, inelastic scattering, impact ionization, photoluminescence,\n273 or electroluminescence, are negligibly small.\n275 applied bias from 0.1 V to 1 V led to an elongation of the tip–substrate distance from ~4 Å to ~6 Å\n276 (Fig. S14a). Based on conventional classical electrodynamic simulations, both the near-field\n277 enhancement factor ((cid:28) ) and the radiation efficiency (! ) are expected to decrease by several tens\n(cid:21)(cid:22)(cid:23) (cid:21)(cid:22)(cid:23)\n278 of percents during this tip–substrate distance elongation [J. Phys. Chem. B 110, 6692 (2006);\n280 (2020)]. Accordingly, the absolute TE-SHG intensity, proportional to"}]

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