Adaptive tip-enhanced nano-spectroscopy

Tip-enhanced nano-spectroscopy, such as tip-enhanced photoluminescence (TEPL) and tip-enhanced Raman spectroscopy (TERS), generally suffers from inconsistent signal enhancement and difficulty in polarization-resolved measurement. To address this problem, we present adaptive tip-enhanced nano-spectroscopy optimizing the nano-optical vector-field at the tip apex. Specifically, we demonstrate dynamic wavefront shaping of the excitation field to effectively couple light to the tip and adaptively control for enhanced sensitivity and polarization-controlled TEPL and TERS. Employing a sequence feedback algorithm, we achieve ~4.4 × 104-fold TEPL enhancement of a WSe2 monolayer which is >2× larger than the normal TEPL intensity without wavefront shaping. In addition, with dynamical near-field polarization control in TERS, we demonstrate the investigation of conformational heterogeneity of brilliant cresyl blue molecules and the controllable observation of IR-active modes due to a large gradient field effect. Adaptive tip-enhanced nano-spectroscopy thus provides for a systematic approach towards computational nanoscopy making optical nano-imaging more robust and widely deployable.


SUPPLEMENTARY NOTE 1. MECHANISM OF DYNAMIC SPP MODULA-TION
While our work demonstrates the ability to control the surface plasmon polariton (SPP) properties of Au tip for tip-enhanced nano-spectroscopy for the first time, there have been many efforts to manipulate the SPP characteristics, e.g., field amplitude, polarization, and spatial field distribution, in plasmonic nano-structures. Recently, dynamical SPP control for plasmonic metal hole array [1], slits [2,3], and gratings [4,5] was demonstrated. Since these SPP controls are based on the coherent conversion from excitation light to SPPs [6], many interesting ideas on SPP control could be achieved under systematic control of excitation light. Specifically, several studies reported that the SPP condition is strongly influenced by the space-variant polarization state of incident light [7][8][9][10], as well as by the spectral and spatial coherence of incident light [11]. Therefore, making the customized excitation light for plasmonic devices is a simple but effective approach to control the SPP characteristics of them.
In our case of tip-enhanced nano-spectroscopy, an incident laser beam E inc is tightly focused at the apex of Au tip with a high NA objective lens. Due to the depolarization effect of the high NA objective lens, the optical field distribution of the focused beam in the vicinity of Au tip can be expressed with the angular spectrum method as follows [12]: where d is the path length between the initial point at lens and the focal point, and the wave vector k = (k x , k y , k z ) is expressed in Cartesian coordinates. Based on this model, we can consider the focused beam as a superposition of plane waves with different wave vectors, i.e., the excitation light can be decomposed into the optical field components with various polarization angles with respect to the tip axis. Therefore, partial optical field components which have the polarization direction close to parallel with respect to the tip axis can be effectively coupled into surface plasmon. On the other hand, the other field components are lost, and thus the excitation rate for tip-enhanced photoluminescence or Raman is significantly low in conventional set-ups. To enhance the field localization, i.e., excitation rate, a radially polarized beam [13] is used, yet the coupling efficiency is still low and it can be only used for the bottom-illumination mode set-ups. In our approach, through S2 wavefront shaping of an excitation beam with a spatial light modulator, we dynamically manipulate the amplitude, phase, and polarization of the SPP customized for the tip shape.
Therefore, this approach can significantly enhance the excitation rate for any TERS or TEPL modality, e.g., bottom-illumination, top-illumination, and side illumination modes.

GENCE OF THE WAVEFRONT SHAPING ALGORITHM
In its simplest form, the optimization target we use is a spectrally integrated intensity of TEPL or TERS spectrum. Specifically, for a-TEPL of a WSe 2 monolayer, the optimization target is an integrated TEPL intensity in the range of 749 ∼ 753 nm. For a-TERS of a WSe 2 monolayer, the target is the spectrally integrated intensity of A 1g + E 1 2g Raman peak. For a-TERS of BCB molecules, the target is the Raman peak of ∼583.5 cm −1 . The algorithm optimizes the optical phase of all the segments in the spatial phase mask sequentially to achieve the maximum intensity for the target signals.
To confirm the convergence, we repeat the algorithm three times continuously with the target signal. With several control experiments with different tips, we can find that the saturation enhancement is obtained and the optimization is converged after completing a single cycle of the algorithm (see Supplementary Figure 1

SUPPLEMENTARY NOTE 4. CALCULATION OF TEPL ENHANCEMENT FACTOR
For an atomically thin spontaneous emitter, i.e., WSe 2 monolayer, we can use the following equation for estimating TEPL enhancement factor (EF) [14]: where I tip−in and I tip−out refer to the PL peak intensity with the tip approached (TEPL) and nm (the empirical factor of 1.5 is used) [15] of the far-field laser spot and r N F with half of the spatial resolution of the used Au tip, 7 nm (derived from Fig. 2c-d). Using Eq. (2) and the derived values from our experiment, we estimate the enhancement factor for the conventional TEPL without using the wavefront shaping as high as ∼ 1.9 × 10 4 (blue in Fig.   2a). By contrast, we achieve TEPL enhancement factor as high as ∼ 4.4 × 10 4 through the proposed wavefront shaping approach (red in Fig. 2a). S6

SUPPLEMENTARY NOTE 5. A-TEPL MEASUREMENT USING A RADIALLY POLARIZED BEAM
We also try a-TEPL experiment with a radially polarized excitation beam to confirm that the enhanced signal with the wavefront shaping is not just due to the radial polarization effect. As seen in Supplementary Figure 5 below, the wavefront shaping gives significant enhancement in a-TEPL intensity compared to the normal TEPL intensity, similar to the experiment with a linear polarizer. Therefore, the increased TEPL/TERS intensity using wavefront shaping is not just due to the radial polarization effect.

SUPPLEMENTARY NOTE 7. OBSERVATION OF IR-ACTIVE MODES WITH TERS
The transitions in vibration levels of molecules induced by optical fields E and optical field gradients ∇E are described by the perturbation Hamiltonian H given by [16] where the subscripts α, β, γ, δ indicate coordinates in the Cartesian system and α αβ , A α,βγ , A γ,αβ , and C αβ,γδ are the dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizabilities of a molecule [17]. In far-field vibrational spectroscopy in the visible region,

dipole-dipole interactions induced by optical fields result in Raman scattering responses,
whereas dipole-quadrupole and quadrupole-quadrupole interactions coupled to optical field gradients result in the activation of IR modes. The IR modes are hard to observe because of much smaller optical field gradient amplitude compared with optical field amplitude. On the other hand, in the tip-enhanced excitation with plasmonic tips, the strong optical field gradients in both in-plane and out-of-plane directions (Fig. 3d) near the tip cannot be ignored. These strong optical field gradients coupled to dipole-quadrupole and quadrupolequadrupole interactions make possible to observe IR-active modes in TERS measurement [18,19]. In our TERS experiment with wavefront shaping, we can observe specific IR-active modes with the ability to turn modes on and off, by modulating the tip-SPP polarization dynamically. S10

SUPPLEMENTARY NOTE 8. DYNAMIC SWITCHING OF IR-ACTIVE MODE WITH A-TERS
First of all, we confirm that the observation of the IR-active mode is solely enabled by the wavefront shaping effect in our experiment. Specifically, we verified that i) the IR-active mode was observed at the same spatial location and ii) it can be switched on and off. We could observe the IR-active mode in a specific phase mask and the signal was very robust. To verify the wavefront shaping effect, we swept the phase of a SLM segment with the relative phase difference of 2nπ (n is an integer). As shown in the Supplementary Figure 9 below, we observed the IR-active mode only at the phases of 0, π, 2π, . . . nπ, reproducibly. In addition, since we can change the spatial phase of the wavefront with 60 Hz, we can turn it on and off with <20 ms temporal resolution. We believe this experiment clarifies that the IR-active mode was observed by the wavefront shaping.
In contrast to the previous studies observing IR-active modes in the static plasmonic cavities [20][21][22], our approach provides 'dynamic controllability' to turn IR-active modes on and off through the systematic phase modulation with <20 ms temporal resolution. The static plasmonic cavity, e.g., NPoM, has very small mode volume but it quite unstable in ambient condition. Hence, the IR-active modes can randomly appear owing to the field gradient effect [23]. In contrast, our approach is based on shear-force AFM and we are able to control the tip-sample distance with 0.2 nm precision under ambient conditions [24].
In our a-TERS experiment, the tip-sample distance was maintained at ∼2 nm to avoid unwanted perturbation effect. Therefore, in addition to tip-enhanced nano-spectroscopy applications, our adaptive near-field approach can be more broadly used to control lightmatter interactions in static plasmonic cavities [25][26][27]. S11 Supplementary Figure 9. Adaptive TERS spectra of BCB molecules with changing the optical phase of a specific segment in a spatial phase mask. The IR-active mode is observed with a period of π, reproducibly. S12 SUPPLEMENTARY NOTE 9.
PROBING CONFORMATIONAL HETERO- Fig. 4f in the main text shows a-TERS spectra with changing spatial phase of the wavefront. This set of spectra was obtained in a specific time segment during the procedure of stepwise sequencing. The observed spectral fluctuation appeared randomly with changing phase mask. Although we cannot quantitatively analyze the rotational or spectral diffusions as in our previous low temperature work [28] due to the inhomogeneous broadenings at room temperature, we could analyze that the observed TERS peak shifts originate from the differ- Since we used the thin gold film (∼10 nm thick) as a substrate for a TMD monolayer, we expect the far-field PL intensity (d > 15 nm) to be decreased due to nonradiative quenching.

GENEITY OF BCB MOLECULES WITH A-TERS
But, when the Au tip approaches the TMD monolayer with a few nm gap, we expect the suppressed PL quenching because the spontaneous emission is coupled to the antenna mode with its fs-radiative decay [24,29,30]. For the far-field PL quenching by the thin gold film, we recently performed control experiment with MoS 2 monolayers. When a MoS 2 monolayer is transferred onto the thin gold film, we expect that there is a thin water layer between them. As shown in the figure below, when the excitation laser power was 3 µW, PL intensity of the TMD crystal was not changed. On the other hand, when we used the high excitation power of >100 µW, the PL intensity was gradually decreased with respect to time up to ∼50 %. From these results, we guess that the water layer was evaporated by the high-power excitation which leads to the increased PL quenching by the reduced distance between the gold film and the TMD crystal. S15 Supplementary Figure 11. (a, b) PL spectra of a MoS 2 monolayer with respect to the excitation time, exhibiting the PL quenching properties at the high excitation power. The CVD-grown MoS 2 monolayer is transferred onto the thin gold film through a wet-transfer method. We assume that there is a water layer between the TMD crystal and the gold film which can suppress the PL quenching phenomenon. When we use an excitation laser power of 3 µW, PL intensity is not changed (a). On the other hand, when use an excitation laser power of >100 µW, PL intensity is gradually decreased due to the PL quenching (b). We believe this PL quenching is originated from the evaporated water layer due to the thermal energy of the excitation laser. S16