Phase-referenced nonlinear spectroscopy of the α-quartz/water interface

Probing the polarization of water molecules at charged interfaces by second harmonic generation spectroscopy has been heretofore limited to isotropic materials. Here we report non-resonant nonlinear optical measurements at the interface of anisotropic z-cut α-quartz and water under conditions of dynamically changing ionic strength and bulk solution pH. We find that the product of the third-order susceptibility and the interfacial potential, χ(3) × Φ(0), is given by (χ1(3)−iχ2(3)) × Φ(0), and that the interference between this product and the second-order susceptibility of bulk quartz depends on the rotation angle of α-quartz around the z axis. Our experiments show that this newly identified term, iχ(3) × Φ(0), which is out of phase from the surface terms, is of bulk origin. The possibility of internally phase referencing the interfacial response for the interfacial orientation analysis of species or materials in contact with α-quartz is discussed along with the implications for conditions of resonance enhancement.

--------------1. The authors mention that the phase shifts by 180 degrees when rotating the sample by 60 degrees along z. However, this is not clear in my view from figure 2, where is shown the signal for different Δφ angles. Is the Δφ in figure 2 the difference between two crystal angles or the absolute value? In the former case looks like 40 degrees is actually larger in amplitude than 60. In the latter case looks like the signal is actually changing phase every 90 degrees. This point can be better clarified by introducing an additional panel where is plotted the difference signal ΔI = I(pH11)-I(pH3) for different Δφ angles.
2. In the setup at figure 1 is shown a λ/2 waveplate and a polarizer along the beam path, which however is not referenced in the text. How does the signal phase depend on the polarization of the incident beam? One can imagine that in the case of quartz/water interface this can potentially be an additional way to control the phase of the observed signal.
3. An additional way to estimate the degree of mixing between χ2 and χ3 is to measure the signal for different laser intensities (flux dependence). Have the authors attempted such a measurement? In any case, the values that were used in the current realizations (both on the quartz and silica) and the focus size should be reported.
Minor comments: --------------1. From a technical point of view this is a very important breakthrough. It is also as important however to discuss what can be concluded about the water/quartz interface. Can one probe differences between the interaction of water with quartz versus that with fused silica? Varying the ionic strength is a good approach, which can potentially provide such an insight.  A. 2009, 106, 15148−15153.]. Can the authors comment on the similarities and differences between the two approaches?
3. It would be helpful to show in figure 1 the axis of rotation z, by implementing a 3D representation like those previously (Achtyl et al. Nature Comm. 2015).
4. The water thickness that was used in 3mm, whereas as a possible outlook is mentioned that this layer can be reduced to a few nm. What are the technical limitations for such a realization? This could help estimate the bulk contribution to the signal and additionally quantify the thickness sensitivity of SHG spectroscopy.

Reviewer #1 (Remarks to the Author)
Comments: This is an interesting, well-written paper describing original studies from top figures in the field of interface spectroscopy. It is likely to be an important and influential paper, and I can recommend that it be published in Nature Comm after the following issues have been addressed: We very much appreciate the reviewer's comments and are addressing the points raised as outlined below.
There are a few trivial typos in the abstract and text that should be fixed. Read carefully!
We apologize for the initial oversight and have carefully read and corrected typos in the abstract and main text.
The authors are not very clear on how their crystal axes are oriented relative to the experimental setup. They discuss the 60 degree rotation, but fail to mention how they initially configured their experiment. In the end this may not be critical, as from figure 3, it looks as if maybe any rotation will achieve their results, but it would helpful to add details in terms of reproducing their results.
We agree with the reviewer that clarifying the absolute orientation of the α-quartz crystal during experimentation will be beneficial to readers. We have replaced the Δφ formulation with the absolute orientation of the crystal, φ, the clockwise rotation of the crystal about its z-axis, measured from its +x-axis (i.e. at 0° the incoming laser beam is aligned with its horizontal projection along the +x-axis of the α-quartz crystal, at 30° the crystal has been rotated 30° clockwise, etc). We have added this information to the main text and changed the figures to include this absolute orientation, as well as added information on determining the absolute orientation of an α-quartz crystal to the SI: Methods Section SIII, Figure S7, and Figure S8. As the reviewer suggests may be the case, we believe that the absolute orientation of the crystal is less important than the periodicity and the fact that constructive and destructive interference is seen at all.
Reference 22, which states that the components of the z cut quartz are always imaginary, seems to be wrong. The paper cited doesn't seem to mention quartz at all.
We agree with the reviewer that this point could use further clarification. The paper in question (Byrnes, S. J.; Geissler, P. L.; Shen, Y. R. Chem. Phys. Lett. 2011, 516 (4-6), 115-124) discusses the theoretical basis of surface and bulk contributions to nonlinear susceptibilites in general. In Eq. 1, describing the interaction between surface and bulk contributions, there is an additional factor of i associated with bulk term. This comes from Maxwell's equations and is also discussed elsewhere, for example (N. Bloembergen, P.S. Pershan, Phys. Rev., 128, 606, 1962; and Kemnitz, K.; Bhattacharyya, K.; Hicks, J. M.; Pinto, G. R.; Eisenthal, B.; Heinz, T. F. Chem. Phys. Lett. 1986, 131 (4-5), 285-290). As the input and output beams are far from resonance with the bulk material in our experimental setup, its bulk signal would be purely real, with this 90° phase shift making it instead, purely imaginary. We have added the Bloembergen reference to the main text as it is the original explicit treatment of the subject. The imaginary component comes from the phase matching factor associated with the depth dependence of the static E-field at the interface; it is nicely derived in the paper mentioned and we have also included a derivation in SI Note 1. We have included a reference to the derivation by Gonella et al. in the main text. Despite the derivation of this phase matching factor, the presence and implications of an imaginary term are not explicitly mentioned by Gonella et al. As this imaginary component from the aqueous interfaces will also interfere with the reference signal produced in heterodyne-detected SFG experiments from buried interfaces, complicating their interpretation, the existence of this term, experimentally measured here for the first time, has broad implications and merits the explicit consideration given in this manuscript.

Reviewer #2 (Remarks to the Author):
Summary: -------The authors investigate experimentally the α-quartz/water interface using second harmonic generation (SHG) spectroscopy. This is an extension of the previous investigation (Achtyl et al. Nature Comm. 2015), where the use of a non-centrosymmetric materials in introduced which enable the control of the phase control of the signal by rotating the crystal. The authors compare the results with those obtained with fused silica, which is used as a reference, as well as vary the ionic strength of the solution. The paper concludes that the observed signal originates from the water/quartz interface, as confirmed by the performed control experiments, and propose the possibility of implementing this method for studying the interface with non-centrosymmetric crystals by using the SHG bulk signal as an internal reference.

General Comments: ----------------
The manuscript is nicely written, concise, well-structured and contains high quality results, which are discussed to the point. The paper discusses the technical advancement of SHG spectroscopy by implementing a non-centrosymmetric α-quartz crystal, which enables to precise control of the phase of the observed signal. This is a major improvement in the field of SHG spectroscopy, which opens up the possibility of studying a large variety of interfaces by using non-centrosymmetric crystals and non-resonant condition. I find that the phase Δφ value discussed between the figure 2 and 3 needs to be clarified in more detail and I encourage the author to reconsider their formulation. Also, it will help validate the experimental results and claims if the authors discussed the polarization and intensity dependence. Therefore, I invite the authors to address these major comments and technical concerns that will strengthen the manuscript before a final decision is reached.
We very much appreciate the reviewer's comments and address the points regarding the Δφ value, the polarization, and intensity dependence in order below. We apologize for any confusion resulting from Figure 3, which shows the angle dependence of the interfacial response. We have followed the reviewer's recommendation and eliminated the Δφ formulation entirely. We have replaced the Δφ formulation with the absolute orientation of the crystal, φ, the clockwise rotation of the crystal about its z-axis, measured from its +x-axis (i.e. at 0° the incoming laser beam is aligned with its horizontal projection along the +x-axis of the α-quartz crystal, at 30° the crystal has been rotated 30° clockwise, etc). We have added this information to the main text and changed the figures to include this absolute orientation, as well as added information on determining the absolute orientation of an α-quartz crystal to the SI: Methods Section SIII, Figure S7, and Figure S8. We thank the reviewer for the suggestion of plotting ΔI as a function of rotational angle, which we have included in the SI ( Figure S3, included below) and helps to demonstrate the flip from constructive to destructive interference that occurs with a 60° rotation for not just one, but three independently obtained samples.

Major Comments
The main text now refers to this plot in the top paragraph of page 5. A B Figure S3. The difference in I SHG at low and high pH conditions, ΔI SHG , as a function of rotational angle of the α-quartz crystal for (A) only the data set included in Figure 3  2. In the setup at figure 1 is shown a λ/2 waveplate and a polarizer along the beam path, which however is not referenced in the text. How does the signal phase depend on the polarization of the incident beam? One can imagine that in the case of quartz/water interface this can potentially be an additional way to control the phase of the observed signal.
The polarization states of the incoming and outgoing beams control which elements of the nonlinear susceptibility contribute to the measured response, and thus control the rotational dependence of the signal intensity from the bulk α-quartz crystal. We have added a figure to the SI ( Figure S7, included below) showing this polarization dependence for the quartz/air interface. The pH jump experiments were performed in the PP, SP, PS, and 45S polarization combinations; the phase was not found to change with different polarizations but the intensity of the jump was the highest in the PP polarization combination ( Figure S1, below).
In addition to this figure, we have added the sentence in the main text: "The PP polarization combination was selected as it demonstrated the highest interfacial sensitivity out of the PP, SP, PS, and 45S polarization combinations (see SI Figure S2)." to the main text. A Figure S1: Polarization combination dependence of the α-quartz I SHG response to pH jump experiments (the first index represents input polarization, the second represents output polarization; 45 represents mixed polarization).
3. An additional way to estimate the degree of mixing between χ2 and χ3 is to measure the signal for different laser intensities (flux dependence). Have the authors attempted such a measurement? In any case, the values that were used in the current realizations (both on the quartz and silica) and the focus size should be reported.
A systematic study of pH jump intensity versus input power has not been performed; however, the dependence of I SHG on input power at constant pH was measured for the α-quartz/water interface to verify quadratic dependence (see below). For all other experiments, the power was set at 0.50 ± 0.01 W and continuously monitored as described in the SI Section SII. The beam waist in the focal region is estimated at 30 µm.We have updated the Methods section in the Supplementary Informtion accordingly. pH 11.5 pH 3 pH 11.5 Figure S5: The power dependence of I SHG for the α-quartz/water interface at pH 3; exponent in power fit = 2.1(1) as expected for a second order process such as SHG.

Minor comments: --------------1. From a technical point of view this is a very important breakthrough. It is also as important
however to discuss what can be concluded about the water/quartz interface. Can one probe differences between the interaction of water with quartz versus that with fused silica? Varying the ionic strength is a good approach, which can potentially provide such an insight.
We appreciate these comments and agree with the reviewer that beyond the implications to SHG spectroscopy, this technique allows important experimental access to the α-quartz/water interface. In particular, it has been theoretically predicted that the repeating crystalline structure of α-quartz could induce a more highly ordered interfacial water layer than that adjacent to an amorphous material such as fused silica ( (24), 244106). We have added this description as a motivation behind studying this system in the main text.
We are thus excited to be able to probe both interfaces directly, and discern differences between them. The initial studies reported here show no difference in behavior between α-quartz and fused silica in terms of finding high SHG signal intensities at high pH and low intensities at low pH (provided the appropriate quartz crystal orientation). A systematic study comparing the behavior of the two substrates across a variety of pH and ionic strength conditions is in progress and will be reported in due course. We have added the specific phrase "In doing so, they open a path for directly comparing the amphoteric properties of amorphous and crystalline materials, such as fused silica and α-quartz." to the future outlooks section.