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Non-resonant second harmonic generation phase and amplitude measurements obtained from the silica:water interface at varying pH and 0.5 M ionic strength point to the existence of a nonlinear susceptibility term, which we call chi(3)X, that is associated with a 90 deg phase shift. Including this contribution in a model for the total effective second-order nonlinear susceptibility produces reasonable point estimates for interfacial potentials and second-order nonlinear susceptibilities when chi(3)Xis about 1.5 times chi(3)water. A model without this term and containing only traditional chi(2) and chi(3) terms cannot recapitulate the experimental data. The new model also provides a demonstrated utility for distinguishing apparent differences in the second-order nonlinear susceptibility when the electrolyte is NaCl vs MgSO4, pointing to the possibility of using HD-SHG to investigate ion-specificity in interfacial processes., Comment: Pre-edited version, 16 Pages main text, 4 Figures, Supporting Information

Waveguides and resonators are core components in the large-scale integration of electronics, photonics, and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e., no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing, and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting, and intense wave-matter interactions, using phonons, photons, or even electrons. The present work further enhances the confidence of using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.

Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order topological crystalline insulator and its topological protection to quantum superposition and entanglement in a two-dimensional lattice. By freely writing the insulator structure with femtosecond laser and directly measuring evolution dynamics with single-photon imaging techniques, we are able to observe the distinct features of the topological corner states in C_4 and C_2 photonic lattice symmetry. Especially, we propose and experimentally identify the topological corner states by exciting the photonic lattice with single-photon superposition state, and we examine the protection impact of topology on quantum entanglement for entangled photon states. The single-photon dynamics and the protected entanglement reveal an intrinsic topological protection mechanism isolating multi-partite quantum states from diffusion-induced decoherence. The higher-order topological crystalline insulator, built-in superposition state generation, heralded single-photon imaging and quantum entanglement demonstrated here link topology, material, and quantum physics, opening the door to wide investigations of higher-order topology and applications of topological enhancement in genuine quantum regime., Comment: 46 pages, 6 figures in main text, 16 figures in Supplementary Materials

Band topology and related spin (or pseudo-spin) physics of photons provide us with a new dimension for manipulating light, which is potentially useful for information communication and data storage. Especially, the quantum spin Hall effect of light, where electromagnetic waves propagate along surfaces of samples with strong spin-momentum locking, paves the way for achieving topologically protected photonic spin transport. Recently, the conventional bulk-edge correspondence of the band topology has been extended to higher-order cases that enables the explorations of topological states with codimensions larger than 1 such as hinge and corner states. Here, for the first time, we demonstrate a higherorder quantum spin Hall effect of light by utilizing an all-dielectric C6v-symmetric photonic crystal. We observe corner states with opposite pseudospin polarizations at different corners owing to nontrivial higher-order topology and finite spin-spin coupling. By applying the spin-polarized excitation sources, we can selectively excite the corner states at different spatial positions through spin-momentum-locked decaying edge states, resembling the quantum spin Hall effect in a higher-order manner. Our work which breaks the barriers between the spin photonics and higher-order topology opens the frontiers for studying lower-dimensional spinful classical surface waves and supports explorations in robust communications., Comment: 24 pages, 4 figures

Bound states in the continuum (BICs) in photonic crystals represent the unique solutions of wave equations possessing an infinite quality-factor. We design a type of bilayer photonic crystal and study the influence of symmetry and coupling between TE and TM polarizations on BICs. The BIC modes possess $C_{3v}$ symmetry in the x-y plane while the mirror-flip symmetry in the z-direction is broken, and they provide selective coupling into different layers by varying frequency. The enhanced TE-TM coupling due to broken mirror-flip symmetry in the z-direction gives rise to high-Q factor BIC states with unique spatial characteristics. We show the emergence of such BIC states even in the presence of coupling between the TE- and TM-like modes, which is different from the existing single polarization BIC models. We propose to study BICs in multilayer systems, and the results may be helpful in designing photonic settings to observe and manipulate BICs with various symmetries and polarizations for practical applications., Comment: 15 pages, 6 figures

Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have been proposed and investigated as novel states of matter. Previous implementations of higher-order topological insulators were based on two-dimensional (2D) systems in which 1D gapped edge states and 0D localized corner states were observed. Here we theoretically design and experimentally realize a 3D higher-order topological insulator in a sonic crystal with a large topological band gap. We observe the coexistence of third-, second- and first-order topological boundary states with codimension three, two and one, respectively, indicating a dimensional hierarchy of higher-order topological phenomena in 3D crystals. Our acoustic metamaterial goes beyond the descriptions of tight-binding model and possesses a band structure which automatically breaks the chiral symmetry, leading to the separation of bulk, surface, hinge and corner states. Our study opens a new route toward higher-order topological phenomena in three-dimensions and paves the way for topological wave trapping and manipulation in a hierarchy of dimensions in a single system., Comment: 29 pages, 4 figures

In a recent letter (PRL,121,246101,2018), Sun et al. reported that combined MD simulation and sum frequency generation vibrational spectroscopy (SFG-VS) measurements led to conclusions of a broad and exponentially decaying orientational distribution, and the presence of the free O-H group pointing down to the bulk at the air/water interface. In this comment, we show that their main conclusions are based on questionable interpretation of the SFG-VS data presented in the letter [1], and are also contrary to the established data analysis and interpretations in the literature [2-5]., Comment: 2 pages, 0 figures

We report ionic strength-dependent phase shifts in second harmonic generation (SHG) signals from charged interfaces that verify a recent model in which dispersion between the fundamental and second harmonic beams modulates observed signal intensities. We show how phase information can be used to unambiguously separate the chi(2) and interfacial potential-dependent chi(3) terms that contribute to the total signal and provide a path to test primitive ion models and mean field theories for the electrical double layer with experiments to which theory must conform. Finally, we demonstrate the new method on supported lipid bilayers and comment on the ability of our new instrument to identify hyper-Rayleigh scattering contributions to common homodyne SHG measurements in reflection geometries., Comment: 21 manuscript pages, four figures, 10 pages supporting information included, pre-edited version

The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been investigated as a novel topological phase of matter beyond the conventional bulk-boundary correspondence. Previous studies of HOTIs have been mainly focused on the topological multipole systems with negative coupling between lattice sites. Here we experimentally demonstrate that second-order topological insulating phases without negative coupling can be realized in two-dimensional dielectric photonic crystals (PCs). We visualize both one-dimensional topological edge states and zero-dimensional topological corner states by using near-field scanning technique. To characterize the topological properties of PCs, we define a novel topological invariant based on the bulk polarizations. Our findings open new research frontiers for searching HOTIs in dielectric PCs and provide a new mechanism for light-manipulating in a hierarchical way., Comment: 23 pages, 4 figures

Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not been found in photonic systems yet. In this article, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically non-trivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily-fabricated structure of the photonic crystals, we can realize different topological phases with unique topological boundary states straightforwardly. Our result can be generalized to higher dimensions and provides unprecedented venues for higher-order photonic topological insulators and semimetals., Comment: 6 pages, 6 figures, Phys. Rev. B 2018

We explore by means of modeling how absorptive-dispersive mixing between the second- and third-order terms modify the imaginary chi(2)total responses from air/water interfaces under conditions of varying charge densities and ionic strength. To do so, we use published Im(chi(2)) and chi(3) spectra of the neat air/water interface that were obtained either from computations or experiments. We find that the chi(2)total spectral lineshapes corresponding to experimentally measured spectra contain significant contributions from both interfacial chi(2) and bulk chi(3) terms at interfacial charge densities equivalent to less than 0.005% of a monolayer of water molecules, especially in the 3100 wavenumber to 3300 wavenumber frequency region. Additionally, the role of short-range static dipole potentials is examined under conditions mimicking brine. Our results indicate that surface potentials, if indeed present at the air/water interface, manifest themselves spectroscopically in the tightly bonded H-bond network observable in the 3200 wavenumber frequency range., Comment: Pre-edited version, 21 pages, 3 figures, supporting information available upon request

Second-order nonlinear spectroscopy has proven to be a powerful tool in elucidating key chemical and structural characteristics at a variety of interfaces. However, the presence of interfacial potentials may lead to complications regarding the interpretation of second harmonic and vibrational sum frequency generation responses from charged interfaces due to mixing of absorptive and dispersive contributions. Here, we examine by means of mathematical modeling how this interaction influences second-order spectral lineshapes. We discuss our findings in the context of reported nonlinear optical spectra obtained from charged water/air and solid/liquid interfaces and demonstrate the importance of accounting for the interfacial potential-dependent \c{hi}(3) term in interpreting lineshapes when seeking molecular information from charged interfaces using second-order spectroscopy., Comment: Pre-edited final accepted version, 24 Pages, 6 Figures, Supplementary Data 1-7 available upon request to geigerf@chem.northwestern.edu

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 {\alpha}-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, \c{hi}(3). {\Phi}(0), is given by ( \c{hi}(3)-i\c{hi}(3)). {\Phi}(0), and that the interference between this product and the second-order susceptibility of bulk quartz depends on the rotation angle of {\alpha}-quartz around the z-axis. Our experiments show that this newly identified term, i\c{hi}(3). {\Phi}(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 {\alpha}-quartz is discussed along with the implications for conditions of resonance enhancement., Comment: Pre-edited, final accepted and updated version, 19 pages, 4 figures, 11 pages supporting information with 8 Supplementary Figures, one Supplementary Table, and one Supplementary Note

Sum frequency generation vibrational spectra of the water molecules at the NaF and KF aqueous solution surfaces showed significantly different spectral features and different concentration dependence. This result is the first direct observation of the cation effects of the simple alkali cations, which have been believed to be depleted from the aqueous surface, on the hydrogen bonding structure of the water molecules at the electrolyte solution surfaces. These observations may provide important clue to understand the fundamental phenomenon of ions at the air/water interface., Comment: 15 pages, 2 figures

Here we report the polarization dependent non-resonant second harmonic generation (SHG) measurement of the interfacial water molecules at the aqueous solution of the following salts: NaF, NaCl, NaBr, KF, KCl, and KBr. Through quantitative polarization analysis of the SHG data,the orientational parameter D value and the relative surface density of the interfacial water molecules at these aqueous solution surfaces were determined. From these results we found that addition of each of the six salts caused increase of the thickness of the interfacial water layer at the surfaces to a certain extent. Noticeably, both the cations and the anions contributed to the changes, and the abilities to increase the thickness of the interfacial water layer were in the following order: KBr > NaBr > KCl > NaCl ~ NaF > KF. Since these changes can not be factorized into individual anion and cation contributions, there are possible ion pairing or association effects, especially for the NaF case. We also found that the orientational parameter D values of the interfacial water molecules changed to opposite directions for the aqueous solutions of the three sodium salts versus the aqueous solutions of the three potassium salts. These findings clearly indicated unexpected specific Na+ and K+ cation effects at the aqueous solution surface. These effects were not anticipated from the recent molecular dynamics (MD) simulation results, which concluded that the Na+ and K+ cations can be treated as small non-polarizable hard ions and they are repelled from the aqueous interfaces. These results suggest that the electrolyte aqueous solution surfaces are more complex than the currently prevalent theoretical and experimental understandings., Comment: 33 pages, 5 figures

In the currently accepted models of the nonlinear optics, the nonlinear radiation was treated as the result of an infinitesimally thin polarization sheet layer, and a three layer model was generally employed. The direct consequence of this approach is that an apriori dielectric constant, which still does not have a clear definition, has to be assigned to this polarization layer. Because the Second Harmonic Generation (SHG) and the Sum-Frequency Generation vibrational Spectroscopy (SFG-VS) have been proven as the sensitive probes for interfaces with the submonolayer coverage, the treatment based on the more realistic discrete induced dipole model needs to be developed. Here we show that following the molecular optics theory approach the SHG, as well as the SFG-VS, radiation from the monolayer or submonolayer at an interface can be rigorously treated as the radiation from an induced dipole lattice at the interface. In this approach, the introduction of the polarization sheet is no longer necessary. Therefore, the ambiguity of the unaccounted dielectric constant of the polarization layer is no longer an issue. Moreover, the anisotropic two dimensional microscopic local field factors can be explicitly expressed with the linear polarizability tensors of the interfacial molecules. Based on the planewise dipole sum rule in the molecular monolayer, crucial experimental tests of this microscopic treatment with SHG and SFG-VS are discussed. Many puzzles in the literature of surface SHG and SFG spectroscopy studies can also be understood or resolved in this framework. This new treatment may provide a solid basis for the quantitative analysis in the surface SHG and SFG studies., Comment: 23 pages, 3 figures

Unexpected spectral features are observed in the two photon spectrum of the pure water in the forward direction when an 80 femtosecond laser pulse is focused at 10^10Wcm-2 or less. Such intensity is much lower than the breakdown or stimulated threshold of the liquid water. The two broad features are about 2700cm-1 and 5000cm-1 red shifted from the hyper-Rayleigh wavelength, respectively, and they are quadratic with the laser intensity. They do not match the known Raman or hyper-Raman frequencies of water, and they are both centered at a narrow angle in the forward direction. Several other liquids also exhibited similar but molecular specific spectral features., Comment: 4 pages, 4 figures

A complete empirical approach from known Raman and IR spectra is used to make corrections to the bond additivity model for quantitative interpretation of Sum Frequency generation Vibrational Spectra (SFG-VS) from molecular interfaces. This empirical correction successfully addresses the failures of the simple bond additivity model. This empirical approach not only provides new understandings of the effectiveness and limitations of the bond additivity model, but also provides a practical roadmap for its application in SFG-VS studies of molecular interfaces.

Here we report a detailed study on spectroscopy, structure and dynamics of water molecules at air/water interface, investigated with Sum Frequency Generation Vibrational Spectroscopy (SFG-VS). Quantitative polarization and experimental configuration analysis of the SFG data in different polarizations with four sets of experimental configurations can shed new lights on our present understanding of the air/water interface. Firstly, we concluded that the motion of the interfacial water molecules can only be in a limited angular range, instead rapidly varying over a broad angular range in the vibrational relaxation time suggested previously. Secondly, because different vibrational modes of different molecular species at the interface has different symmetry properties, polarization and symmetry analysis of the SFG-VS spectral features can help assignment of the SFG-VS spectra peaks to different interfacial species. These analysis concluded that the narrow 3693cm-1 and broad 3550cm-1 peaks belong to C_ v symmetry, while the broad 3250cm-1 and 3450cm-1 peaks belong to the symmetric stretching modes with C_2v symmetry. Thus, the 3693cm-1 peak is assigned to the free OH, the 3550cm-1 peak is assigned to the single hydrogen bonded OH stretching mode, and the 3250cm-1 and 3450cm-1 peaks are assigned to interfacial water molecules as two hydrogen donors for hydrogen bonding (with C_2v symmetry), respectively. Thirdly, analysis of the SFG-VS spectra concluded that the singly hydrogen bonded water molecules at the air/water interface have their dipole vector direct almost parallel to the interface, and is with a very narrow orientational distribution. The doubly hydrogen bond donor water molecules have their dipole vector point away from the liquid phase.

It has been generally accepted that there are significant quadrupolar and bulk contributions to the second harmonic generation (SHG) reflected from the neat air/water interface, as well as common liquid interfaces. Because there has been no general methodology to determine the quadrupolar and bulk contributions to the SHG signal from a liquid interface, this conclusion was reached based on the following two experimental phenomena. Namely, the broken of the macroscopic Kleinman symmetry, and the significant temperature dependence of the SHG signal from the neat air/water interface. However, because sum frequency generation vibrational spectroscopy (SFG-VS) measurement of the neat air/water interface observed no apparent temperature dependence, the temperature dependence in the SHG measurement has been reexamined and proven to be an experimental artifact. Here we present a complete microscopic analysis of the susceptibility tensors of the air/water interface, and show that dipolar contribution alone can be used to address the issue of broken of the macroscopic Kleinman symmetry at the neat air/water interface. Using this analysis, the orientation of the water molecules at the interface can be obtained, and it is consistent with the measurement from SFG-VS. Therefore, the key rationales to conclude significantly quadrupolar and bulk contributions to the SHG signal of the neat air/water interface can no longer be considered as valid as before. This new understanding of the air/water interface can shed light on our understanding of the nonlinear optical responses from other molecular interfaces as well.

Analysis of SFG vibrational spectra of OH stretching bands in four experimental configurations shows that orientational motion of water molecule at air/water interface is libratory within a limited angular range. This picture is significantly different from the previous conclusion that the interfacial water molecule orientation varies over a broad range within the vibrational relaxation time, the only direct experimental evidence for ultrafast and broad orientational motion of a liquid interface by Wei et al. [Phys. Rev. Lett. 86, 4799, (2001)] using single SFG experimental configuration.