The advent of resonant dielectric nanomaterials has provided a new path for concentrating and manipulating light on the nanoscale. Such high-refractive-index materials support a diverse set of low-loss optical resonances, including Mie resonances, anapole states, and bound states in the continuum. Through these resonances, high-refractive-index materials can be used to engineer the optical near field, both inside and outside the nanostructures, which opens up new opportunities for Raman spectroscopy. In this review, we discuss the impact of high-refractive-index nano-optics on Raman spectroscopy. In particular, we consider the intrinsic Raman enhancement produced by different dielectric resonances and their theoretical description. Using the optical reciprocity theorem, we derive an expression which links the Raman enhancement to the enhancement of the stored electric energy. We also address recent results on surface-enhanced Raman spectroscopy based on high-refractive-index dielectric materials along with applications in stimulated Raman scattering and nanothermometry. Finally, we discuss the potential of Raman spectroscopy as a tool for detecting the optical near-fields produced by dielectric resonances, complementing reflection and transmission measurements.
Optical nanomaterials with a high refractive index are receiving high and increasing attention due to their ability to support low-loss optical resonances , , . The most prominent of which are Mie-type resonances, which arise when materials with high refractive index n are structured on a scale comparable to the wavelength of light inside the material λ/n, where λ is the wavelength of light in free space. Examples of such materials include silicon, gallium arsenide, gallium phosphide, titanium dioxide, and transition metal dichalcogenides . Mie resonances can be both electric or magnetic in nature  and enable control over different properties of light, such as polarization, amplitude and phase. In addition to Mie resonances, high-refractive-index nanostructures also host other intriguing effects, such as the anapole state , bound states in the continuum , and supercavity modes . These desirable optical properties have turned high-refractive-index nanostructures into key ingredients in the design of novel nanophotonic devices, such as metasurface-based control of light , metalenses , structural color , Huygens’ surfaces , lasing , directional control of emitters , [ 15], biosensing , [ 17], amplification of nonlinear response , and active control of light , [ 20].
The common denominator for resonant high-refractive-index nanostructures is that they provide strong light confinement with an accompanying enhancement of the electromagnetic near-fields. This opens up new possibilities for controlling and enhancing Raman scattering, since the Raman intensity scales dramatically with the electric near-field intensity. Raman spectroscopy measures the inelastic scattering of photons due to vibrations in molecules or phonon modes in crystalline materials. Here, we focus primarily on the latter since crystalline dielectric nanostructures show prominent phonon response, which is detectable in Raman spectroscopy. The typically weak Raman signal from phonon modes can be enhanced by engineering the dielectric nanostructure to support optical resonances, which has applications in nanoscale Raman lasers and nanothermometry. Conversely, the optical resonances may be designed to enhance the near-field outside the nanostructure for molecular Raman sensing, such as in surface-enhanced Raman spectroscopy. These applications highlight the importance of Raman spectroscopy as well as optimizing high-refractive-index nanostructures for maximal Raman enhancement.
The aim of this review is to provide an overview of Raman scattering in optical nanomaterials with a high refractive index (n > 2) and discuss future directions. In Section 2, we review the state-of-the-art of intrinsic Raman enhancement due to resonant dielectric nanostructures. We find that a range of different silicon nanostructures, including nanowires, nanoparticles, and nanodisks, demonstrate resonantly enhanced Raman signal of the silicon optical phonon mode. Section 3 is devoted to the theoretical description of spontaneous Raman scattering due to phonon modes in such structures. Here, we derive an expression for the Raman intensity in the backscattering configuration using the optical reciprocity theorem and find that the Raman enhancement is linked to the enhancement of the stored electric energy. Section 4 focuses on emerging applications of Raman spectroscopy using high-refractive-index nanostructures, including surface-enhanced Raman spectroscopy, stimulated Raman scattering, nanothermometry, and near-field detection. Finally, Section 5 concludes the review.
2 Raman enhancement in high-index nanostructures
The ability of high-refractive-index nanostructures to resonantly confine light can lead to a dramatic enhancement in intrinsic Raman scattering. One of the first works to experimentally demonstrate this effect was performed by Murphy et al. , where they observed a Raman enhancement of the optical phonon mode in different silicon nanostructures. Inspired by earlier theoretical work , Murphy et al. showed that in particular silicon nanoparticles with diameters of approximately 100 nm produced a 100-fold enhancement in the Raman signal, when excited at 488 nm wavelength. They attributed the Raman enhancement to the excitation of the magnetic dipole resonance, which occurs at a wavelength of λMD ≈ nD, where n and D denote the refractive index and diameter of the nanoparticle, respectively. While these initial results were exciting, the importance of Raman enhancement due to Mie resonances was not appreciated until the pioneering work by Hayashi et al.  Here, the authors systematically studied the Raman enhancement due to resonant gallium phosphide (GaP) nanoparticles in a broad size range. They demonstrated that Raman scattering from both the phonon modes in GaP as well as Raman signal from nearby molecules could be resonantly enhanced, opening up the possibility of performing surface-enhanced Raman spectroscopy without metals.
The results were later extended to nanowire geometries, which support polarization-dependent Mie resonances. In particular, Cao et al.  demonstrated a strong Raman enhancement in micrometer-long nanowires and nanocones made of silicon (Figure 1a). By measuring from the base to the tip of the nanocone, the authors tracked the Raman enhancement as a function of the local diameter of the nanocone. Here, a continuous increase in the Raman enhancement of the optical phonon line is observed as the diameter of nanowires decreases. The measurements were performed with several different excitation wavelengths as well as different polarization states of the incident light. The authors interpreted their results using Mie theory for infinite cylinders, which agreed with the continuous increase in Raman enhancement, but also showed Mie-enhanced peaks at specific diameters. However, such diameter-specific enhancements were not clearly observed in the experiments, presumably due to the finite size of the laser spot, which averages the Raman signal across a large range of local diameters. Shortly after these results, Raman scattering measurements on GaP nanowires of varying diameters were reported by Chen et al. . Raman enhancement of the longitudinal optic and transverse optic phonon modes in GaP were observed at specific diameters, where the nanowires supported Mie resonances. In addition, the authors also observed Raman enhancements due to standing waves along the length of the GaP nanowires due to their few-micrometer length. Another study by Lopez et al.  on tapered silicon nanowires confirmed the diameter-dependent Raman enhancement due to cylindrical Mie resonances.
In recent years, there has been a shift in focus from nanowires to nanoparticles, which offer subwavelength confinement in three dimensions. Such high-refractive-index nanoparticles of different shapes, such as spherical and disks, host of variety of Mie resonances with intriguing properties. A particular enlightening geometry is that of a spherical nanostructure as it lends itself to an exact description based on analytical Mie theory. Dmitriev et al.  systematically studied the diameter-dependent Raman intensity of the optical phonon mode in crystalline silicon nanoparticles of spherical shape (Figure 1b). The authors experimentally observed a 140-fold enhancement of the Raman intensity due to the magnetic dipole resonance, which confines light strongly inside the silicon nanoparticle. In contrast, the electric dipole resonance confines most of the light outside the nanoparticle, leading to a modest Raman enhancement. These results were subsequently extended to polycrystalline silicon nanodisks by Matthiae et al. , who experimentally demonstrated a 100-fold enhancement of the Raman intensity due to the magnetic dipole resonance (Figure 1d). For thin nanodisks with large diameter-to-height aspect ratio, other optical effects occur beyond the fundamental Mie resonances. In such systems, the toroidal and electric dipole moments can interfere destructively in the far-field, leading to the optically dark feature known as the anapole state , . Interestingly, the reduced far-field scattering of the anapole state is accompanied by a strong near-field enhancement. This intriguing interference effect was exploited by Baranov et al.  to demonstrate an 80-fold enhancement in the Raman intensity from polycrystalline silicon nanodisks (Figure 1c). In contrast to the Raman enhancement based on radiative Mie resonances (e.g., the magnetic dipole), the maximal anapole-enhanced Raman intensity coincides with a minimum in the far-field extinction. Consequentially, Raman scattering offers a route to reveal not only radiative resonances but also nonradiative states in high-refractive-index nanostructures. This insight was harnessed by Baryshnikova et al.  to reveal low-radiative magnetic quadrupole modes in silicon nanoparticles on glass and gold substrates. Raman enhancements have also been reported from silicon nanostructures of octahedral shape ,  as well as irregular nanostructured silicon surfaces , , , .
These recent advancements provide insight into the intrinsic Raman scattering from resonant dielectric nanostructures, which may be exploited in different applications such as those discussed in Section 4. However, several venues still remain unexplored. In particular, there have been no studies on the angular distribution of the Raman scattering from high-refractive-index nanostructures, and whether or not the Raman scattering may be directed in a controllable fashion, akin to the Kerker condition seen for elastic light scattering , ,  and dipole emission , . Such directional Raman scattering ,  may boost the detected Raman signal and act in concerto with the Raman enhancement due to near-field enhancements. In addition, there have been limited studies on nanostructures without in-plane symmetry, where the polarization of the incident and Raman scattered light is expected to play a role in the Raman signal. Indeed, as we show in the next section, polarized Raman spectroscopy of dielectric nanostructures provides information on the stored electric energy, which is strongly related to linear and nonlinear light–matter interactions.
3 Theory of Raman enhancement
Raman scattering describes the inelastic scattering of photons due to vibrational states in molecules or phonon modes in a crystalline material. The theoretical description of Raman scattering in the picture of classical electromagnetism is similar for both types of system. However, in this section, we only outline the theoretical description of inelastic scattering from phonon modes, as we are primarily interested in the intrinsic Raman signal from subwavelength-scale nanostructures. The Raman signal stems from a two-step process. The first involves the excitation of the phonon due to an incident electromagnetic field E0 at the frequency ωex. The excitation frequency and the spatial profile of the exciting field depend on the laser source and the optical system used to focus the illumination. This is often suitably approximated with a monochromomatic plane wave. The second step is the emission of light due to the excited phonon modes occurring at the Stokes-shifted frequency ωem = ωex − Ω, where Ω is the phonon frequency. As the polarization induced by the phonon modes extends only few interatomic distances, the phonon emission is approximated by that of a point electric dipole. This theoretical model for Raman scattering was first described in a seminal paper by Chew et al. . The authors used Mie theory to analytically calculate the Raman scattering from molecules embedded in spherical particles. Notably, their results show that both the excitation and emission processes depend on the electromagnetic modes of the spherical particle (at the excitation and emission frequencies, respectively), implying that a significant enhancement of the Raman signal can occur under resonant conditions.
Having outlined the general physical process, we now take a closer look at the mathematical description of the Raman enhancement. We consider an arbitrarily shaped dielectric nanostructure with relative permittivity ε, which is illuminated by a monochromatic plane wave with amplitude E0 and frequency ωex (Figure 2a). The nanostructure may be placed in an inhomogeneous environment, such as on a substrate. The incident field induces a Raman polarization in the nanostructure, which in the point-dipole approximation can be written as
Here, is the Raman polarizability tensor for a particular phonon mode, and denotes the local electric field at the dipole position r set up by the incident field. It is of value to note that the local electric field can be significantly enhanced compared to the incident field under resonant conditions. The total Raman intensity emanating from the dipole can be calculated by integrating the Poynting vector over a spherical surface which encompasses the nanostructure. Dmitriev et al.  developed a Green’s function approach for calculating the Raman intensity from a spherical high-index nanoparticle, which was subsequently generalized by Frizyuk et al.  to particles of arbitrary shape. In the latter, the authors show that the Raman intensity from a single phonon mode can be written in an enlightening way
where c is the speed of light in vacuum, FP is the Purcell factor, and the integration is performed over the volume V of the nanostructure. From Eq. (2), we see that the Raman intensity depends on both the excitation and emission processes. The former may be enhanced through a large local electric field, as seen from Eq. (1), while the latter is enhanced due to the Purcell effect, namely an increase in the optical density of states. In addition, the integral in Eq. (2) highlights the spontaneous nature of Raman emission, since each excited dipole contributes incoherently to the Raman intensity emanating from the nanostructure.
The derivation of Eq. (2) assumes that the Raman photons emitted in all directions are collected by the detector (i.e., a solid angle of 4π steradians). However, such Raman measurements are rare, and the most common Raman setups collect Raman photons in the backscattering (BS) configuration. In this configuration, the objective lens, which focuses the incident light, is also used to collect the Raman signal, akin to reflection measurements. For comparison between BS measurements and theory, we now derive an expression for the Raman intensity in the BS configuration. We neglect the effect of the numerical aperture of the objective lens, and assume that the excitation light impinges at normal incidence along the z-axis. Likewise, the Raman signal is collected along the direction of the z-axis. The intensity of light emitted in a given direction from a Raman dipole is given by radial component of the Poynting vector, which in the BS configuration simplifies to . The objective lens, which collects the emitted signal, is typically placed many wavelengths away from the nanostructure. This allows us to consider the Poynting vector in the far-field Sff, where the electric field is transverse and has only x and y components. With these considerations in mind, we may write the Raman intensity in the BS configuration from a single Raman dipole Idp as
Consequently, the Raman intensity from a single Raman dipole is now reduced to determining the electric far-field components, and . These can be expressed in terms of the electric field at the position of the dipole r by using the optical reciprocity theorem . The reciprocity theorem states that the electric far-field emitted by the Raman dipole at position r is related to the electric field at position r produced by a dipole located in the far-field. In other words, the position of the emitter and detector can be interchanged. The radiation created by a dipole in the far-field at the position of the nanostructure reduces to that of a plane wave polarized along the dipole axis, and we may write 
Here, EX (EY) denotes the local electric field at the Raman dipole position r set up by an incident plane wave polarized along the x-axis (y-axis). From Eqs. (4) and (5), we notice that the problem of calculating the electric far-field from the Raman dipole reduces to calculating the local electric field produced by a plane wave source at the emission frequency. For an isotropic Raman tensor, , the intensity from a single Raman dipole becomes
where we have introduced the enhancement factor
Since each Raman dipole contributes incoherently to the Raman intensity, the total Raman signal emanating from a single phonon mode in the dielectric nanostructure becomes
Eq. (8) is our main result and provides an approach for calculating the intrinsic Raman signal from dielectric nanostructures in the BS configuration. Although the enhancement factor M requires two independent plane-wave calculations with different polarizations (along x and y), such calculations are typically computationally inexpensive compared to those involving a dipole emitter.
An interesting special case of Eq. (8) is that of polarized detection parallel to the excitation polarization. Here, the enhancement factor simplifies to a single plane-wave calculation at two different frequencies
For polarized measurements, the Raman intensity is closely related to the enhancement of the stored electric energy density, , where uE and u0 denote the electric energy density in the nanostructure and free space, respectively. Dielectric nanostructures for Raman applications are therefore more suitably optimized with respect to the stored electric energy rather than far-field quantities, such as the scattering cross section.
Figure 2b–d shows simulation results of the Raman enhancement in individual silicon nanostructures of different shapes, when tuning the excitation wavelength. The simulations are performed in COMSOL Multiphysics (ver. 5.5), which numerically solves Maxwell’s equations using the finite-element method. We obtain the Raman enhancement by numerically evaluating Eqs. (8) and (9) and normalizing it to the BS Raman intensity from the same volume of bulk silicon, given by . With this normalization procedure, the Raman enhancement RE becomes
For the spherical and nanodisk particles (Figure 2b,c), we find that the magnetic dipole and quadrupole resonances provide the most prominent Raman enhancements. Indeed, the magnetic-type resonances provide stronger light localization inside the dielectric material than electric-type resonances. Interestingly, the magnetic quadrupole produces two peaks in the Raman spectrum due to the high quality factor of the mode, as also seen in the study by Frizyuk et al. . The short-wavelength peak occurs when the emission wavelength matches the magnetic quadrupole resonance wavelength, while the long-wavelength peak is due to the enhancement of the excitation process. The low quality factor of the magnetic dipole mode masks this effect, leading to a single peak in the Raman enhancement. As for the thin nanodisk in Figure 2d, the Raman enhancement occurs due to the formation of an anapole state. As discussed in relation to Figure 1d, the anapole is a specific state occurring due to far-field destructive interference of the incident and scattered fields. Consequentially, it depends on the incident field and is therefore not an eigenmode of the system . Nonetheless, the anapole state enhances the stored electric energy in the nanodisk and thereby also the Raman signal.
As an additional demonstration of the usefulness of Eqs. (8) and (9), we simulate the Raman enhancement of a silicon nanosphere of varying diameter D at a fixed excitation wavelength of 633 nm (Figure 2e). We purposely choose to represent the Raman enhancement in terms of a dimensionless diameter D/λSi for direct comparison with the experimental measurements in Figure 1b. Here, λSi denotes the wavelength of light in silicon. We find excellent agreement between our theoretical model and the experimental results, despite not including the substrate in the simulations. The maximum value of the Raman enhancement differs, which is due to a difference in the normalization procedure. We also calculate the enhancement of the stored electric energy, which shows a similar profile to the Raman enhancement. The stored electric energy peaks at a different particle diameter, since it is only evaluated at the excitation wavelength, while the Raman enhancement has both the excitation and emission wavelengths as inputs. Nonetheless, the enhancement of the stored electric energy provides an excellent figure-of-merit for predicting the Raman enhancement of different optical resonances.
These results highlight that high-refractive-index nanostructures display a variety of different optical resonances, which are attractive for enhancing Raman scattering. In addition to the aforementioned Mie resonances, properly designed dielectric nanostructures can support Fano resonances , bound states in the continuum , as well as supercavity modes , which may offer unprecedented Raman enhancements due to their high quality factors. In addition, new nanoscale design tools for tailoring the near-field have recently emerged , , which enable a more deterministic approach to dielectric Raman enhancements. Eq. (8) provides a straight-forward tool to evaluate the potential of these novel optical resonances. Our theoretical description of Raman scattering can be extended to include anisotropic Raman tensors as well as including the finite size of the numerical aperture of the objective lens . The former can be achieved by defining a Raman tensor according to a suitable coordinate system, which ultimately leads to a modified expression for the enhancement factor in Eqs (6) and (8). These additional considerations may be important for accurate representation of certain experimental setups and anisotropic crystalline high-refractive-index materials, such as MoS2  Nevertheless, based on our theoretical analysis, we expect the enhancement of the stored electric energy to provide an easy-to-use measure for designing Raman-enhancing dielectric nanostructures.
Controlling Raman scattering with high-refractive-index nanostructures has a number of attractive applications. In this section, we review recent advances in four different areas: surface-enhanced Raman spectroscopy (SERS), stimulated Raman scattering, nanothermometry, and the potential of detecting near-field enhancements using Raman scattering. We highlight the state-of-the-art in these areas of application and discuss possible future directions.
4.1 Surface-enhanced Raman spectroscopy
SERS is a vibrant and burgeoning field, which exploits enhanced Raman scattering from nanostructured surfaces for ultrasensitive sensing and related analytical techniques , , . The unique Raman spectra of individual molecules provide a fingerprint-like identification method for their presence. However, Raman scattering from molecules is a weak process, and has therefore lead to the development of predominantly nanostructured metal surfaces, which provide dramatic enhancements of the local electric field due to plasmonic light confinement. For a comprehensive overview of the field, we refer the reader to the recent reviews by Alessandri and Lombardi and Langer et al. , . Here, we highlight selected results using Mie resonances and related optical phenomena in high-refractive-index dielectric and semiconductor nanostructures.
The first observation of Mie-enhanced SERS can be traced to the work of Hayashi et al., where the authors demonstrated a 700-fold enhancement of the Raman scattering from molecules due to resonant GaP nanoparticles , see Figure 3a. The authors compared their experimental results with the near-field enhancement efficiency QNF derived by Messinger et al. . The near-field efficiency is strictly applicable only to spherical nanostructures and is obtained by integrating the scattered field at the sphere surface. Although the GaP nanoparticles tended to be more ellipsoidal in shape, the authors found qualitative agreement between theory and experiments, highlighting the electromagnetic contribution to the Raman enhancement.
In more recent years, an increasing number of different semiconductor materials have shown potential as SERS substrates due to a synergy of contributions to the Raman enhancements , . As in metal-based SERS substrates, the electromagnetic enhancement plays a key role in enhancing the Raman signal from nearby molecules, which can be described within the theoretical framework developed in Section 3. In particular, Eqs. (6) and (7) describe the intensity from a single Raman dipole, which, in the context of SERS, is due to vibrational states of the molecule. The electromagnetic Raman enhancement now stems from the enhanced fields outside the high-refractive-index nanostructure, which spatially overlap with the nearby molecules. Besides the electromagnetic part, contributions from the valence-band plasmon resonances, exciton resonances, and charge-transfer resonances between the molecule and the semiconductor turn out to play prominent roles in the Raman enhancement . Combined with the high chemical stability and tunable photoelectrical properties, semiconductor materials are becoming attractive for use in SERS. Tailoring the electromagnetic contribution using high-refractive-index optical phenomena may lead to unforeseen Raman enhancements comparable to plasmonic-based SERS.
Alessandri  demonstrated the potential of high-refractive-index materials by using titanium dioxide (TiO2) core–shell resonators, which support whispering-gallery-mode resonances , even in nanometer-thin shells. The author exploited the electromagnetically enhanced Raman signal to detect and monitor the photodegradation of low concentrations of methylene blue molecular aggregates. In another study, Rodriguez et al.  used Mie resonances in individual silicon nanoparticles to enhance the Raman signal from nearby molecules and found, quite surprisingly, that silicon nanoparticles may outperform gold nanoparticles in Raman enhancement. Caldarola et al.  capitalized on the large field enhancement occurring in the gap of a silicon nanodisk dimer ,  to demonstrate a 103 enhancement in the Raman signal from an encapsulating polymer film. The authors also demonstrated a similar enhancement in the fluorescence signal from an assembly of emitters in the gap, which was later extended to the single-molecule limit by Regmi et al. . Another promising approach to realizing large near-field enhancements is by placing high-refractive-index nanoparticles on a metal substrate . Tseng et al.  exploited this architecture to amplify the Raman signal from graphene, which was placed in between silicon nanoparticles and a copper substrate (Figure 3b). The authors convincingly demonstrate that silicon nanoparticles on a copper substrate outperform other common architectures for surface-enhanced Raman spectroscopy. Related studies on similar hybrid dielectric-plasmon surfaces also demonstrated large enhancements of the Raman signal , .
An alternative class of optical resonances, which are promising for SERS, are the so-called bound states in the continuum (BICs). Originally an old idea from quantum mechanics , BICs have in recent years been revealed in nanophotonics . BICs are an unusual type of wave resonance, which due to their radiationless nature can trap light for a long time—in principle, forever. This unique property of BIC modes leads to strong light–matter interaction and has been realized in different architectures, such as dielectric photonic crystal membranes , ,  and dielectric metasurfaces , . Romano et al.  applied BICs to SERS detection of crystal violet probe molecules (Figure 3c). The BIC mode is realized using a silicon nitride photonic crystal membrane. The authors find that the BIC-enhanced amplification of the Raman signal leads to a clear spectral signature of the probe molecules, which is absent when the Raman signal is collected outside the structure. The Raman enhancement factor exceeds 103 and demonstrates that BICs can be used to strongly amplify the Raman signal in purely dielectric nanostructures.
The rich diversity of optical resonances supported by dielectric nanostructures, such as the discussed Mie resonances and BICs, provide new opportunities to design all-dielectric SERS substrates. Judiciously designed dielectric and semiconductor substrates enable large electromagnetic enhancements along with the aforementioned desirable chemical properties. High-refractive-index nanostructures may therefore usher a new era of SERS substrates, which can be independent on plasmonic hot-spots generated by noble metal nanostructures.
4.2 Stimulated Raman scattering
Stimulated Raman scattering (SRS) is essentially a light amplification process similar to stimulated emission, and consequently the precursor to achieving Raman laser emission , . In SRS, two optical fields are present in the Raman scattering material, one at the excitation frequency and the second at the Stokes-shifted emission frequency. This can be achieved by illuminating the material with two different lasers with suitable frequencies, or by using a single excitation laser and generating the Stokes-shifted light through spontaneous Raman scattering. In the latter situation, the Raman-shifted light can be trapped in a resonant cavity and thereby stimulate the generation of Raman photons. This process leads to the formation of a coherent beam at the Stokes-shifted frequency. The net result is that the energy of the excitation laser is transferred to the weaker Stokes beam, which experiences a dramatic amplification. SRS therefore leads to orders of magnitude larger intensities than spontaneous Raman scattering.
The SRS amplification is a third-order nonlinear process, which is characterized by the Raman gain coefficient of the material. Silicon has a relatively large bulk Raman gain , which has been exploited to realize Raman lasers, first on the centimeter-scale , ,  and later shrunken to the micrometer-scale using a photonic crystal design . Raman lasers have important applications in realizing compact light sources, especially for silicon photonics, where the indirect band gap of silicon hampers the development of lasers based on conventional stimulated emission. Shrinking the footprint of Raman lasers to the nanoscale is therefore desirable for dense integration into photonic circuits and for reducing the Raman lasing threshold power. This miniaturization can be achieved by manipulating the electromagnetic landscape through nanostructuring, which effectively tailors the quality factor and mode volume of the optical cavity. Wu et al.  exploited the Mie resonances in short GaP nanowires to demonstrate SRS with two orders of magnitude smaller threshold power than that reported using silicon photonic crystals. This was extended to silicon nanowires by Agarwal et al. , who demonstrated Mie-enhanced SRS with a 106 increase in the net effective Raman gain compared to bulk silicon. Recently, Zograf et al.  observed SRS from subwavelength silicon nanodisks supporting higher-order Mie resonances (Figure 4a). The onset of SRS is marked by a deviation from the expected linear trend of spontaneous Raman scattering with increasing pump intensity. The authors optimized the SRS conditions by designing the nanodisk to support Mie resonances at both the excitation and emission wavelengths. In addition, they used a sapphire substrate as a thermal sink to mitigate the optically induced heating of the nanoparticle, which would otherwise have been detrimental for SRS.
These initial reports are promising demonstrations of nanoscale SRS empowered by optical resonances in high-refractive-index nanostructures. However, Raman laser emission in these systems has yet to be reported. This may be in part due to optically induced heating of the nanostructures, which shifts the phonon energy (details in Section 4.3), as well as the need for optical resonances with larger quality factors. The former was effectively mitigated by Zograf et al.  using a sapphire substrate, while the latter may be addressed using supercavity modes . Supercavity modes are based on the physics of BICs and offer high quality factors with small mode volumes. Conventional lasing using BICs has been demonstrated , , which underpins the promising potential of these modes for SRS and Raman lasing.
The phonon modes in a variety of crystalline materials are sensitive to temperature due to anharmonic effects in the vibrational potential energy . In particular, the optical phonon mode of crystalline silicon shows high thermal sensitivity . Such temperature dependence is marked by a shift and linewidth broadening of the optical phonon mode, which is detectable in the Raman spectrum. Zograf et al.  demonstrated that optically induced heating of crystalline silicon nanoparticles can be tracked using Raman spectroscopy (Figure 4b). By comparison with theory, the thermal-induced shift of the optical phonon peak can be converted to an absolute temperature, enabling nanoscale thermometry (inset of Figure 4b). The authors exploited the magnetic quadrupolar resonance in the silicon nanoparticle to demonstrate a fourfold enhancement of the light-to-heat conversion compared to a similar gold nanoparticle, which is often used in thermoplasmonics. As such, resonant silicon nanoparticles provide efficient optical heating despite their low optical losses and, importantly, their temperature can be directly monitored using Raman spectroscopy. These desirable properties have been exploited to track the temperature of silicon nanostructures during laser reshaping  and laser crystallization , [ 88], real-time observations of protein unfold in a hybrid plasmon-dielectric nanocavity , and, recently, for controllable drug release with high-refractive-index iron oxide nanoparticles . These results demonstrate that Raman spectroscopy of high-refractive-index nanostructures offer emerging opportunities in biological applications, such as photothermal therapy, drug release, and nanosurgery.
4.4 Detecting near-field enhancements
The enhancement of spontaneous Raman scattering in dielectric nanostructures is linked to the enhancement of the internal near-field (cf. Eq. (8) and Figure 1). Thus, Raman spectroscopy offers a unique opportunity to measure the electric near-field inside dielectric nanostructures, which is challenging with existing measurement techniques. While existing near-field instruments, such as near-field scanning optical microscopy (NSOM) and cathodoluminescence (CL), have successfully probed the near-field distribution of Mie resonances on a deep subwavelength scale , , , , , they do not provide quantitative information on the enhancement. Quantitative measurements of the near-field are important for optimizing both linear and nonlinear light–matter interactions in the design of efficient optical nanodevices. In addition, the aforementioned techniques have drawbacks ranging from the perturbing tip in NSOM to specific sample requirements in CL. Given that Raman spectroscopy is a far-field technique, it cannot compete with SNOM and CL on spatial resolution, but instead inherits the benefits of far-field optical microscopy, which include versatility and noninvasiveness.
A current technical limitation of Raman spectroscopy for near-field-enhancement measurements is the fixed excitation wavelength set by the Raman laser. The fixed excitation wavelength entails that resonances can only be detected by fabricating multiple samples, which gradually shift the resonance wavelength across the Raman excitation wavelength (as seen in Figure 1). It is important from both a practical and scientific point-of-view to be able to measure the Raman signal in a broad range of wavelengths from individual samples. State-of-the-art tunable lasers offer a solution to this problem, as they cover most of the visible spectrum and have linewidths suitable for Raman spectroscopy , , . Matthiae et al.  recently provided a proof-of-principle for tunable Raman spectroscopy of dielectric nanostructures. Using a tunable near-infrared laser, the authors demonstrated that both the Fabry–Pérot and the magnetic dipole resonance can be identified in the Raman signal from thin silicon films and silicon nanodisk arrays, respectively (Figure 4c). Interestingly, the Raman intensity peaks at a slightly shorter wavelength than the Fabry–Pérot resonance of the thin film. It turns out that this provides the best conditions for amplifying both the excitation and emission processes. On the other hand, the magnetic dipole resonance wavelength coincides with the Raman intensity peak. These initial results show the potential of tunable-excitation Raman spectroscopy for measuring the internal field enhancements due to Mie resonances and can be extended to other nanostructure designs and spectral ranges. This insight is important for controlling near-field-based processes, such as spontaneous emission, strong coupling, and nonlinear interactions, and complements far-field transmission and reflection measurements.
It is also worth noting that the connection between the Raman signal and the near field has been exploited in plasmonic nanocavities , [ 98]. Here, judiciously positioned molecules act as Raman probes for the near-field in few-nanometer-sized gaps, enabling Ångstrom spatial mapping of the local electric field. These Raman measurements provide insight to the limit of plasmonic field enhancement as well as the field distribution in nanocavities, which would otherwise only be accessible using simulations. We anticipate that similar experimental insight into the internal field of dielectric nanostructures (using the material itself as the Raman probe) may propel the understanding and engineering of their optical response.
In conclusion, we have provided an overview of Raman scattering in high-refractive-index nanostructures. In particular, we have shown that the Raman intensity is linked to the enhancement of the stored electric energy, which can be significantly amplified through optical resonances in dielectric nanostructures. We have discussed emerging applications of enhanced Raman spectroscopy and discussed potential future directions for maximizing the Raman signal. We hope that the background provided here will drive future research into new designs of dielectric resonators with exciting Raman-based applications.
Funding source: Det Frie Forskningsråd
Award Identifier / Grant number: 7026-00117B
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: S. R. acknowledges support by the Independent Research Funding Denmark (7026-00117B).
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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