Polarization properties of Raman scattering by surface phonon polaritons in GaAsP nanowires

Strong resonant enhancement of Raman scattering on photonic resonance was observed in GaAsP semiconductor nanowires. The enhancement allowed for detailed studies of the surface phonon polariton (SPhP) scattering peak on individual nanowires. In particular, for the first time, the effect of the nanowire cross section shape on SPhP properties has been investigated. It was found that the cross section flattening induces a strong polarisation and a spectral shift of SPhPs supported by such nanowire. The assisting numerical simulations allowed to link the induced polarisation effect to a splitting of the resonant HE11 mode in the flattened nanowire. The observed spectral shift of SPhP has been also theoretically reproduced in elliptical approximation for the flattened cross section. The obtained results pave a ground for engineering of SPhP polarisation response and accurate spectral control of SPhPs in applications utilising the nanowire morphology.


Introduction
Surface phonon polaritons (SPhPs) are quasiparticle excitations associated with surfaces and interfaces of noncentrosymmetric dielectric crystalline materials [1,2]. They represent mixed optical-phonon-photon states, which can * Authors to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. be obtained as solutions of Maxwell's equations for the frequency range where the real part of dielectric permittivity is negative. For natural crystalline dielectrics this range is found in far infra-red (IR) spectral window. The surface nature of SPhPs makes them sensitive to the dielectric permeability of surrounding environment [1], which creates potential for diagnostics of surface dielectric properties [3]. Arising from far-IR frequency window, SPhPs spectrally overlap with molecular vibrations and hence they have been considered for developing ultrasensitive molecular spectroscopy [4,5] and even for alteration of molecular chemical activity [6][7][8].
Recently there have been a sharp increase of interest to SPhPs as an attractive platform for IR miniaturised photonic circuits due to the extremely high compression of free-space wavelength corresponding to far-IR photons [2,[9][10][11] at relatively low losses that can be achieved with SPhPs. Thermal emission is another rapidly growing area for SPhP applications. Distance, spectral, polarisation, and angular control of thermal emitters-absorbers has been demonstrated via coupling of far-field [12] or near-field [13,14] radiation to SPhPs. In addition, energy routing and focussing by means of SPhP has been predicted [15]. SPhP based photonic control of thermal emission has allowed for improvement of traditional applications such as thermophotovoltaics [13,14] and also lead to emerging application opportunities such as daytime radiative cooling [16] and night-time photovoltaics generation [17]. These new application areas created a demand for SPhP characterisation methods, which would allow for accurate evaluation of the energy spectrum, polarisation, lifetime and other properties of SPhP excitations in supporting nanostructures. This includes a demand for novel efficient SPhP sources and detectors, especially in on-chip integrable format [18].
Recently we have demonstrated [39] the amplification of Raman scattering by SPhPs on HE11 photonic resonance in GaAs nanowires, establishing the required experimental conditions. In this paper, we have reproduced the resonance amplification effect on GaAsP nanowires and utilised it for detailed characterisation of polarisation properties of SPhPs in nanowires of different cross section shape.

Sample processing
For obtaining NWs detached from a substrate (cut-off NWs), the as-grown sample was sonicated in ethanol using an ultrasonic bath (60 W) for 5 min. The obtained dispersion of NWs in ethanol has been subsequently applied in drops on Si/SO x substrate or TEM lacey carbon grids to deposit the cutoff NWs. The sonicated substrates ('shaved' substrates) have been removed from the ethanol and dried in nitrogen gas flow. The other method of local 'shaving-off' NWs was also used. In this method, the local stamping of the as-grown sample with non-sticky gel was used, which allowed to remove the NWs but leave the clusters in place (see figure S2).

Raman measurements
All Raman measurements have been conducted at room temperature using LabRAM (HORIBA) spectrometer equipped with confocal microscope, Peltier-cooled CCD detector, and HeNe laser (λ = 632.8 nm). The microscope is equipped with precise X-Y scanning sample stage (min step of 0.2 µm), piezo focus lens positioner, and ×100 dry objective lens (NA = 0.92). Excitation laser power was adjusted using a built-in set of reflective neutral density filters. Excitation laser power level of 12 µW was selected. Polarisation unanalysed Stokes-Raman spectra (z (x ′ x ′ + x ′ y ′ )z, or 'unanalysed' spectra) were normally collected except where crossed (z (x ′ y ′ )z) or parallel (z (x ′ x ′ )z) polarisation is explicitly noted. For polarisation control, the half-wave plate and absorptive polarizer have been used. For a polarisation diagram, a series of unanalysed Raman spectra were taken at different in-plane polarisation angles covering 180 • range and the diagram was constructed showing the integral intensity of the Raman spectrum as function of the in-plane polarisation angle. The obtained results were corrected for the spectrometer instrumental polarisation function.

Numerical simulation
The numerical simulations were performed using the finite element method implemented in commercial COMSOL Multiphysics software. The excitation field distributions and mode dispersions were calculated by solving Maxwell equations in the frequency domain for a suspended finite-length NW and an infinite non-absorbing NW respectively. The finite-length NW was simulated as a 4 µm/2 µm long cylinder or truncated cone suspended in a large cavity bounded by artificial perfectlyabsorbing walls implemented using perfectly matched layer feature of COMSOL software. For the truncated cone shape, the top diameter was kept at half of the pedestal diameter. Plane wave excitation has been employed unless mentioned otherwise. Material optical parameters for GaAsP have been taken from [40][41][42].

Hot spots in Raman mapping
GaAs 1−x P x nanowires were fabricated by MBE with selfcatalysed mode on silicon substrates. They have typical characteristics for the chosen growth method which was described in details in earlier publications [43,44], and have an average diameter of 50-70 nm and length of 4-6 µm as confirmed by SEM and TEM images (figure S1). A small percentage of nanowires are with a spike-like morphology grown at angle of ∼35 • to the substrate (figure S1(a)). At the bottom level of nanowires, there is a layer of aggregates of thickness of 300-500 nm, known as 'parasitic clusters'. The phosphorus content x = 0.28 ± 0.01 has been established using EDX analysis combined with TEM.
Raman mapping of as-grown GaAsP nanowire samples taken in backscattering geometry (see figure 1(a)) revealed strong highly localised maxima (hot spots), as shown in figure   S3. They have a signal intensity exceeding signal from the individual cut-off nanowires (see note S1) by two orders of magnitude. The density of these maxima varies across the sample, but it is always less than 10% of the average NW density. This Raman hot spots phenomenon is similar to that observed on GaAs nanowire samples [39]. However, the intensity of the hot spots tends to be higher in GaAsP samples, which can be explained by the lower laser light absorption coefficient in this material. Lower absorption also leads to lower laser damage, allowing for multiple scanning of the same hot spot. Zooming into figures S3(b) and 1(b) shows the averaged Raman map obtained from three subsequent scans, illustrating the repeatability of mapping (see more in figure S3(c)). A representative Raman spectrum collected from the hot spot area (figure 1(c)) shows GaAsP phonon peaks grouped into two bands related to the parent compounds of GaAs and GaP, in agreement with earlier reports for bulk [45,46] and nanowire samples [47]. The integral intensity of the strongest GaAsP phonon band (green, GaAs-related) has been used for mapping in figures 1(b) and (d). In addition, the spectrum in figure 1(c) also shows a background peak from the silicon substrate (∼520 cm −1 ). The integral intensity of this peak has been mapped in figure 1(e). The composite images in figures 1(d) and (e) show GaAsP and Si components of the Raman map overlaid on top-view SEM image of the same area of the sample. The hot spots from the green GaAsP map (figure 1(d)) appear as dark spots on the red Si map (figure 1(e)), indicating an efficient absorption of the laser emission at the hot-spot locations. Correlated study of the Raman maps and corresponding SEM images allowed to establish that the hot spots are related to individual nanowires characterized by larger than average diameter (cross-section size) and pronounced tapering. The geometrical parameters of these thicker NWs were obtained from their SEM images taken at inclined view to the sample's normal (figures 1(f) and (g)). Averaging over 13 of such hot spots from different sampling areas, the mean diameter of hot-spot nanowires at half-height level is 118.5 ± 20 nm whereas their lengthaveraged taper is within 0.3 • -0.7 • range. This taper corresponds to ≈2 times diameter variation over the typical nanowire length of 5 µm. The hot-spot nanowires also often have a flattened blade-like shape characterized by an elongated crosssection (figures 1(f) and (g)).
For thick spike-like nanowires (see figure S1(a)) grown at low angles to the sample surface (indicated by yellow arrow in figures 1(e) and S3(d)), the prominent Raman signal is not observed, despite the fact that their geometrical parameters (cross-section size, taper and length) are similar to those nanowires with the hot spots.
On the other hand, these spikes appear as dark areas on the silicon map (figures 1(e) and S3(d)), indicating local shadowing of the substrate due to strong absorption (or scattering) of the laser light on these objects similar to that on the hot spots.
This implies that the standing up orientation (ensuring a backscattering geometry along the nanowire axis) is a principal condition for obtaining a strong Raman signal in the thick tapered nanowires, as suggested in [39].
3D Raman mapping of the hot spots shown in figures 1(h) and S3(f) allow for assessment of the intensity variation along vertical (z) direction. It can be seen that centres of mass of green isosurfaces are lifted above the substrate level. The linked maximum intensity projections in X and Y directions show that the maximum of the Raman signal is often located at 2 and 3 µm above the substrate level, i.e. at the mid-height range of the nanowire. Similar feature was observed for hot spots in GaAs samples [39], where it was related to the effect of tapering on the excitation light intensity distribution. The 3D map also indicates that the Raman signal from the underlayer of thick clusters typically present in our samples (figure S1) is much weaker than that of the hot spots, despite the larger volume of material involved in the clusters. That was directly confirmed by mapping of the 'shaved' samples (see note S1 and figure S2).

Raman spectra of hot spots
When comparing the hot-spot Raman spectrum with that of clusters (figure 2(a)), strong extra peak is present in spectrum of the hot spot in between LO Ga-As and TO Ga-As (GaAs-band) in addition to 'bulk' LO Ga-As and TO Ga-As modes, mimicking the SPhP peak appearance in pure GaAs samples [39]. The separation of this SPhP Ga-As peak from LO Ga-As is not that obvious due to the narrower LO GaAs -TO GaAs splitting (6.5 cm −1 against 13 cm −1 in pure GaAs) and larger peaks broadening in the alloy compound (7-9 cm −1 against 3-4 cm −1 in pure GaAs). However, it can be accurately established via peak fitting (figures 2(b) and (c)) assuming that LO Ga-As and TO Ga-As peak frequencies are fixed within the ranges obtained from the fitting of the clusters and cut-off nanowires spectra (figures S5(a), (c) and note S2). Following this procedure, we have found that SPhP Ga-As peak position varies within 281.5-284 cm −1 range, while its width (FWHM) is 8.5 ± 0.7 cm −1 . The peak width value is close to that of the 'bulk' LO Ga-As and TO Ga-As modes. This is different from the SPhP peak characteristics in GaAs nanowires, where the SPhP peak width was significantly larger than that of the bulk modes [39].
Importantly, similar SPhP-like spectral weight redistribution is also observed in the GaP-band of the hot-spot spectra ( figure 2(a)). For GaP band, the theory predicts [46] four bulk phonon modes, of which only LO As GaP has been tabulated [45] with moderate accuracy (LO As GaP = 369.6 ± 0.4 cm −1 for x = 0.28). Such modal complexity in combination with strong broadening makes fitting of the GaP band not very reliable and hence accurate SPhP GaP value cannot be produced. Figure 2(b) show the fitting example of GaP band and the predicted mode assignment. Despite the inaccurate fit of the GaP band, the fact of synchronous appearance of SPhP contribution in both GaAs and GaP bands allows to rule out any accidental coincidence of these features with contribution from some unaccounted impurity compound like surface oxide.
Raman spectra of the GaAsP hot spots with elongated cross-section demonstrate sensitivity to in-plane orientation of the laser polarisation. Due to the relatively low laser absorption in GaAsP, detailed polarisation series can be conducted on these hot spots. Figures 3(a) and (d) show polarisation diagrams obtained for the hot-spot nanowire of round and elongated cross-sections, respectively. The diagrams display the integrated unanalysed Raman signal intensity as function of the incident polarisation angle. For the nanowire of round cross-section, no prominent effect of polarisation rotation is observed on the spectral content and intensity (figures 3(a) and (b)). Whereas in case of the elongated cross-section, the maximum of the Raman signal is achieved when the incident laser polarisation is placed along the larger dimension of the nanowire cross-section (figures 3(d) and (e)). Similar correlation has been observed over a number of hot spots as shown in figure S6. It should be noted that no spectral sensitivity to the in-plane polarisation rotation is expected from the bulk Raman scattering tensor of III-V zinc blende crystals for backscattering in <111> direction [48,49]. Figures 3(e) and (g) compare spectra obtained at the polarisation angles corresponding to minimum and maximum of the polarisation diagram. The spectral difference between these two polarisations is largely due to SPhP Ga-As peak amplitude variation, which decreases by ∼7 times between the maximum and minimum polarisation angles, whereas amplitudes of LO Ga-As and TO Ga-As peaks drop by ∼2 times only. Similar trend was observed over a number of hot spots as shown in figure S7 (column ii). Additionally, the position of SPhP Ga-As peak at the maximum is redshifted against that at the minimum ( figure 3(g)). The variation of SPhP Ga-As peak position is summarised in figure 4(a) for a number of hot spots. For both polarisation angles, it shows a redshift proportional to maximum/minimum ratio of the polarisation diagram. Adopting the pedestal image of a hot-spot nanowire (shown in figures 3(a), (d) and S6) as a good representation of its cross-section shape, the correlation between the polarisation diagram maximum/minimum ratio and the crosssection geometrical aspect ratio can be established as shown in figure 4(b). This allows for plotting the SPhP Ga-As frequencies as function of the aspect ratio ( figure 4(c)). We are not aware of any other study of the NW cross section shape on SPhP properties. The only remotely similar Raman study has been conducted on ZnS nanobelts [38]. In terms of broad NWrelated research, the effect of the NW cross section was also noted for polarisation control in NW-based lasers [50].
In addition to the in-plane polarisation rotation, a standard analysis in parallel and crossed polarisers has been conducted for GaAsP hot spots. The results for the different cross-section shapes are shown in figures 3(c), (f) and (h). At the maximum of polarisation diagram, the spectrum is always prominently polarised (figures 3(c) and (f)), and the degree of polarisation (I ll /I ⊥ ) is increasing continuously with the cross-section elongation as illustrated by figure S7 (column iii). In contrast, at the minimum intensity condition, the spectra tend to be unpolarised (see figures 3(h) and S7 (column iv)). Judging from the GaAs band, the polarisation is largely due to the dominant SPhP GaAs peak, with smaller contribution from LO GaAs and TO GaAs peaks (figures S5(d) and (e)). The I ll /I ⊥ ratio for SPhP GaAs peak is 2.6 ± 0.3 for the hot spot with the round NW cross-section (figures 3(c) and S5(d)). We are aware of only one report of SPhP Raman peak polarisation measurements in nanowires [37]. The data was obtained on a random GaAs nanowire in the similar backscattering geometry. The polarisation degree (I ll /I ⊥ ) of ≈2 can be evaluated from the reported data, that is in qualitative agreement with our results. The further detailed comparison is prevented by non-elementary shape of the SPhP peak in [37].

Numerical simulations
Similar enhancement of Raman scattering signal in GaAs nanowires was explained by photonic resonance based on excitation of HE11-like waveguiding modes in nanowires of resonant diameter under employed excitation geometry. Simulation of excitation of GaAs 0.72 P 0.28 nanowires confirms the same origin for the hot spot appearance. Indeed, the volumeaveraged excitation light intensity inside the 4 µm length GaAs 0.72 P 0.28 nanowire shows a resonant dependence from the nanowire radius ( figure 5(a)) with peak at R = 56 nm. The value of the resonant diameter 2R = 112 nm is in close agreement to 118.5 ± 20 nm obtained for the mean mid-height thickness of the hot-spot nanowires. Also, the electric field distribution at the resonance (see insert to figure 5(a)) is typical for HE11 mode.
For quantification of Raman signal enhancement, it will be assumed that both excitation and Raman Stokes components are described by the HE11-like modes. Since the |E| 2 vs radius dependence does not change much between the laser and Stokes-shifted wavelengths as shown in the figure 5(a), the variation of the Raman signal can be approximated as variation of the product of I laser × I Stokes ∝ |E laser | 2 × |E Stokes | 2 ≈ |E laser | 4 (ignoring any modal overlap and Raman tensor effects). In |E laser | 4 approximation, the 20-30 times difference ( figure 5(a)) in |E laser | 2 between the peak diameter (112 nm, hot spots) and the average-NW diameter (50-70 nm) transforms into 400-900 times difference in Raman signal, which explains the negligible contribution from the average-diameter NWs in experimental Raman maps.
To simulate the effect of the elongated NW cross-section on the HE11 resonance, the cylinder was changed to an elliptical cylinder. As a result, the excitation efficiency became sensitive to in-plane polarisation of the excitation light. As shown in figure 5(b), the HE11 resonance peak is split into two, reflecting two basic polarisations along the semi axes of the elliptical cross section. For E∥a, the excitation field intensity is peaked at slightly lower average radius than that for the circular cylinder ( figure 5(c)). At E∥b, the resonance appears at larger radius and it is of smaller amplitude. The difference in amplitude and position of the resonance peaks for E∥a and E∥b is further increasing with the a/b aspect ratio. This resonance splitting agrees with the known splitting of HE11 wave-guiding mode in the infinite elliptical cylinder into two HE11-like modes with basic polarisations along the shorter and longer semi-axis [51]. This splitting is reproduced by numerical simulation of the dispersion diagram for GaAsP nonadsorbing infinite elliptical cylinder shown in figure 6(a). The dispersion diagram is calculated for the varied average cylinder radius at fixed excitation wavelength and a/b = 1.5 ratio. It shows that HE11b (E∥b) mode is shifted up to higher average radius ((a + b)/2) values against the HE11a (E∥a) branch. The splitting is further increasing with a/b ratio (figure S8(a)), quickly moving HE11b branch outside the practical NW diameter distribution.
Stronger resonance peak at E∥a is in excellent agreement with the experimental results, which consistently showed strongest signal at E∥a condition (figures 3(e) and S6). Moreover, the large variation of SPhP GaAs peak intensity between E∥a and E∥b polarisations observed in experiment (figures 3(g) and S7) provides further evidence of connection between the resonance appearance and SPhP peak amplification.
The predicted |E| 4 in-plane polarisation diagrams (insert in figure 5(b)) are in qualitative agreement with the experimental data shown in figures 3(d) and S6, confirming that the photonic properties of the flattened waveguide are responsible for the polarisation diagrams observed in experiment. Quantitatively, the simulated diagram signal variations are much stronger than the experimental values for the comparable a/b ratios (figures 3(d) and S6). However, once the simulations have adopted the more realistic conditions including the cone shape and the Gaussian beam excitation, the simulated polarisation diagram min/max ratio becomes significantly weaker (see figure 5(d)) approaching the experimental values.
The flattened waveguide also affects the band polarisation measurements. In particular at E∥a resonance, it supports light propagation with polarisation parallel a and attenuates light polarised along b. This explains the apparent enhancement of the Raman band polarisation (I ll /I ⊥ ratio) observed for the hot spots with elongated cross-section (figures 3(c), (f) and S7 (column iii)). This indicates that the true polarisation ratio can be obtained only on NWs of circular cross section.
Adopting HE11 resonance diameters obtained from the finite NW simulations ( figure 5(b)), HE11 modal k z wavevectors can be found from the dispersion diagram as shown in figure 6(a). That obtained k z values are close to that of the free light dispersion, indicating that electromagnetic field of the excited resonant HE11 modes is still largely distributed outside the nanowire. This agrees with more detailed analysis of HE11 modes in GaAs nanowires [39].
To calculate the expected SPhP frequencies appearing in Raman spectra we adopt the model where both incident and scattered light are propagating as HE11 (or HE11a) modes with k z parameters indicated in figure 6(a). The dispersion of SPhP modes is calculated in approximation of infinite nonabsorbing GaAsP elliptical cylinder by numerical simulation with the cylinder dielectric function represented as: where ε 0 is the static permittivity, ε ∞ is the permittivity at high (optical) frequencies, and ω TO is the transverse optical lattice vibration for zinc-blende GaAsP. Taking ω TO = 269.8 cm −1 , ε 0 = 11.63, ε ∞ = 10.33, (equivalent to ω LO = 286.3 cm −1 ), the dispersion of SPhP modes has been calculated at HE11 (HE11a) resonances. The results for the 1st two modes (SPhP 0 and SPhP 1 ) obtained for the circular and elliptic (a/b = 1.5) cylinders are shown in figure 6(b) (see also figure S8(b)). For the elliptical nanowire, the dipolar SPhP 1 mode is split and the symmetrical SPhP 0 mode is shifted down as compared to the circular nanowire case. The wavevector of SPhP (k z SPhP ), involved in the backscattering Raman geometry, has the twice of k z value of the involved HE11 mode (ignoring the difference in k z between the incident and scattered light). For that defined k z SPhP , the diagram in figure 6(b) gives ω SPhP0 = 283.12 cm −1 and 282.82 cm −1 for circular and elliptic cross section respectively. The ω SPhP0 and ω SPhP1a values obtained for a range of a/b ratio are plotted in figure 4(d). Both SPhP frequencies ( figure 4(d)) show a red shift with a/b ratio, which broadly reproduces the experimental dependence observed in figure 4(c). Since the symmetrical SPhP 0 mode is normally expected [52][53][54] to produce a dominant contribution to the Raman signal, we compare the calculated SPhP 0 data with experimental SPhP GaAs frequencies obtained at E∥a. At E∥b, the experimental SPhP peak is strongly diminished and blue-shifted by ∼1 cm −1 ( figure 4(a)), which can be explained by the decreased contribution from SPhP 0 and large relative contribution from SPhP 1 . Including SPhP 1 mode into analysis extends the predicted spectral shift range, which further improve the quantitative agreement with the experimental data. To predict the accurate contribution from two SPhP modes into experimental spectra, the more detailed calculations involving modal overlap will be required.
Since the actual nanowires are hexagonal faceted, we have assessed an effect of the faceting on the NW photonic properties. The obtained results (shown in figure S9) clearly prove a negligible effect of the hexagonal faceting, at least for the NW diameters satisfying the HE11 resonance conditions.
To summarise, the photonic properties of flattened nanowire are responsible for the observed SPhP peak's amplitude and spectral variations at the rotated in-plane polarisation. Control of these properties via engineering of the NW's cross section offers new prospective in SPhP applications in surface and chemical sensors, heat emission and IR micro-photonic.

Conclusions
The strong photonic-resonance enhancement of SPhP Raman signal previously observed on GaAs nanowires has been reproduced on GaAsP nanowires. High amplitude of SPhP peak in combination with low laser-induced overheating in GaAsP allowed for the extended studies of SPhP properties on individual NW level. In particular, the polarisation properties of SPhP and effect of flattening of the NW cross section has been investigated. It was shown that the flattening induces the in-plane polarisation and spectral red shift of SPhP peak. Supporting experimental results analysis with extensive numerical simulations, the observed effects were linked to the transformation of governing HE11 photonic resonance and SPhP dispersion in flattened nanowires. The obtained results create the basis for polarisation control and precise sensing of SPhPs in dielectric nanowires.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).