This dataset contains experimental results supporting the research article titled 'Single nanoparticle chiroptics in a liquid: optical activity in hyper-Rayleigh scattering from Au helicoids'. The folder 'CTAB' contains power-dependence measurements of hyper-Rayleigh scattering (HRS) in 1 mM aqueous cetrimonium bromide (CTAB). A polariser in a rotation stage was used to control incident laser power. The file '20191210-power_calibration-720nm.xlsx' specifies the laser powers corresponding to the various angles of the polariser. The .shg text files contain the results of measurements of CTAB. Each file name includes 'pwrpol', 'QWP' and 'wln'. The number after 'pwrpol' is the angle of the polariser, 'QWP' specifies the angle of the quarter-wave plate (in our case 45 degrees and 225 degrees corresponded to left circular polarisation, and 135 degrees and 315 degrees to right circular polarisation), 'wln' describes the wavelength of the incident laser beam. The second column in each of the .shg files contains the measured HRS intensity in counts/second - the intensity was measured 3 times for each combination of polariser angle and QWP angle. The folder titled 'Helicoids' contains results of experiments done on the helicoidal nanoparticles. 'Emission_spectra' contains results of HRS experiments where the incident wavelength was fixed and the bandpass filters in front of the detector were changed. Results are split into folders based on the illumination wavelength and the used filter. The number in the filter/folder name indicates the central transmission wavelength of the bandpass filter (e.g. results in folder EO365-10 were obtained with a bandpass filter with the centre wavelength of 365 nm). As with the CTAB results discussed above, 'QWP' in the filename specifies the angle of the quarter-wave plate and thus the circular polarisation of the incident beam. The second column in each of the .shg files contains the measured HRS intensity in counts/second. 'Linear_CD' contains results of chiral optical characterisation in the linear optical regime. Both of the enantiomorphs of the bare and silica-coated helicoids were measured. Prior to these measurements, a CD spectrum of 1 mM aqueous CTAB (the solvent in which the helicoids were dispersed) was measured. This spectrum was then automatically subtracted from the CD spectra of helicoids as background. 'Linear_polarisation_dependence' contains results of HRS experiments where the plane of the incident linearly polarised light was rotated using a half-wave plate. Measurements were carried out for both enantiomorphs of silica-coated helicoids. The number after 'HWP' in the file name indicates the angle of the half-wave plate. To get the angle of the plane of polarisation of the incident light, the HWP angle needs to be multiplied by 2. The second column in each of the .shg files contains the measured HRS intensity in counts/second. 'Power_dependence' contains results of HRS experiments where the power was varied. The experiments were carried out for various incident wavelengths for both the bare and the silica-coated helicoids - the results are separated into folders based on the wavelength and the sample. Each folder contains a power calibration file, which specifies the laser powers corresponding to the various angles of the polariser. Like in the case of CTAB, the filename of each of the .shg files specifies the angle of the polariser and the quarter-wave plate and the incident wavelength. The second column in each of the .shg files contains the measured HRS intensity in counts/second. The folder titled 'Spherical_Au_NPs' contains HRS power-dependence measurements of spherical Au nanoparticles. As with the power dependence measurements above, it contains a calibration file and .shg files. The filenames specify the angle of the polariser and the quarter-wave plate and the incident wavelength. The folder titled 'Z-stack_scan' contains a Z-stack_scan of a fluorescent bead. Zeiss ZEN software is needed to open the file.