Application of the wavelet transform to the problem of the detection and determination of the Lorentzian positions of the $2D$ band in the Raman spectrum of bilayer graphene

The possibility of quantifying the number of graphene layers using the integral wavelet transform is shown. The integral wavelet transform is applied to process the $2D$ band of the Raman spectra of single-layer and bilayer graphene obtained by micromechanical cleavage and transferred to a SiO$_2$/Si substrate. The wavelet transform revealed hidden Lorentzian peaks in the $2D$ band, their number and positions are determined. The coordinates of the Lorentzian maxima determined by the wavelet transform coincide with published data. The number of detected Lorentzians confirms the theory of the origin of these peaks on account of the double resonant process of Raman scattering and splitting of the band structure of bilayer graphene.