Multiresolution analysis signal in a three beam path Mach-Zehnder interferometer based on a discrete wavelet transform

In this work, we present an analytical methodology to evaluate the response of a three-beam path Mach-Zehnder interferometer (MZI) based on a multiresolution signal analysis using a discrete Wavelet transform (DWT). Here, the MZI was implemented by fusion splicing of a segment of ytterbium-doped double cladding photonic crystal fiber (Yb-d-DCPCF) between two pieces of single mode fibers. Moreover, Yb-d-DCPCF core and claddings were used as the arms of the MZI, while the hole collapsed regions acted as optical fiber couplers. So, the MZI interference pattern occurs of two main modal interferences, between the core and cladding. Hence, as a result, an interference spectrum with aperiodic sinusoidal waveform was observed. In this way, in our proposed methodology we decompose the interference spectrum into eight bands of spatial frequency (SF) using the DWT with a wavelet mother Daubechies order twenty (db20) for detecting the two main modal interferences. The spectral analysis of the decomposed signal reveals that the level 7 and 8 contain the two main modal interference between the core and the cladding 1 and cladding 2, respectively. Additionally, the fundamental mode is obtained in the level 8. In the same way, the decomposed signal provides information about the wavelength and spatial frequency simultaneously that can be used for knowing the energy spectral density. Finally, we claim that the proposed methodology provides the best accuracy in SF of MZI intermodal and DWT indicates the wavelength region in which the propagation modes occur, improving the description of the refractive index difference.