Fig. 1. (a) Images of the speckle patterns with various spectrum information and polarization states. (b) The experimental setup of the proposed spectropolarimeter. EPC, electro-polarization controller; LUT, lighwave under test; SMF, single-mode fiber; PAS, polarization analysis system; OSA, optical spectrum analyzer; MMF, multi-mode fiber; CCD, charge-coupled device.

Fig. 2. (a) Measured spectral correlation function of the speckle pattern intensity obtained from Fig. 1(a), showing a half-width at half-maximum (HWHM) of 150 pm. (b) The correlation coefficient matrix composed of the correlated results of six speckle patterns with a fixed wavelength of 1550 nm.

Fig. 3. (a) The distribution of two actual values of the polarization state on the Poincaré sphere and the corresponding reconstructed results. (b)–(d) The wavelength of the input lightwave is fixed at 1550 nm. Calculated polarization resolution as a function of (b) length of MMF, with a fixed CD of 105 µm and NA of 0.22; (c) NA, with a fixed CD of 105 µm and length of 2 m; (d) number of the guided modes, with a fixed CD of 105 µm, NA of 0.22, and length of 2 m.

Fig. 4. (a) Simultaneous measurement results for spectrum and polarization. Upper part: reconstructed spectra. Lower part: reconstructed Stokes parameters. (b) Reconstructed spectrum of two probe lines separated by 100 pm. (c)–(e) Measurement error distributions for AOP, DOCP, and DOLP of the reconstructions in (a). AOP, angle of polarization; DOCP, degree of circular polarization; DOLP, degree of linear polarization.

Fig. 5. (a) The change of speckle pattern over 30 min with a fixed wavelength and polarization state. (b) The MSE of the reconstructed results for polarization measurement as a function of the number of polarization channels. (c) The MSE of the reconstructed results for polarization measurement as a function of SNR. (d) Linear relationship between the incident lightwave field intensity and the weighted integral of the speckle patterns.