Fig. 1. (a) Three fiber types considered in the simulation. Simulated optical field evolution in the xz-slices for (b) fused fiber, (d) SMF, and (f) MMF. Intensity probability density function distribution of (c) fused fiber, (e) SMF, and (g) MMF. The insets are the simulated output speckle patterns corresponding to three cases.

Fig. 2. (a) Schematic diagram of the experimental setup. When a high-power laser is inputted into an optical fiber under sub-optimal conditions, a self-destructive phenomenon typically occurs, characterized by a propagating mass of blue-white plasma that travels from the damage point back toward the laser source end. PMF: polarization-maintaining fiber. OL: objective lens. (b) The speckle patterns captured experimentally from the output of the fused fiber correspond to wavelengths of 1550.00, 1550.05, and 1550.10 nm. (c) Microscope images of the fused fiber revealing micro-void structures. (d) Spatial intensity distributions (stretched into one dimension) for three representative wavelengths, illustrating pseudo-random variations across the spatial domain. (e) Spectral correlation function of three independently prepared fused fibers. The HWHM of the curve is 0.1 nm. A negative C value indicates the presence of anticorrelation [37].

Fig. 3. (a) Speckle stability of the proposed spectrometer in 20 h: temporal evolution curve obtained by calculating the correlation coefficient between each time point and the reference time t0. Temporal evolution curve derived from computing the correlation coefficient between (b) each time point and its previous point, and between (c) intermediate time points and their preceding and succeeding offset time points. (d) Schematic diagram of the weighted transmission matrix concept. (e) Flowchart of spectral reconstruction. The equation system solving process consists of two main components: initial estimation and refinement.

Fig. 4. (a) Reconstructed spectra of dual peaks separated by 0.1 nm. (b) Reconstructed peak wavelength as a function of input wavelength. The input single wavelength is tuned with a step of 0.02 nm. (c) Reconstructed spectra of tunable peak within the range of 1525–1565 nm. (d) Reconstructed FWHM linewidth error and PSNR over the operation range. (e) Reconstructed spectra of two filtered spectral peaks with FWHM linewidths of 2.5 nm, and (f) filtered spectrum with an FWHM linewidth of 10 nm.

Fig. 5. Reconstructed spectra under different (a) applied forces and (b) temperatures. (c) Reconstructed peak-wavelength error as a function of temperature.

Fig. 6. (a) Normalized average intensity of the speckle patterns captured by the detector as a function of the input power. (b) Speckle contrast as a function of input power. (c) Reconstructed spectra under different input powers.

Fig. 7. (a) Reconstructed spectra under different input polarization angles. (b) Reconstructed peak-wavelength error as a function of polarization angle.

Fig. 8. Reconstructed spectra corresponding to (a) fixed wavelength and (b) flexibly varied wavelengths across the full spectral range over a 20 h period.

Fig. 9. The reconstruction performance corresponding to (a) individual transmission matrix at different time points and (b) different combinations of transmission matrices.

Fig. 10. Spectral reconstruction accuracy under different recalibration rates.

Fig. 11. The reconstructed spectrum corresponding to (a) only Tikhonov regularization, (b) Tikhonov regularization combined with the weighted transmission matrix, and (c) our full method. (d) Relative errors and PSNRs of the three algorithms.