Fig. 2. Spectrometer design and simulation.

a Schematic of our proposed programmable spectrometer with multiple stages of unbalanced MZIs, each with a singular input and output port. The insets show the increasing spectral randomness in the cascaded interferogram. b Concept illustration of the transmission matrix generated through temporal phase manipulation. The insets depict two exemplary sampling channels with different combinations of phase shifts, thus exhibiting decorrelated spectral responses. The two dashed lines at ${\lambda }_1$ and ${\lambda }_2$ highlight the differences of phase shifts. c Auto-correlation width δλ of the sampling channels simulated using the spectrometer designs with different stage numbers. The inset shows the auto-correlation function of a 6-stage design with a δλ of 0.58 nm. d Averaged cross-correlation between the sampling channels generated by spectrometer designs with varying numbers of MZI stages and phase states per stage. e Several example channel spectral responses from a 6-stage spectrometer design with 3 phase tuning states per stage. The red solid and dashed lines represent the closest pair of sampling channels that have diverse phase tuning at only one stage, but still feature a significant spectral difference.