Determining the transfer function of a reconstructive spectrometer using measurements at two wavelengths

The transfer function is the characteristic function of the dispersive element of a reconstructive spectrometer. It maps the transmitted spatial intensity profile to the incident spectral intensity profile of an input. Typically, a widely tunable and narrowband source is required to determine the transfer function across the entire operating wavelength range, which increases the developmental cost of these reconstructive spectrometers. In this Letter, we utilize the parabolic dispersion relation of a planar one-dimensional photonic crystal cavity, which acts as the dispersive element, to determine the entire transfer function of the spectrometer using measurements made at only two wavelengths. Using this approach, we demonstrate reliable reconstruction of input spectra in simulations, even in the presence of noise. The experimentally reconstructed spectra also follow the spectra measured using a commercial spectrometer.