Reconstructive spectrometer using a photonic crystal cavity

Abstract

Optical spectrometers have propelled scientific and technological advancements in a wide range of fields. While sophisticated systems with excellent performance metrics are serving well in controlled laboratory environments, many applications require systems that are portable, economical, and robust to optical misalignment. Here, we propose and demonstrate a spectrometer that uses a planar one-dimensional photonic crystal cavity as a dispersive element and a reconstructive computational algorithm to extract spectral information from spatial patterns. The simple fabrication and planar architecture of the photonic crystal cavity render our spectrometry platform economical and robust to optical misalignment. The reconstructive algorithm allows miniaturization and portability. The intensity transmitted by the photonic crystal cavity has a wavelength-dependent spatial profile. We generate the spatial transmittance function of the system using finite-difference time-domain method and also estimate the dispersion relation. The transmittance function serves as a transfer function in our reconstructive algorithm. We show accurate estimation of various kinds of input spectra. We also show that the spectral resolution of the system depends on the cavity linewidth that can be improved by increasing the number of periodic layers in distributed Bragg mirrors. Finally, we experimentally estimate the center wavelength and linewidth of the spectrum of an unknown light emitting diode. The estimated values are in good agreement with the values measured using a commercial spectrometer.