The dispersive element based on porous silicon photonic crystal for ultra-compact optical spectrometers
Compact and inexpensive devices able to measure the optical spectrum in a visible range have a lot of applications in wearable devices, remote sensors and are widely demanded in physical, medical and many other studies. In this paper, the new type of dispersive element for the spectral decomposition of light is proposed. Due to the unique dispersion properties of photonic crystals (PCs), near the spectral edge of the photonic band gap (PBG), light significantly reduces its group velocity. This makes it possible to observe in the PC the giant Goos-Henchen shift: the spatial displacement of the reflected beam. It was shown earlier  that this shift can reach values that are an order of magnitude larger than the geometric thickness of the PC. In the case when a PC has a spatial modulation of the period and, consequently, the spectral position of the bandgap, the Goos-Henchen shift depends significantly on the wavelength, which makes it possible to use the PC as a dispersive element in optical devices.
The photonic crystal produced by electrochemical etching  has a linear modulation of the PBG position from 180 to 1150 nm. Light with a longer wavelength reflects off deeper layers and experiences more shear. For light detection, a 640x480-pixel CMOS matrix is used, applied to the PC surface. The proposed spectrometer has a resolution of 9 nm, its spectral range is limited by the sensitivity of the detector, compared to diffraction spectrometers, it has lower losses and does not require filtration of higher diffraction orders. The study was supported by the grant of the President of the Russian Federation for young scientists MK-2761.2019.2.
 S. E. Svyakhovskiy, E. A. Kekkonen, A. A. Konovko, A. V. Andreev and T. V. Murzina. Giant Goos-Hanchen effect and focusing of Gaussian light beam by one-dimensional photonic crystal with modulated band gap // 2016 International Conference Laser Optics (LO), St. Petersburg, pp. R8-43-R8-43, 2016.
 Svyakhovskiy, S.E., Maydykovsky, A.I. and Murzina, T.V. Mesoporous silicon pho-tonic structures with thousands of periods // Journal of Applied Physics, vol. 112(1), p. 013106, 2012.
Lomonosov Moscow State University
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