Fourier transform spectrometer on silicon with thermo-optic non-linearity and dispersion correction

Abstract

Miniaturized integrated spectrometers will have unprecedented impact on applications ranging from unmanned aerial vehicles to mobile phones, and silicon photonics promises to deliver compact, cost-effective devices. Mirroring its ubiquitous free-space counterpart, a silicon photonics-based Fourier transform spectrometer (Si-FTS) can bring broadband operation and fine resolution to the chip scale. Here we present the modeling and experimental demonstration of a thermally tuned Si-FTS accounting for dispersion, thermo-optic non-linearity, and thermal expansion. We show how these effects modify the relation between the spectrum and interferogram of a light source and we develop a quantitative correction procedure through calibration with a tunable laser. We retrieve a broadband spectrum (7 THz around 193.4 THz with 0.38-THz resolution consuming 2.5 W per heater) and demonstrate the Si-FTS resilience to fabrication variations-a major advantage for large-scale manufacturing. Providing design flexibility and robustness, the Si-FTS is poised to become a fundamental building block for on-chip spectroscopy.

Fig. 1

On-chip Fourier transform spectrometer. a Schematic of a MZI with integrated metal microheaters on silicon-on-insulator (SOI) platform. b Device cross-section illustrating the quasi-TE mode (energy density) of the strip silicon waveguide and the heated area (light red) when current flows through the microheater. c Optical micrography of the experimental device with a total footprint of 1 mm² (see fabrication details in the Methods section). d Dark field optical micrography of the MZI arm underneath the heater trails. e SEM image of the broadband power splitter/combiner

Fig. 2

Si-FTS calibration using a tunable laser source. Measurements are performed in the C-band. a–c Interferogram at 183.37 THz (1600 nm) as a function of dissipated power in heater H₂. The mean power (red trace in a) and the envelope (red trace in b) are subtracted to obtain the curve in c, fitted (dashed-red trace) using Eq. 13. The envelope in b is the absolute value of the interferogram’s Hilbert transform. d–f Data in blue and red are related to heaters H₁ and H₂, respectively. d Parameter K(ν) obtained from the non-linear fit, adjusted according to Eq. 14. Error bars are s.d. (95% confidence level). e Non-linear parameters γ_W,1 = (36.2 ± 0.3) × 10⁻³ W⁻¹ and γ_W,2 = (40.5 ± 0.3) × 10⁻³ W⁻¹ obtained from the non-linear fit. Error bars are s.d. (95% confidence level). f Current vs voltage (IV) response of both heaters and calculated electric resistance. g Experimental (black trace) and calculated (red trace) transmission spectrum of the MZI at non-zero optical delay (0.172 ps). The calculated transmission is obtained using Eq. 15 to extract the MZI transfer function T(ν) shown in h

Fig. 3

Broadband spectrum recovery with the Si-FTS. The parameters used to obtain these plots are summarized in Table 1. a ASE of a C-band EDFA used as the light source. b Theoretical interferogram of the ASE for an ideal (linear TOC, dispersionless, balanced) MZI. c Experimental interferogram, shifted to 0.172 ps and distorted due to differences between the two arms of the MZI. The optical delay axis corresponds to $\mathcal{T}$. The insets show a zoom-in of the interferogram at different optical delays superposed to a cosine (gray traces) at the ASE mean frequency ν_s = 193.44 THz, highlighting: the oscillations at ν_s when the envelope varies slowly (blue-colored zoom-in); phase changes when the envelope varies rapidly (green-colored zoom-in). d–f Experimental (red) and reference (black) PSD at different conditions. The red points are the experimental data obtained from the IFT and the red line is a second-order interpolation curve. d No correction. e Corrected thermo-optic non-linearity, but no dispersion correction nor PSD re-normalization with T(ν). f All effects properly accounted for