Optoelectronic Chromatic Dispersion in a Single Photodiode for Machine-Learning-Based Computational Spectroscopy

TL;DR

This paper introduces a compact, single-photodiode spectrometer leveraging optoelectronic chromatic dispersion and machine learning for high-precision spectral reconstruction, enabling portable and alignment-free optical sensing.

Contribution

It presents the first method using multi-frequency OED features from a single photodiode combined with machine learning for spectral reconstruction.

Findings

Achieves 0.178 nm accuracy in single-wavelength reconstruction.

Demonstrates robust generalization with RMSE of 0.342 nm across conditions.

Successfully reconstructs dual-wavelength inputs with sub-nanometer accuracy.

Abstract

Spectroscopy requires high-precision wavelength discrimination but typically requires bulky, alignment-sensitive instrumentation. To address this, we present a compact computational spectrometer built from a single germanium PN photodiode. The system exploits optoelectronic chromatic dispersion (OED), a phenomenon whereby wavelength-dependent absorption depth produces carrier diffusion delays that encode spectral information as measurable RF amplitude and phase signatures in the photodiode output. We extract DC voltage, RF amplitude, and RF phase across 15 modulation frequencies (0.1-1.5 MHz), forming a 31-dimensional feature vector per optical input. Spectral reconstruction was formulated as a high-dimensional inverse problem and solved using five machine learning models, utilizing group-wavelength splitting and k-fold cross-validation to prevent spectral leakage and ensure unbiased evaluation. Across the C- and L-bands, single-wavelength reconstruction using Gaussian Process Regression (GPR) achieves an accuracy of 0.178 nm on a wavelength-grouped, held-out test set spanning seven optical power levels. Five-fold cross-validation yields a robust Root Mean Square Error (RMSE) of (0.342 +/- 0.117) nm, confirming excellent generalization under wavelength and power variations. For dual-wavelength inputs, GPR yields accuracies of 0.362 nm for the swept wavelength and 0.434 nm for the fixed wavelength. This is the first spectral reconstruction method exploiting a multi-frequency OED feature space from a single photodiode. By merging the physics of OED with data-driven learning, this work enables alignment-free, on-chip-compatible spectrometers suitable for portable optical sensing, smartphone-integrated diagnostics, and field-deployable environmental monitoring.