Mode visualisation and control of complex lasers using neural networks

TL;DR

An experimental lasing spectroscopy method is introduced that visualizes the gain profiles of the modes in a complex, disorderly coupled microring array laser using an artificial neural network to extract hidden spatial mode features from photonic structures, which could improve the understanding and control of complex photonic systems.

Abstract

Understanding the behaviour of complex laser systems is an outstanding challenge, especially in the presence of nonlinear interactions between modes. Hidden features, such as the gain distributions and spatial localisation of lasing modes, often cannot be revealed experimentally, yet they are crucial to determining the laser action. Here, we introduce a lasing spectroscopy method that can visualise the gain profiles of the modes in complex lasers using an artificial neural network. The spatial gain distributions of different lasing modes in a disorderly coupled microring array are reconstructed without prior knowledge of the laser topology. We further extend the neural network to a tandem neural network that can control the laser emission by matching the modal gain/loss profile to selectively enhance the targeted modes. This mode visualisation method offers a new approach to extracting hidden spatial mode features from photonic structures, which could improve our understanding and control of complex photonic systems.

Figures (5)

• Figure 1: Uncovering complex lasing modes with neural networks. (a) The pseudo-colour bright field image (left) and schematic sketch (top right) of a disorderly coupled 10$\times$10 QD-SiN microring array with varying gaps and diameters. For detailed characteristics of the structure and material, see Supplementary FIG. \ref{['SUPPFIGURE_RingChars']}. The cross-section of a microring (SiN/QD/SiN stack on $\rm SiO_{2}$ substrate) is illustrated in the bottom right. (b) The lasing spectrum of the disorderly coupled laser array under uniform excitation, which shows a complex and multi-mode lasing behaviour. (c) Gain profile visualisation and spectral control through artificial neural networks. The excitation beam, patterned via a digital micromirror device (DMD), illuminates the microring array, resulting in different emission spectra. The modal spatial gain profile can be visualised from the emission spectrum by unfolding the neural network model. To control laser emission, the excitation pattern of a spectrum can be predicted by solving the inverse problem through a tandem neural network. Scale bars are 20 $\mu$m.
• Figure 2: Mode visualisation using a multi-layer perceptron. (a) The mode visualisation scheme via multi-layer perceptron (MLP) neural network. The network connects the excitation patterns to the emission modes. The spatial gain profile $\mathbf{P}$ of each mode can be estimated from the network weight matrices ($\mathbf{W} = \mathbf{W_{HO}} \cdot \mathbf{W_{HH}} \cdot \mathbf{W_{IH}}$). (b) A visualised gain profile for a lasing mode at 624.90 nm with the microring sample structures superimposed. (c) The spatial similarity map between all the gain profiles of the lasing modes. The highly similar mode pairs form super- and sub-diagonal lines representing a constant spectral distance between the modes. Two pairs of modes (AB and BC) with high and low similarities are also highlighted. (d) Three spectrally uncorrelated modes (A, B, and C) are highlighted in the lasing spectrum of the disorderly coupled microring array. Their spatial mode profiles are displayed in (e). The similarity between the modes can be found by crossing two corresponding lines in (c). This shows a high similarity between modes A and B ($\rm S_{AB} = 0.9577$), but not between modes B and C ($\rm S_{BC} = -0.0473$).
• Figure 3: Lasing control using a tandem neural network (TNN). (a) The architecture of the TNN, which combines 2 artificial neural networks --- the control network and the spectral prediction network --- for lasing control. The number of nodes for each layer is shown at the top. The control network stands alone as a model to predict the excitation pattern required for the targeted modes after training. (b) Controlled single-mode emissions on the disorderly coupled microring array, with the best side-mode suppression ratio (SMSR) of 14.41 dB. (c) The predicted excitation profiles for different single-mode emissions in (b). The target lasing modes of the spectra are (1) 624.41 nm, (2) 624.90 nm, (3) 625.67 nm, (4) 627.78 nm, (5) 629.44 nm, and (6) 630.58 nm. (d) Dual-mode (624.90 nm and 627.78 nm) lasing control performed on the same system using the same model. The asterisks indicate the spectral positions of the target modes. The right panel shows the corresponding predicted illumination pattern, which is complex and not equivalent to the sum of two corresponding single-mode profiles (modes 2 and 4 in (c)).
• Figure S1: Characterisations of the hybrid QD-SiN microring array. (a) The gain spectrum of the CdSe/CdS quantum dots measured via transient absorption at 3 ps delay under different pump fluences bisschopImpactCoreShell2018. (b) The emission spectrum of a standalone single microring laser with 10 $\mu$m diameter and 2 $\mu$m width. Multiple lasing modes are supported in the ring. (c, d) The statistical distributions of the (c) ring diameters and (d) ring-to-ring gaps in the 10$\times$10 disorderly coupled microring array.
• Figure S2: Architecture of the spectral prediction network. The 3-layer multi-label classification neural network model for mode visualisation. For the input and hidden layers (except the last hidden layer), a ReLU activation function is used. A sigmoid activation function is applied at the last hidden layer to produce a one-hot encoded mode spectral profile. The number of nodes in each layer is shown at the bottom