Statistical Insight into the Correlation of Geometry and Spectral Emission in Network Lasers

Abstract

Optically active networks show feature-rich emission that depends on the fine details of their geometry, and find diverse applications in random lasers, sensing devices and photonics processors. In these and other systems, a thorough and predictive characterization of how the network geometry correlates with the resulting emission spectrum would be highly important, however such outright description is still lacking. In this work, we take a step toward filling this gap, by using the well-known Steady-State ab Initio Laser Theory (SALT) equations [L. Ge et al., Phys. Rev. A 82, 063824 (2010)] to carry out an extensive set of statistical analyses and establish connections between the random network geometry and their ultimate emission spectrum. Our results show that edge crowding is key to tune the uniformity of the modal intensity distribution of the emission spectrum. A statistical framework for the comprehensive understanding of the network statistical properties is highly significant to establish precise design rules for network-based photonic devices and intelligent systems.

Figures (5)

• Figure 1: (a),(b) Distributions of the edge lengths for two different network configurations (insets), with Poisson (a) and Wigner-Dyson (b) edge lengths distribution (fits with dashed lines), respectively. Inset: the red arrows highlight the suppression of short segments in the Wigner–Dyson network, in contrast to their abundance in the Poisson case.
• Figure 2: (a) Emission spectrum for a pump strength $D_0$ slightly above the gain-clamping threshold --- set here to 105% of $0.044\times D_c$, which corresponds to the gain-clamping pump strength of the sample. (b) Network geometrical configuration. The dashed lines show the spatial profile of the most intense mode at $D_0$, which is significantly localized. The colorscale shows the intensity of the electric field in $E_c^2$ units.
• Figure 3: Distribution of the spectral inverse participation ratio (SIPR) of the modal intensity of the emission spectrum, for Poisson (a) and Wigner–Dyson (b) edge lengths distribution, respectively. Examples of the length distributions of the fiber segments used in the calculations are shown in Fig. \ref{['fig:ESdistribuzioni']}(a) and Fig. \ref{['fig:ESdistribuzioni']}(b), corresponding to the Poisson and the Wigner–Dyson cases, respectively.
• Figure 4: (a),(b) IWD distributions for the Poisson (a) and Wigner--Dyson cases (b), respectively. (c),(d) MID distributions for the Poisson (c) and Wigner--Dyson cases (d), respectively.
• Figure 5: Anomaly score computed using the Isolation Forest algorithm (IFA) as a function of the SIPR values. By convention, outliers---defined as the lowest 10th percentile---correspond to negative scores. Data are grouped in normal (circles) and anomalous (crosses) cases. Panels (b) and (c) show the SIPR distributions for the normal and anomalous cases, respectively.