X-ray microcomputed tomography of 3D chaotic microcavities

TL;DR

This work addresses the lack of precise 3D geometric data for chaotic microcavities by applying X-ray μCT to nondestructively image deformed silica microspheres at submicron resolution. By fitting the CT-derived surfaces with deformation parameters $e$, $q$, and $d$, the authors quantify the full 3D geometry and perform 3D ray tracing to map chaotic dynamics in phase space, revealing Arnold diffusion and the critical role of complete 3D deformation. The results show that increased 3D deformation lowers the onset of chaotic diffusion and enhances phase-space mixing, with refractive escape governed by the critical angle $\chi_c = \sin^{-1}(1/n)$. The methodology provides a general, nondestructive route to characterize complex photonic structures and enable accurate chaotic dynamics analysis applicable to broader studies in nonlinear and quantum chaos.

Abstract

Chaotic microcavities play a crucial role in several research areas, including the study of unidirectional microlasers, nonlinear optics, sensing, quantum chaos, and non-Hermitian physics. To date, most theoretical and experimental explorations have focused on two-dimensional (2D) chaotic dielectric microcavities, while there have been minimal studies on three-dimensional (3D) ones since precise geometrical information of a 3D microcavity can be difficult to obtain. Here, we image 3D microcavities with submicron resolution using X-ray microcomputed tomography (micro CT), enabling nondestructive imaging that preserves the sample for subsequent use. By analyzing the ray dynamics of a typical deformed microsphere, we demonstrate that a sufficient deformation along all three dimensions can lead to chaotic ray trajectories over extended time scales. Notably, using the X-ray micro CT reconstruction results, the phase space chaotic ray dynamics of a deformed microsphere are accurately established. X-ray micro CT could become a unique platform for the characterization of such deformed 3D microcavities by providing a precise means for determining the degree of deformation necessary for potential applications in ray chaos and quantum chaos.

Figures (5)

• Figure 1: Fabrication of deformed microspheres. (a) Schematic diagram of the experimental setup. Optical microscope images of (b) a rotationally symmetric microsphere and (c) a deformed (asymmetric) microsphere.
• Figure 2: X-ray $\mu$CT characterization of a deformed microsphere. (a) Illustration of the X-ray $\mu$CT setup and workflow. The projection images are obtained by rotating the sample in increments of $\theta$. The raw output of the tomogram is a series of projections of the sample taken at different viewing angles. The iterative reconstruction output can be visualized in both 3D rendered volume and 2D cross-sectional slices. (b) Projection images of the deformed microsphere at different $\theta$. (c) 3D rendered volume result of the deformed microsphere. (d) 2D cross-sectional slice results of the deformed microsphere at different positions along the $z$ axis.
• Figure 3: Dependence of the voxel size. (a) Schematic diagram of the X-ray $\mu$CT system, showing its two-stage magnification technique. The object illuminated by the X-rays is a microsphere in our case. (b) Voxel size at various source-to-object distances ($d_{\text{SO}}$) and detector-to-object distances ($d_{\text{DO}}$). A 20$\times$ objective was used.
• Figure 4: Computational results illustrating the evolution of ray trajectories in a deformed microsphere under varying deformation levels.. (a--e) Ray trajectory in real-space (left panel) and two selective SOSs (middle and right panels). A single trajectory starting in the plane inclined ($\sim5$ degrees) from the vertical ($z$-axis) with $\text{sin}(\chi_0)=0.9+0.01*(\sqrt{2}-1)$ was followed for about 1,000,000 reflections in (a--d) and 100,000 reflections in (e), respectively. The deformation $\{q,e,d\}$ is $\{0,0,0\}$ in (a), $\{0.005,0,0\}$ in (b), $\{0.005,0.06,0\}$ in (c), $\{0.005,0.06,0.05\}$ in (d), and $\{0.02,0.08,0.05\}$ in (e), respectively. Black dashed line: critical line $\text{sin}(\chi_c)=1/n$.
• Figure 5: Surface fitting results. Extracted surfaces from X-ray $\mu$CT data in STL (stereolithography) format (left panel) and the fitting results using \ref{['Eq1']} for a rotationally symmetric microsphere (a) and a deformed (asymmetric) microsphere (b) with a deformation of $\{q,e,d\}=\{0.02,0.08,0.05\}$.