Exploiting Structural Flexibility in SIM-Enabled Communications: From Adaptive Inter-Layer Spacing to Fully Morphable Layers

Stacked intelligent metasurfaces (SIMs) have recently emerged as a promising metasurface-based physical-layer paradigm for wireless communications, enabling wave-domain signal processing through multiple cascaded metasurface layers. However, conventional SIM designs rely on rigid planar layers with fixed interlayer spacing, which constrain the propagation geometry and can lead to performance saturation as the number of layers increases. This paper investigates the potential of introducing structural flexibility into SIM-enabled communication systems. Specifically, we consider two flexible SIM architectures: distance-adaptive SIM (DSIM), where interlayer distances are optimized, and stacked flexible intelligent metasurface (SFIM), where each metasurface layer is fully morphable. We jointly design the meta-atom positions and responses together with the transmit beamformer to maximize the system sum rate under per-user rate, quantization, morphing, and interlayer distance constraints. An alternating optimization framework combining gradient projection, penalty-based method, and successive convex approximation is developed to address the resulting non-convex problems. Perturbation analysis reveals that the flexibility gains of both DSIM and SFIM scale approximately linearly with the morphing range, with SFIM exhibiting a faster growth rate. Simulation results demonstrate that flexible SIM designs mitigate performance saturation with increasing layers and achieve significant transmit power savings compared to rigid SIMs.