Photonic crystals (PCs) are nano-scale, dielectric structures with periodically varying refractive index and unique light propagation properties. Recently, PCs with tunable structural and optical characteristics under external stimuli have garnered extensive attention due to their potential application in smart optical devices. Liquid crystal polymers (LCPs) can generate recoverable deformation upon exposure to external stimuli. Recent experimental studies have demonstrated the tunability of PC films on LCP substrates under thermo- and/or photo-stimuli, which was primarily attributed to the bending of the bilayers. Furthermore, based on Timoshenko's classical bimetallic model, the reflective band shift has been assumed to be proportional to the bending curvature. In this study, based on some analytical solutions that extend the classical model, we demonstrate that the band shifts are proportional to the upper-surface transversal strain that is closely connected but generally not proportional to the bending curvature of the PC/LCP bilayer. Furthermore, it is found that the incorporation of spontaneous bending in addition to spontaneous contractions in the LCP substrates can be extremely helpful for the tunability of PC. This can be achieved either by programming the liquid crystal alignment or/and by light attenuation. The optimized bilayer structures exhibit immense potential to generate large reflective band shifts, especially for relatively softer PC films on stiffer LCP substrates. Overall, our results provide useful insights on the design of tunable PCs and other stimuli-responsive bilayer structures.
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