Cosmology analogy for perfect hyperlens

With the emergence of super-resolution lenses such as superlens and hyperlens, coupled with advancements in metamaterials, the diffraction limit of approximately half wavelength is no longer unbreakable. However, superlenses are easily affected by weak intrinsic losses and hyperlenses cannot achieve perfect imaging, significantly constraining their practical utility. To address these challenges, here we propose a perfect hyperlens based on the metric of de Sitter spacetime in cosmology. Importantly, perfect hyperlens is capable of self-focusing in geometrical optics while supporting propagating waves with exceptionally large wavenumbers, which endows it with key advantages such as ultra-high resolution, no aberration and strong robustness. Furthermore, we demonstrate the hyperbolic focusing performance and mimic the de Sitter spacetime in naturally in-plane hyperbolic polaritons of {\alpha}-MoO3 films numerically, which can be achieved with a gradient thickness profile. Our work provides cosmological insights into the field regulation in hyperbolic materials, greatly innovates the design principles of traditional imaging lenses.