Perfect absorbers, which can achieve total absorption of all incoming energy, have been extensively studied in the last decades for various important technologies in general wave systems. Here, we show that perfect absorption (PA) is generically associated with topological spectral phase singularity (SPS), carrying conserved and tunable quantized topological invariants in spectral space. The order of topological invariant $\tilde{v}$ depends on the number of degenerate outgoing channels. Two commonly studied absorbers, mirror-backed and all-dielectric structures, are reexamined from a topological perspective to reveal the generation, evolution, and annihilation of SPSs with $\tilde{v}=\pm 1$ or even high orders (i.e., $\tilde{v}=\pm 2,\pm 4$). A strategy based on charge conservation of SPSs to design dual-band perfect absorbers has been established. Our findings establish the topological origin of the robust existence of PA. More broadly, in this letter, we highlight topology as the fundamental property of conventional scattering behaviors. This insight could lead to opportunities in applications such as biosensing, topological metasurfaces, and micro/nano thermal radiation.

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• Light-matter interaction
• Nanophotonics
• Optical & microwave phenomena
• Topological effects in photonic systems