We study a system tuned to an absorbing exceptional point and explore its use to efficiently receive and store an incoming wave with an envelope different from the absorbing-eigenmode envelope. Specifically, while absorbing states of lossless resonators have an exponentially increasing envelope, we focus on capturing naturally emitted waves with an exponentially decreasing envelope. We find that, when tuning a cavity to an $n\mathrm{th}$-order absorbing exceptional point (EP), $n+1$ temporal orders of any incoming waveform can be perfectly captured, leading to significantly less scattering and increasing the overall absorption efficiency for general waveforms. We present an approach to tune a cavity to an EP and demonstrate less scattering by an order of magnitude for a decaying incoming waveform. Our results may be used for efficient passive state transfer and detection of spontaneous emission.

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• Optical transient phenomena
• Scattering theory
• Spontaneous emission
• Atomic systems
• Molecules
• Non-Hermitian systems
• Quantum cavities
• Trapped ions