Magnetic interaction between photons and dipoles is essential in electronics, sensing, spectroscopy, and quantum computing. However, its weak strength often requires resonators to confine and store the photons. Here, we present mode engineering techniques to create resonators with ultrasmall mode volume and ultrahigh quality factor. In particular, we show that it is possible to achieve an arbitrarily small mode volume only limited by materials or fabrication with minimal Q degradation. We compare mode-engineered cavities in a trade-off space and show that the magnetic interaction can be strengthened more than $10^{16}$ times compared to free space. These methods enable new applications from high-cooperativity microwave-spin coupling in quantum computing or compact electron paramagnetic resonance (EPR) sensors to fundamental science such as dark matter searches.
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