We theoretically investigate the control of a magnetic Feshbach resonance using a bound-to-bound molecular transition driven by spatially modulated laser light. Due to the spatially periodic coupling between the ground and excited molecular states, there exists a band structure of bound states, which can uniquely be characterized by some extra bumps in radio-frequency spectroscopy. With the increasing of coupling strength, the series of bound states will cross zero energy and directly result in a number of scattering resonances, whose position and width can be conveniently tuned by the coupling strength of the laser light and the applied magnetic field (i.e., the detuning of the ground molecular state). In the presence of the modulated laser light, universal two-body bound states near zero-energy threshold still exist. However, compared with the case without modulation, the regime for such universal states is usually small. An unified formula which embodies the influence of the modulated coupling on the resonance width is given. The spatially modulated coupling also implies a local spatially varying interaction between atoms. Our work proposes a practical way of optically controlling interatomic interactions with high spatial resolution and negligible atomic loss.
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