Resonances
in optical systems are useful for many applications,
such as frequency comb generation, optical filtering, and biosensing.
However, many of these applications are difficult to implement in
optical metasurfaces because traditional approaches for designing
multiresonant nanostructures require significant computational and
fabrication efforts. To address this challenge, we introduce the concept
of Fourier lattice resonances (FLRs) in which multiple desired resonances
can be chosen a priori and used to dictate the metasurface
design. Because each resonance is supported by a distinct surface
lattice mode, each can have a high quality factor. Here, we experimentally
demonstrate several metasurfaces with flexibly placed resonances (e.g.,
at 1310 and 1550 nm) and Q-factors as high as 800
in a plasmonic platform. This flexible procedure requires only the
computation of a single Fourier transform for its design, and is based
on standard lithographic fabrication methods, allowing one to design
and fabricate a metasurface to fit any specific, optical-cavity-based
application. This work represents a step toward the complete control
over the transmission spectrum of a metasurface.