Two design strategies are presented to create dual-band frequency selective surfaces based on multi-arm Archimedean spirals. A single-band element is first presented as the basis for the surface. The individual arm lengths of the spirals are utilised as the primary design parameter to synthesise the passband and stopband responses. The first approach uses a lattice of four-arm spirals with alternating sizes, and the second combines these into an eight-arm uniform lattice of elements. Measured and simulated results are included for a fabricated S-band prototype of each topology to demonstrate the basic design strategies.Introduction: The ubiquitous use of wireless technologies in communications, sensing, and automation has thrown light on many new applications of frequency selective surfaces (FSSs). This includes the design of electromagnetic architectures in buildings and other spaces to enhance information security, control wireless coverages, and provide a number of other functionalities which extend the use of the FSS beyond more traditional applications such as radome design, antenna sub-reflectors, radar cross-section reduction, and electromagnetic interference reduction [1][2][3]. Fundamentally, the FSS acts as a spatial filter for electromagnetic waves the unit cell configuration of which governs its frequency response. There are a number of singleand multi-band design strategies as well as frequency tuning. Some recent examples of multi-band designs use fractal FSSs [4] or passive structures [5] that use reactive loading mechanisms to alter their frequency response.In general, the synthesis of a FSS unit element can present many challenges. Iterative approaches using numerical simulations can be used to explore the design space, but they offer little physical insight into the fundamental operation of the structure when the topology is geometrically complex and/or sub-wavelength. This Letter examines the topology of the Archimedean spiral as a sub-wavelength resonant element from which first principles are used to predict the approximate passband or stopband response. Other work has been done on Archimedean spiral FSSs [6,7], but the focus has been on an experimentally quantitative analysis of the surface's polarisation properties. However, it is possible to synthesise a dual-band response by only manipulating the geometry of the unit cell(s). In this Letter, the synthesis of a single-band structure is examined first along with its complementary topology to link the geometry to the performance metrics of the FSS. Next is a discussion of two approaches for creating a dual-band structure, where simulated and measured results are included for each of the design procedures. The Letter concludes with a brief discussion on the performance of the two designs, and the extension of the concepts to other related topologies.