## 1 Introduction  
The diffractive sail [1, 2] can be considered a sort of evolution of the more classical reflective solar sail (RSS), which, as is well known, converts the Sun's solar radiation pressure into a propulsive thrust through the aid of a large (and sufficiently light) reflective surface, thus making a spacecraft propelled by an RSS resemble a large orbiting mirror that moves in space without consuming propellant [3]. In the context of an RSS and other currently available propellantless propulsion systems as, for example, the Electric Solar Wind Sail [4, 5] or the Magnetic Sail [6, 7], the recent review article by [PERSON] et al. [8] offers an interesting analysis of the technologies available today and a comprehensive discussion of their possible advances in the near future. The useful review articles by [PERSON] et al. [9] or by [PERSON] and [PERSON] [10], while slightly older than Ref. [8], instead focus exclusively on the potentialities of RSSs, allowing the interested reader to also appreciate the evolution of this fascinating space propulsion concept over the decades, starting from the pioneering works of [PERSON] [11] and [PERSON] [12] to arrive at the recent space missions that have effectively tested this type of spacecraft thruster in space [13; 14]. A historical perspective on the development of that propellantless propulsion system can also be found in [PERSON]'s now classic book [15], which places particular emphasis on the rapid evolution of solar sail technology due to JPL's mid-1970s project (unfortunately, only at the proposal stage) to launch an RSS-based mission to [PERSON]'s comet. Unlike a typical and well-known RSS, the diffractive sail, proposed by [PERSON] [2] in his seminal 2017 work, exploits the behavior of an advanced metamaterial that constitutes the film covering the membrane of the sail to obtain a thrust vector whose properties cannot be obtained from a classical RSS, which in fact passively reflects the photons coming from the Sun [16]. In this context, the recent work of [PERSON] et al. [17] compares the flight performance and the design of a (more general) transmissive sail with that of a typical RSS under realistic conditions. The original mathematical model proposed by [PERSON] in 2017 [2] has recently been refined in a 2022 paper by the same author [18], which analyzes in detail the momentum transfer efficiency, obtainable by a diffractive sail that maintains a fixed attitude in an orbital reference frame, as a function of the characteristics of the sail film's prism grating. Moreover, a simple thrust vector model for a diffractive sail is also illustrated in [1], while the work by [PERSON] et al. [19] extends the diffractive sail concept by studying an advanced (and passively stable) laser-driven sail. This latter solution, which can actually be considered an evolution of the diffractive sail concept, could constitute a valid alternative to more conventional propulsion systems for the design of advanced scientific missions such as those, for example, requiring reaching the boundaries of the Solar System [20] or even traveling into interstellar space [21]. In this regard, the works of [PERSON] et al. [22] and [PERSON] et al. [23] provide a recent snapshot of the current state of research in this rather advanced propulsion system concept, while the paper by [PERSON] et al. [24] analyzes the required characteristics of the material of the sail's membrane in a set of high-energy mission scenarios. In the field of a diffractive sail-propelled spacecraft (in the rest of the paper indicated as \"diffractive sail craft\"), as widely discussed in Refs. [2; 18], among the attractive properties of such propulsion system, one of the most interesting is the possibility of generating a transverse (i.e., an off-radial component of the) thrust even when the nominal plane of the membrane is perpendicular to the line joining the Sun to the space vehicle. In that case, the transverse component of the thrust vector has a fixed direction in a body reference frame.