## 1 Introduction
This specific configuration, commonly called \"Sun-facing\", can be maintained during heliocentric flight in a passive manner. Indeed, according to [PERSON] [25], this useful characteristic can be obtained, appropriately designing the shape of the sail structure and carefully choosing the distribution of masses in order to have a suitable position of the center of mass relative to the center of pressure, i.e., designing a slightly conical sail with the apex directed towards the Sun. The presence of a transverse component of the thrust vector when the attitude is Sun-facing is a peculiarity of the diffractive sail craft, since an RSS produces exclusively an outward radial thrust in this configuration. The RSS, for example, exploits a Sun-facing attitude in a heliocentric scenario to reduce the local value of the Sun's gravitational acceleration and, therefore, to generate non-Keplerian orbits, which can however be described still through classical conic sections [25]. On the other hand, an RSS must vary the orientation of its nominal plane with respect to an orbital reference frame and, therefore, must perform an appropriate attitude maneuver [26], both to generate a transverse thrust component of appreciable magnitude and to direct the sail-induced thrust vector towards a specific direction, which is usually obtained through the solution of a suitable optimal control problem [27]. A Sun-facing diffractive sail, instead, is able to change the azimuthal direction of the transverse component of the local thrust vector by simply rotating the sail nominal plane around the Sun-sailcraft (radial) direction. This interesting property has been exploited by [PERSON] et al. [28] to investigate the transfer performance of a diffractive sailcraft in obtaining a large change in the inclination of a given heliocentric orbit, and by [PERSON] et al. [29] to obtain the optimal flight time in a typical interplanetary mission that requires the transfer between two assigned Keplerian orbits. However, in the context of a two-dimensional mission scenario involving a diffractive sailcraft, [PERSON] [2] proposed another simple and elegant strategy to modify (i.e., reverse in this two-dimensional case) the verse of the transverse component of the thrust vector without rotating the sail nominal plane along the radial line. More precisely, the method illustrated in section 3.B of [2] is based on the employment of a set of electro-optically controlled diffractive panels, which use a binary metamaterial arrayed grating to vary the direction of photons leaving the membrane's film. This solution allows for rapidly \"switching\" between two opposite, but equal in modulus, diffraction orders [2]. From a trajectory design point of view, this type of binary characteristic of the (controlled) diffractive film can be used to change the direction of the transverse component of the sail-induced thrust by 180 deg, simply by applying an appropriate voltage to the diffractive panels. In broad terms, this ingenious design concept recalls that used in the Japanese solar sail IKAROS [30], that is, the first RSS deployed in an interplanetary environment, to achieve attitude control via a set of electrochromic panels installed on the edge of the sail's square membrane. Starting from the work of [PERSON] [2], the interesting paper by [PERSON] et al. [31] extends the concept of controlling the transverse component of the diffractive sailcraft's thrust using a set of liquid crystal optical phased arrays, which are also able to generate suitable (and adjustable) torques without employing other devices. The model proposed in [31], although more complex than the one originally discussed in [2], is elegant in its analytical form and can be potentially used to design the trajectory of future generations of advanced, electro-optically controlled diffractive sailcraft.