1D leaky-wave antenna based on a sinusoidally modulated reactance surface, implemented with a biased graphene sheet, for operation at 

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... and all the reflections at the periodic discontinuities add in phase back to the input port, determining a purely reactive input impedance and large mismatch. 3 The issue of poor broadside radiation in periodic leaky-wave antennas has been one of the main motivations to pursue novel metamaterial-inspired designs, as we discuss in the following. Another important category of leaky-wave antennas is represented by quasi-uniform structures, which are also characterized by a periodic modulation of their geometry. In this case, however, the fundamental mode is a fast wave, as in uniform structures, and the period is chosen to be small enough such that radiation comes only from the fundamental mode, and is not coupled to other space harmonics [7]. In general, quasi-uniform structures with subwavelength period can be conveniently modeled with effective homogenous material parameters or surface impedance concepts. Although in quasi-uniform leaky- wave antennas the periodicity does not play a direct role in determining the radiation, since the fundamental mode is already a fast wave, the periodic modulation can be used to control the attenuation and phase constants of the leaky mode. A basic example of quasi-homogenous leaky-wave antenna is the so-called holey waveguide , first introduced in [26], in which a series of closely spaced holes is realized on the short side of a rectangular waveguide. The resulting radiating structure is quasi-uniform, as the leakage comes from the fundamental space harmonic of the periodic structure. Compared to a uniform slitted waveguide, this design has the advantage of providing smaller attenuation constants (and thereby a narrower beam), since the periodic holes do not completely disrupt the current lines on the waveguide wall, as a long slit would do [8]. A recent example of quasi-uniform radiating structures are the leaky-wave antennas based on transmission-line metamaterials, which allow controlling the complex propagation constant of the leaky modes to a large extent [25], as we discuss in the next subsection. While historically 1D leaky-wave antennas have been the most explored geometries at microwave frequencies, 2D geometries have been attracting increasing attention in the past years, since several designs based on metamaterial concepts belong to this category. 2D leaky-wave antennas consist of a planar guiding structure, e.g., a parallel-plate waveguide with a partially reflective wall, supporting a cylindrical leaky wave radially propagating outward from the source (which may be a short dipole embedded in the open guiding structure). Notably, 2D leaky-wave antennas with homogenous or quasi-homogenous geometry can realize, at a given frequency, a directive pencil beam at broadside, with maximum broadside radiation when the phase and attenuation constants of the leaky mode are nearly equal [7], [8]. At other frequencies, the radiation will be in the form of a conical beam with axis parallel to the surface normal. Typical 2D leaky-wave structures are based on partially reflective metallic screens, or grounded dielectric and metamaterial slabs [7], [8]. A few examples involving metamaterials will be discussed in the following subsection. Recent trends in leaky-wave antenna research include the planarization, miniaturization and tunability of the antenna structure, as well as the possibility to achieve continuous frequency scanning over the entire angular range, including broadside, which may be facilitated by exploiting metamaterial concepts, as discussed next. Another important trend is the investigation of leaky- wave antennas for frequencies above the millimeter-wave region, in particular the optical frequency range, which will be the main subject of Section IV. Planar leaky-wave antennas often involve periodically- modulated surfaces and artificial surfaces, e.g., patterned metallic screens, which offer further degrees of freedom in the design of their leakage properties. The investigation of such artificial surfaces is an important research direction, also in relation to the rising field of metasurfaces V the planarized version of metamaterials V particularly at optical frequencies [27]–[29]. Leaky waves on periodic surfaces were first investigated by Oliner and Hessel in their studies of guided waves on sinusoidally-modulated reactance surfaces [30]. Although this work was mainly motivated by improving the performance of endfire surface wave antennas, it has inspired many leaky-wave antenna designs (e.g., [31], [32]), in which the sinusoidal modulation allows an indepen- dent control of the phase and attenuation constants of the leaky mode. Interestingly, these ideas have also been recently applied to the THz frequency range, in the form of sinusoidally-modulated graphene leaky-wave antennas [33], [34]. In these designs, the complex conductivity of the graphene sheet can be modulated by applying DC bias voltages at different gating pads along the structure, as shown in Fig. 4, or launching an acoustic wave traveling along the surface, allowing a unique dynamic control of the leaky-wave radiation from the surface. Another important related concept is the one of high-impedance surfaces , introduced by Sievenpiper, Yablonovitch, and co-workers [35]. While a perfect electric conducting surface allows propagation of transverse magnetic (TM) surface waves, but forbids transverse electric (TE) ones, a high impedance surface behaves as an artificial magnetic conductor, which provides the dual operation, forbidding TM surface waves, but supporting TE propagation in the form of leaky waves. High-impedance surfaces owe their interesting properties to periodic structures with a resonant unit cell, as shown in Fig. 5(a) and (b), which corresponds to a lumped inductor-capacitor (LC) resonator. The dispersion diagram for a typical artificial surface of this kind is depicted in Fig. 5(c), within the first Brillouin zone of the periodic structure. As seen from this diagram, the high impedance surface can be employed as a leaky- wave antenna by using the leaky portion of the TE mode above the ‘‘light line,’’ namely, for k k G != c , where k k is the parallel wavenumber of the surface wave, ! is the angular frequency and c the speed of light in vacuum. As usual, the main beam can be scanned with frequency, following the dispersion of the leaky mode; alternatively, it is also possible to steer the beam at a fixed frequency by changing the resonance frequency of the LC unit cell, which results in a modification of the modal dispersion as shown in Fig. 5(c). Based on these principles, several tunable and reconfigur- able leaky-wave antennas have been proposed, which exploit a modification of the capacitance and/or inductance of the unit cell obtained with different mechanisms, e.g., mechanically [36], or electronically [37]. Notably, artificial impedance surfaces have also been used to realize holographic surfaces [38]–[41], which have been interestingly connected to leaky-wave antennas [42]. Moreover, artificial surfaces with subwavelength resonant unit cells in a leaky-wave antenna configuration have been recently exploited as ‘‘metamaterial apertures’’ for computational imaging [43], [44]. Other important advances for leaky-wave antennas have come from the field of transmission-line metamaterials, introduced independently by Caloz and Itoh [45], Eleftheriades, and co-workers [46]–[48], and Oliner [49], [50], in the early 2000s. The application of composite right/left handed (CRLH) transmission-line metamaterials to leaky-wave antennas has led to several important breakthroughs in this area of research and technology, the most important being the possibility of continuously scanning the main beam through broadside [51], [52]. As discussed above, conventional periodic leaky-wave antennas suffer from the open stopband problem, which leads to beam degradation when approaching the broadside direction. From a transmission-line point of view, it was realized that any periodic structure with only series or shunt radiating elements would always exhibit an open stopband at broadside [25]. A CRLH metamaterial is composed of a transmission-line structure (e.g., a microstrip line) altered by periodically loading it with so-called ‘‘left- handed elements,’’ namely capacitances in series and inductances in parallel, which are combined with the elements of a conventional transmission line, i.e., per- unit-length series inductances and shunt capacitances [25]. The unit cell of a CRLH metamaterial and an example of its practical implementation are shown in Fig. 6(a) and (b). When the unit cell periodicity is subwavelength, the structure is quasi-uniform, and radiation occurs from the fundamental n 1⁄4 0 mode, which is a fast wave. The dispersion diagram in Fig. 6(c) (blue curve) shows that the fundamental mode has indeed a branch with negative phase velocity (backward radiation; antiparallel phase and group velocity) at lower frequencies, and a branch with positive phase velocity (forward radiation) at higher frequencies, separated by a gap at 1⁄4 0, which corresponds to the open stopband of the periodic structure. The edges of this bandgap are determined by the resonance frequency of the series and parallel branches of the unit cell, which are generally different [25]. These considerations reveal that the open stopband at the broadside point can be completely closed (Fig. 6(c), red curve) by designing a ‘‘balanced’’ structure with identical series and shunt resonance frequencies, corresponding to the following condition for the inductances and capacitances of the unit cell [53], ...