## 1 Introduction  
Beaming electromagnetic waves is highly important in communication applications and in the formation of high contrast images in medical imaging. Beaming an electromagnetic wave with high gain at multi-band frequencies normally requires a two-dimensional antenna array. At the time of writing, the majority of two-dimensional antenna arrays are embedded with a complex feeding network that simultaneously excites each antenna element, but this mechanism inevitably incurs significant losses, especially at high frequencies. In addition, two-dimensional antenna arrays are extremely bulky. There is an obvious demand for antennas with a low profile, high directivity, and the feasibility of scanning at multi-band frequencies. In this paper, we propose a methodology for designing a small-sized dual-band or multiple band antenna, which in essence overcomes the above problems, and due to its compactness, it can be used for many applications in the frequency of operation [1; 2; 3; 4; 5; 6]. One of the most unique features of left-hand materials is their negative permittivity and permeability. Over the past few decades, left-handed materials have been highly popular in the research communities because of their unprecedented characteristics. Composite right-hand/left-hand (CRLH) transmission lines have been used in the implementation of leaky wave antennas with the ability to perform frequency scanning of an electromagnetic beam from backfire to endfire. As of right now, however, most of the antennas falling into this category contain vias and interdigital structures, which not only increase the degree of design complexity, but also limit their applications. In recent years, most research groups have been focusing on novel designs that increase the pattern bandwidth of the antenna and that reduce the thickness of the antenna [7; 8; 9; 10; 11; 12; 13; 14]. The emergence of dual-band or multi-band leaky wave antennas (LWA) with CRLH structures and dual CRLH structures for beam scanning applications has enormously advanced the field of leaky wave antennas [15; 16]. Substrate integrated waveguide (SIW)-based leaky wave antennas on one the one hand are simple to design to achieve leaky wave characteristics, but on the other hand, they increase the cost. SIW leaky wave antennas leak out the energy through their holes or slots. These types of antenna can steer the beam in a forward and backward direction, which also offers dual-band operations. Recently, an SIW based on CRLH structures has been used to achieve a three-band substrate integrated waveguide leaky wave antenna. These antennas may contain two CRLH bands along with a new right-handed (RH) band in between. In our previous work [17], a modified lossy transmission line model has already been developed to analyze and to synthesize non-uniform leaky wave antennas where a forward and reverse frequency scanning has been achieved in the right-hand quadrant, but not in the left-hand region. With the help of a truncated superstrate, another leaky wave-based dual-band phased array has been achieved for on-board satellite communications with the bandwidth extended for use in the K-band (17.7-20.2 GHz) and the Ka-band (27.5-30 GHz) [17]. Some leaky wave antenna designs have been proposed recently for Ku-band applications, but are mostly based on substrate integrated waveguides. These designs have achieved good antenna performance, but at the expense of increased fabrication costs and design complexity. Furthermore, this is to point out that very limited research has been done on microstrip leaky wave antennas in the Ku-frequency band [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. In this work, the sharpness of the bends along the body of a microstrip transmission line is advantageously used to realize a fundamentally different leaky wave antenna with a broadband impedance matching and high gain characteristics in the Ku-band.