1. Introduction

Surface plasmons (SPs) are electromagnetic waves that are confined on and propagate along and the surface of a conductor, usually a metal or a semiconductor [1]. SPs are caused by the resonant oscillation of the free electrons in the conductor with the incident electromagnetic waves. The resonant oscillation can be denoted by a characteristic frequency—the plasma frequency ωp, which decides the scale of the free electrons response to time-varying perturbations [2]. Since SPs depend on the free electron motions, it can be imagined that an external

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

magnetic field may have modulations on the SPs, due to the Lorentz force which can change the response of carriers. In this situation, another characteristic frequency called cyclotron frequency ω<sup>c</sup> is often used, which is a function of the effective mass of the charge carriers and the strength of the applied magnetic field [3]. One of the important consequences of magnetizing the plasmons is that the polarizability becomes highly anisotropic (the permittivity of the conductor becomes a tensor)—even though the medium is isotropic when the magnetic field is not applied. Therefore, SPs may have different properties when they are propagating under an external magnetic field. In this situation, they are usually called surface magneto plasmons (SMPs) [4].

as �10<sup>3</sup> Tesla, which is difficult to realize in laboratories. So far, there are two ways to solve this problem. One is using ferromagnetic materials, such as Ni and Co in nanostructures [50– 57]. By this method, the intensity of the applied magnetic field can be decreased to a scale of �mT. But it introduces large loss. The other solution is using semiconductors instead of metals in THz regime to decrease both ω<sup>p</sup> and ω. ω<sup>p</sup> of a doped semiconductor can be decreased in an order of �1013 Hz. Therefore, the required external magnetic field can be less than 2 Tesla. Some researches of SMP devices consisting of semiconductors have also been proposed

In this chapter, we will introduce the basic theory of SMPs in the Voigt configuration and their applications in SMP devices design. In Section 2, we will give the dispersions of SMPs on a surface, in a metal-insulator-semiconductor structure, and in a semiconductor-insulatorsemiconductor structure of the Voigt configuration. The nonreciprocal effect and the two propagating bands will be discussed. In Section 3, some intriguing plasmonic devices based on the SMPs will be presented, including one-way waveguides, broadly tunable THz slow

The first theory of SMPs on a conductor plane surface in the Voigt configuration was presented by Chiu et al. [8]. However, they only found the nonreciprocal effect. In the same year, Brion et al. gave a more comprehensive study on SMPs, including the nonreciprocal effect and the two propagating bands [4]. They also gave an explanation of why the higher band appears. We will give a review of his research in this section. Although the energy of SMPs is confine on the plane surface, the confinement is not subwavelength scale (in the order of �2–3λ). In order to solve this problem, in this section, we derive the dispersion of SMPs in a slot waveguide, which can confine light in 1/10 λ in the lateral direction [63–66]. Some results are very similar with that in Ref. [4], while some are quite different. For example, the nonreciprocal effect is elimi-

The schematic structure is shown in Figure 1. The material of x < 0 is a metal or a semiconductor, and its surface is oriented to +x-axis. The SMPs is propagating along the z-axis. In the Voigt configuration, the applied magnetic field B is applied along the y-axis. Then the permittivity of

> εxx 0 εxz 0 εyy 0 �εxz 0 εxx

3 7 7

5: (1)

Surface Magneto Plasmons and Their Applications http://dx.doi.org/10.5772/intechopen.79788 91

ε ¼

light waveguides, and focal-length-tunable plasmonic lenses.

nated in a symmetric structure [63].

2.1. Dispersion of SMPs on a plane surface

the metal/semiconductor becomes a tensor:

The parameters in Eq. (1) have the expressions of

2. Theory of SMPs on a surface and in a slot waveguide

recently [58–62].

SMPs can be divided in three principal configurations, according to three directions—the orientation of applied magnetic field B, the propagation of the surface wave k, and the surface. The first one is called perpendicular geometry, in which B is perpendicular to both the surface and k. The second one is called Faraday geometry, in which B is parallel to the surface and k. The third one is called Voigt geometry, in which B is parallel to the surface and perpendicular to k. Compared with traditional SPs, SMPs have several unique properties. For instance, SMPs in perpendicular geometry and Faraday geometry can support pseudo-surface waves, which means they attenuate on only one side of the surface [5, 6]. SMPs in this Voigt configuration support nonreciprocal effect, which means the SMP dispersions are different when they propagate along two opposite directions. In addition, unlike SPs only has one propagating frequency band which is below the plasma frequency [2], SMPs support two propagating bands.

The basic theory of SMPs in the perpendicular configuration was first given by Brion et al. [5] in 1974. Then, in the same year, Wallis et al. reported the theoretical study of SMPs in the Faraday configuration [6]. In 1987, Kushwaha [7] gave the theoretical derivation of SMP on a thin film in the Faraday configurations. For the Voigt configuration, the pioneer work was implemented by Chiu et al. [8] and Brion et al. [4] as early as 1972, separately. Then De Wames and coworkers studied the dispersion relation of Voigt-configured SMPs on a thin film [9]. Then SMP properties considering holes [10], optical phonons [11–13], diffuse electron density profiles [14], and metal screen [15] were theoretically proposed. They were also studied both theoretically and experimentally in various structures [16–27]. In 2001, a review work of SMP was given [28].

In recent years, due to the extraordinary optical transmission through periodic holds in nanometer scale, which is found in 1998 [29], numerous plasmonic devices, made of metals, have been theoretically proposed and experimentally realized in the visible frequencies [1, 30]. Compared with studies about SPs before 2000 [31–40], these structures have been mostly focused on the subwavelength confinement of electromagnetic waves [41]. For example, in the slot waveguides [42] or metal-insulator-metal structures [43], electromagnetic waves can be confined in a space as small as 0.1λ. Inspired by these structures, some SMP devices composed of metals were proposed [44–49]. However, all of these SMP structures are difficult to realize because they require unreachable magnetic fields. The reason is that in order to observe the effect of an external magnetic field, it requires ωp, ω<sup>c</sup> and the incident angular frequency ω be comparable. However, for a metal in the visible frequencies, ω<sup>p</sup> and ω are usually in the order of 1016 and 1015 Hz, respectively. Therefore, it needs a magnetic field as strong as �10<sup>3</sup> Tesla, which is difficult to realize in laboratories. So far, there are two ways to solve this problem. One is using ferromagnetic materials, such as Ni and Co in nanostructures [50– 57]. By this method, the intensity of the applied magnetic field can be decreased to a scale of �mT. But it introduces large loss. The other solution is using semiconductors instead of metals in THz regime to decrease both ω<sup>p</sup> and ω. ω<sup>p</sup> of a doped semiconductor can be decreased in an order of �1013 Hz. Therefore, the required external magnetic field can be less than 2 Tesla. Some researches of SMP devices consisting of semiconductors have also been proposed recently [58–62].

In this chapter, we will introduce the basic theory of SMPs in the Voigt configuration and their applications in SMP devices design. In Section 2, we will give the dispersions of SMPs on a surface, in a metal-insulator-semiconductor structure, and in a semiconductor-insulatorsemiconductor structure of the Voigt configuration. The nonreciprocal effect and the two propagating bands will be discussed. In Section 3, some intriguing plasmonic devices based on the SMPs will be presented, including one-way waveguides, broadly tunable THz slow light waveguides, and focal-length-tunable plasmonic lenses.
