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DESCRIPTIONDescribes Application of Layered Metallo-Dielectric Medium
One Dimensional Metallo-Dielectric Structures and their ApplicationsI. Introduction
It is known that both electrons and electromagnetic waves have both particle and wave nature. From solid state physics, it is also known that when an electron wave travels in a periodic potential of a crystal, they are arranged into discrete energy bands separated by energy bands called Band Gaps. Analogues to this, EM waves travelling in a periodic structure experience frequency band gaps, and the waves which fall in this gap do not propagate. These frequency gaps are called as Photonic Band Gaps (PBG). (Soukoulis, 1996)
Nearly all early applications of PBGs have been in optical domain and numerous techniques and structures for the application of PBGs have been proposed in literature. Many of these devices have electronic analogs. Some of these are (Scalora, 1998):
1. Optical Transistor or Switch: This is an optical limiter that allows the propagation of a low intensity beam of light, while it reflects a high intensity beam. When used in combination with a second reference beam, it has been shown that the limiter can operate as an optical transistor or switch.2. Optical Diode: a beam can either be reflected or transmitted through a device depending on the direction of approach: right propagating waves may be reflected, while a left propagating signal may be transmitted. 3. Frequency Up Converter: These are second harmonic generator that utilizes band-edge and nonlinear effects to provide the phase matching needed for efficient frequency up-conversion. All these early band gap structures have a generic structure as shown in Figure 1, which are composed of alternating high and low index layers. Each layer can be chosen such that its width is a fraction of the size of a reference wavelength, usually one quarter of the reference wavelength. This forms a quarter wave stacks. As a consequence of this arrangement of the dielectric layers, interference effects cause some wavelengths to be transmitted, while a range of wavelengths centered about the reference wavelength, often referred to as band-gap wavelengths, are completely reflected (Soukoulis, 1996).
Figure 1. Transmittance vs frequency for the generic PBG structure shown in the inset (Scalora, 1998)Typically, the materials used in the fabrication of PBG structures are dielectric or semiconductor substances, due to their low absorption characteristics. The main concern over the material choice is, however, that the materials used should not absorb light to any significant extent, so as not to compromise device operation. For this reason, metallic substances are almost exclusively used to enhance the reflective properties of dielectric or semiconductor materials by designing and incorporating within particular device thick metallic films, such as silver, nickel, copper, aluminum, or gold.
Nevertheless, owing to the interesting properties metallic inclusions inside dielectrics exhibit a number of 2-D and 3-D PBG structures have been studied and applied to various applications in both Optical (Scalora, 1998) and lower RF frequency domains. At the RF frequency they are however categorized into Electromagnetic Band Gap Structures (EBG), which have been widely used previously in Antenna applications for miniaturization and surface wave reduction. But in all these cases only the reflective property of metals is used.In this report the focus is on the applications of transmissive properties of Metals by using alternate layers of metals and dielectrics. At this point it is important to notice that, we know from skin depth theory that externally incident waves will propagate approximately these respective distances inside the metal, depending on the incident wavelength, before most of the part is reflected back. However, the concept of skin depth is applicable only when the wave is incident on uniform, thick, highly reflective, metal films. However, we find that the concept of skin depth looses its meaning in the case of a periodic structure, where the presence of closely spaced boundaries, i.e., spatial discontinuities of the index of refraction, alters the physical properties of the structure as a (Scalora, 1998). The important modifications include;1. Effective group velocity near the band edge
2. Transmission and Reflection Coefficient
3. Absorption Coefficient inside the metal.
It is worth noticing that each of this modification of properties from conventional thick metal could be used separately in different applications. In the following sections firstly a brief theory and results reported in (Scalora, 1998) on One Dimensional Metallo-Dielectric Photonic Band Gap Material is presented, followed by some of its applications in Optical Frequency Domain (section II), low frequency power line applications (section III) and some limited applications at Microwave frequencies (section IV).II. 1 D Meallo-Dielectric Material at Optical Frequencies1. StructureSimilar to the generic PBG Structure shown in figure 1, the 1 D Meallo-Dielectric structure has alternating layers of Metals and dielectric. The usual metals used are gold, silver and copper. For the material separating the metal films a low loss dielectric or semiconducting materials may be used (Soukoulis, 1996). The individual metal layers are required to be as small as possible (of the order of skin depth), however, the net thickness across the entire structure may be a hundreds of skin depth. The thickness of the dielectric layers may be greater than skin depth.
2. Examples and Theory
Figure 2 shows an example of the 1 D Meallo-Dielectric structure and its Transitivity compared to a single layer of metal, in this case silver (Ag). These calculations are performed using Transmission Matrix Method. It is shown here that this sample transmits 2.5% of the incident red light, 8% of green light, and about 15% of blue light for the case of single solid Ag layer. Thus, this film is fairly opaque to visible light. However, if original 40 nm film is sliced into four films each about 10 nm in thickness, and space each Ag layer with approximately 110 nm of MgF2 then the total transmission of visible light increases to an average of 70%. Another similar example is shown in figure 3, for longer periodicity and compared to 200nm thick silver layer. Similar to the generic materials involving only dielectric materials the periodicity determines the number of peaks/ valleys in the transmission coefficient. Also, increasing the overall thickness reduces the transitivity of the material.
Figure 2. Transmission vs wavelength for a four-period PBG sample (solid line) and a solid silver film 40 nm thick (dotted line). Silver layers are 10 nm thick, while the MgF2 layers are 110 nm thick. (Scalora, 1998)Inherently, these structures could be used for shielding or other transparent circuits. Figure 4 shows a plot for three layers of 30nm thick Ag layers staked between 140nm thick MgF2 layers using Transmission Matrix Method (TMM) method and in Figure 5 using drude model approximation, which hold the best for metals. It can be seen here though the transmission properties are found to accurate the drude model fails to predict the transmission occurring due to the plasma resonance of metals.It was also shown in (Scalora, 1998)that it is also possible to use a combination of two or more metals, or two or more types of dielectric or semiconductor materials within the same structure, without any significant departure from the basic characteristics that we have described. The frequency range where light is transmitted can be changed by either increasing or decreasing the thickness of the magnesium fluoride layers. Increasing the thickness of the dielectric material cause a shift of the band structure toward longer wavelengths.
Figure 3. Same as Fig. 2, except that for the PBG sample MgF2 layers are 140nm thick, and the solid silver film is 200 nm thick. (Scalora, 1998)
Figure 4 TMM- Transmission vs wavelength for a Ag/MgF2 PBG (solid line) and the continuous silver film (dotted line) (Scalora, 1998)
Figure 5 Drude model - Transmission vs wavelength for a Ag/MgF2 PBG (solid line) and the continuous silver film (dotted line) (Scalora, 1998)
The physical interpretation of this high transmission through these structures may be explained using resonant enhanced tunnelling of Electromagnetic waves in periodic structures similar to the electron tunneling effect through crystal lattice. The optical path of the 40 nm silver film is only approximately where is the wavelength of light in silver. The introduction of a second metal layer, and hence additional boundary conditions, can create the right set of circumstances that lead to a kind of induced transparency such that the effective absorption coefficient inside the metal is also suppressed. This suggests that boundary conditions cause a significant redefinition of skin depth for metals. (Scalora, 1998)
In (C Sibilia, 1999) it has been shown that the transitivity and the operational frequency can further be optimized by using quasi periodic structures (Figure 6), for the results on transitivity see (C Sibilia, 1999). Proposed applications for these structures include sensors, UV blocking films, transparent electrodes for light-emitting polymer stacks, and conductive displays just to name a few. Figure 6 (a) Periodical multilayer, (b) 3-stage Cantor-like multilayer, (c) Fibonacci multilayer, (d) chirped set (C Sibilia, 1999)III. Laminated Conductors at Low Frequency Power Transmission
We have seen in the previous section that 1-D layered metal-dielectric structure could be used to make an electromagnetic wave penetrate(transmitted) more into metallic medium before they are absorbed (lost) in the material due to its high conductivity. In this section implementation of similar techn