Physics and applications of negative refractive index materials pdf
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- Physics of Negative Refraction and Negative Index Materials
- Optics Express
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The underlying mechanism originates from the different existence conditions for TE graphene plasmons in negative and positive refractive-index environments. In their seminal work in , Mikhailov S. Another key feature for TE graphene plasmons is the spatial confinement. Note that highly confined surface plasmons 2 , 3 , such as the transverse magnetic TM, or p -polarized graphene plasmons 4 , 5 , 6 , 7 , can enable the flexible control of light flow in the subwavelength scale and even the extreme nanoscale; as such, they can enable many promising applications, including the on-chip terahertz to X-ray radiation sources 8 , 9 , miniaturized modulators 10 , subwavelength guidance 11 , 12 , 13 , deep-subwavelength imaging 14 , 15 , 16 , 17 , and light energy harvesting and scattering 18 , 19 , Here the skin depth 21 is defined as the penetration depth of the evanescent fields carried by graphene plasmons into the surrounding environment.
As severely limited by the weak spatial confinement, only several potential applications of TE graphene plasmons have been reported, such as Brewster effects 22 , polarizers 23 , optical sensors 24 , waveguide phase, and amplitude modulators On the other hand, rapid progress in nano-photonics has fuelled a quest for highly confined TE graphene plasmons, in addition to the highly confined TM graphene plasmons. This way, highly confined graphene plasmons can be achieved without stringent requirement on the polarization of light and can benefit more practical applications based on TE waves.
Such a quest still remains elusive, although many researches of TE polaritons in graphene 26 , 27 , 28 , 29 and other 2D materials 30 , 31 , 32 , 33 , 34 have been ignited by the pioneering work in Here we theoretically reveal a viable way to largely enhance the spatial confinement of TE graphene plasmons by using the environment with the negative permeability or refractive index.
In principle, the environment with the negative permeability or refractive index can be effectively constructed, for example, by metamaterials 36 , 41 , 51 and photonic crystals 52 , 53 , 54 , We find the existence condition of TE graphene plasmons in negative refractive-index environments is drastically different from that in positive refractive-index environments.
We focus on the discussion of TE surface plasmons supported by the monolayer graphene. Figure 1 shows the general existence condition for TE graphene plasmons. The monolayer graphene is located at the interface between region 1 and region 2 Fig.
From the classical electromagnetic wave theory see Supplementary Notes 1 and 2 , the dispersion for TE graphene plasmons is governed by. Equation 2 explicitly indicates the existence condition for TE graphene plasmons, as briefly summarized in Fig.
On the other hand, Eq. This way, the minimum skin depth of TE graphene plasmons in negative permeability environments would be much smaller than that in positive permeability environments.
Then in negative permeability environments, these parameters could enable us the capability to flexibly modulate the basic features of TE graphene plasmons Figs. In addition, the loss in the surrounding environment is artificially neglected, since the reasonable amount of loss will not have a drastic influence on the confined TE graphene plasmons.
In c the colored dots are extracted from b ; the black solid line i. Figure 2 shows the influence of relaxation time on TE graphene plasmons in negative refractive-index environments, from the perspective of the in-plane wavevector. According to Eq. If the relaxation time increases i. Such a large value of n eff,0 is favored for the practical application of TE graphene plasmons. In short, if the temperature or the chemical potential increases, the achievable maximum value of n eff,0 for TE graphene plasmons would increase, e.
We note that in Fig. This phenomenon is caused by the fact that in Eq. Correspondingly, if the temperature or the chemical potential increases, the minimum skin depth of TE graphene plasmons would decrease Fig.
Moreover, it is worthy to highlight that the phenomenon of the temperature-induced large enhancement of the spatial confinement for TE graphene plasmons is only exists in negative refractive-index environments Fig. The setup of monolayer graphene is the same as that in Fig. From Fig. Importantly, these TE graphene plasmons can become highly confined in the direction perpendicular to the graphene plane.
To be specific, their skin depth can decrease down to the deep-subwavelength scale e. Then the existence of these highly confined TE graphene plasmons should be robust to various surrounding environments i. Such a feature is drastically different from the weakly confined TE graphene plasmons in the positive refractive-index environment, which exist mainly in the almost symmetric environments the substrate and superstrate should have the negligible difference in their permittivity or permeability 1 , Our findings in this work further indicate that the negative refractive-index materials might serve as a versatile platform to enable more practical applications of TE graphene plasmons, such as subwavelength guidance, some exotic scattering phenomena of light, and the exploration of TE plasmons in controlling the free electron radiation e.
Without loss of generality, the monolayer graphene is located at the interface between region 1 and region 2 Fig. For TE graphene plasmons, their electric fields are along the y direction. According to the electromagnetic theory 19 , one can set the electric fields in each region as. By enforcing the boundary conditions:. The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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Physics of Negative Refraction and Negative Index Materials
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Negative-index metamaterial or negative-index material NIM is a metamaterial whose refractive index for an electromagnetic wave has a negative value over some frequency range. NIMs are constructed of periodic basic parts called unit cells , which are usually significantly smaller than the wavelength of the externally applied electromagnetic radiation. The unit cells of the first experimentally investigated NIMs were constructed from circuit board material, or in other words, wires and dielectrics. In general, these artificially constructed cells are stacked or planar and configured in a particular repeated pattern to compose the individual NIM. For instance, the unit cells of the first NIMs were stacked horizontally and vertically, resulting in a pattern that was repeated and intended see below images. Specifications for the response of each unit cell are predetermined prior to construction and are based on the intended response of the entire, newly constructed, material.
It seems that you're in Germany. We have a dedicated site for Germany. Editors: Krowne , Clifford M. This book deals with the subject of optical and electronic negative refraction NR and negative index materials NIM.
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Metamaterials possess extraordinary linear optical properties never observed in natural materials such as a negative refractive index, enabling exciting applications such as super resolution imaging and cloaking. In this thesis, we explore the equally extraordinary nonlinear properties of metamaterials. Nonlinear optics, the study of light-matter interactions where the optical fields are strong enough to change material properties, has fundamental importance to physics, chemistry, and material science as a non-destructive probe of material properties and has important technological applications such as entangled photon generation and frequency conversion. Due to their ability to manipulate both linear and nonlinear light matter interactions through sub-wavelength structuring, metamaterials are a promising direction for both fundamental and applied nonlinear optics research.
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Им станут известны имена и местонахождение всех лиц, проходящих по федеральной программе защиты свидетелей, коды запуска межконтинентальных ракет. Мы должны немедленно вырубить электроснабжение. Немедленно. Казалось, на директора его слова не произвели впечатления. - Должен быть другой выход. - Да, - в сердцах бросил Джабба.
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