Metamaterials[共50页]

1、Introduction of Metamaterials,Many desired electromagnetic properties, similar to the case of monopole magnets, seem tobe lacking in nature even though there are no physical laws preventing the existence of such phenomena,Metamaterials,The prefix “meta” means “beyond,” and in this sense the name “me

2、tamaterials” signifies systems that are beyond conventional materials. The word “metamaterial” first appeared in literature in 2000 when Smith et al. published their seminal paper on a structured material with simultaneously negative permeability and permittivity at microwave frequencies,Metamateria

3、ls are defined a metamaterial as “an arrangement of artificial structural elements, designed to achieve advantageous and unusual electromagnetic properties” Such a definition,although it addresses the “artificial” nature of metamaterials, is perhaps overly inclusive and fails to recognize the import

4、ant difference between metamaterials and other man-made structures such as photonic crystals. Many leading experts in the field prefer to put terms like “properties unlike any naturally occurring substance” or “not observed in nature” in the definition of a metamaterial. These definitions usefully e

5、mphasize the major pursuit of metamaterial research to achieve electromagnetic features not found in conventional materials. However, it might be too glib to exclude any naturally occurring property from the focus of metamaterial research. Negative refraction has been astonishingly observed in compo

6、und eyes of some lobsters,A metamaterial is an artificially structured material which attains its properties from the unit structure rather than the constituent materials. A metamaterial has an inhomogeneity scale that is much smaller than the wavelength of interest, and its electromagnetic response

7、 is expressed in terms of homogenized material parameters. The structural units of a metamaterial, known as meta-atoms or meta-molecules, must be substantially smaller than the wavelength being considered, and the average distance between neighboring meta-atoms is also subwavelength in scale. The su

8、bwavelength scale of the inhomogeneities in a metamaterial makes the whole material macroscopically uniform, and this fact makes a metamaterial essentially a “material” instead of a device,The Lycurgus Cup viewed (a) in reflected light and (b) in transmitted light,Perhaps one of the first modern met

9、amaterials with engineered, subwavelength meta-atoms was attributed to the “twisted jute” material proposed by Bose in 1898 to produce an artificial chiral effect. Artificial dielectrics, which are usually periodic arrays of metallic wires, spheres or plates, were studied extensively by microwave en

10、gineers more than half of a century ago. Other examples of metamaterials or their elements developed before the term metamaterial was coined include the split-ring resonators , arrayed frequency filters, bianisotropic and chiral materials, and others,In our opinion, there are three milestone papers

11、that should be mentioned in this regard. The first is Veselagos paper on lefthanded materials. This paper studied the strikingly unusual phenomena to be expected in a hypothetical left-handed substance in which the field vectors E, H and the wave vector k form a left-handed system. The paper also ex

12、plicitly presented the required material parameters to achieve the material simultaneously negative values of permittivity and permeability. The first experimental demonstration of a Veselago medium by Smith et al., which makes the huge leap from a theoretical prediction to experimental validation.

13、The third seminal paper is Pendrys work on a perfect lens 21, which represents the initial attempt to fill the gap between novel metamaterials and exciting applications,optical metamaterials Light is the ultimate means of sending information to and from the interior structure of materials it package

14、s data in a signal of zero mass and unmatched speed. The burgeoning optical metamaterial research activities are a result of the combination of a wealth of nanofabrication techniques with advances in nanoscale imaging and computational electromagnetic design and simulations. Within the rapidly devel

15、oping and highly multidisciplinary field of optical metamaterials, several key research directions have been emerging, including optical magnetism, optical negative index materials, giant artificial chirality, nonlinear optics in metamaterials, super resolution with metamaterials, and electromagneti

16、c cloaks of invisibility,Optical metamaterials revolutionarily altered the way that people propose and design functional optical devices. Materials used in conventional optical designs are usually both homogeneous and isotropic; therefore the design of devices is largely an issue of engineering the

17、interfaces between different media. For instance, in the lens-making industry, cascaded lenses of different materials with finely controlled curvatures are often used to minimize multiple types of aberrations. The emergence of photonic metamaterials allows us to tailor optical space and provide new

18、responses that are precluded in the constituent materials,The design strategy of optical devices is radically changed when metamaterials are involved the desired functionality is achieved not only by configuring the interfaces between different materials, but by the control of essentially every sing

19、le point in optical space. This enables applications using novel, spatially varying architectures of metamaterials where the electromagnetic properties of every position are carefully prescribed. Optical metamaterials can have numerous and far-reaching implications. These materials bring the promise

20、 of creating entirely new prospects for controlling and manipulating photons, and they provide potential benefits in various fields including optical sensing, miniature antennae, novel waveguides, subwavelength imaging, nano-scale photolithography and photonic circuits,Macroscopic Effective Paramete

21、rs,Conventional materials,the permittivity and the permeability the refractive index n=sqrt(*) and the impedance Z =sqrt(/) Origin of the permittivity and permeability parameters of materials. Microscopically, a piece of crystal consists of atoms arranged in a periodic manner with a lattice constant

22、 of a few angstroms. On the atomic scale, in each atom or molecule, tiny electric dipoles can be excited by the electric component of incident light, and subsequent radiation of the energy in the dipoles occurs with a certain delay in time. The excited dipoles create a periodic local field in the cr

23、ystal, referred to as Lorentz local field; therefore the field distribution inside the crystal is certainly not uniform. Macroscopically, the detailed features and responses of the inhomogeneous structure are averaged, and relationships can be established between the macroscopic field vectors in Max

24、wells equations, namely the electric field E, the magnetic field H, the electric displacement field D, and the magnetic flux density B,At optical frequencies, this complicated physics is usually described using the transmittance and reflectance of light with a certain retardation (delay) in addition

25、 to the energy absorbed in the material, and a complex value of the refractive index or permittivity is used to describe such phenomena,Optical metamaterials,The inhomogeneity scale corresponds to the lattice constant of the artificial structure for the case of periodic metamaterials. Therefore, tho

26、ugh the interaction between electromagnetic fields and meta-atoms is quite complicated at the scale of the inhomogeneities, macroscopically the wave feels a homogeneous medium. Furthermore, similar to the treatment of conventional materials, the electromagnetic responses of the metamaterial to exter

27、nal fields can be homogenized and are described using effective parameters including the permittivity, permeability, refractive index and impedance. From the point of view of Maxwells equations, a material is a collection of subwavelength units with global properties described by permittivity and pe

28、rmeability . Through the dedicated design of meta-atoms, which is usually a delicate metal-dielectric structure, metamaterial research allows us to tailor the electromagnetic response of media in an unprecedented manner,Since the response of a material to external fields is largely determined only b

29、y the two material parameters permittivity and permeability , we can use an electromagnetic parameter space to classify materials based on the two values,Optical Properties of Metal Dielectric Composites,Optical Materials and Electronic Structures,Simplified energy band diagram for a typical dielect

30、ric, semiconductor, and metal,In a crystalline solid, for example, discrete energy levels are created due to the covalent bonding of atoms in the crystal lattice. These allowed energy levels are lumped into two energy bands, the conduction band and the valence band. The valence band consists of nume

31、rous closely spaced levels which are mostly filled by electrons, while the conduction band represents electronic levels at higher energies that are mostly unoccupied. The two bands are separated by an energy region where no electron states are allowed. The width of this empty energy region, called a

32、 band gap or forbidden band, determines whether a substance is a dielectric, semiconductor or conductor,In optics, however, it is the photons that excite electrons in the valence band. Therefore, the critical consideration becomes the comparison of photon energy and the bandgap of a crystal, which s

33、pecifies the shortest wavelength (the “critical” wavelength) atwhich the dielectric remains transparent. The critical wavelength is related to the bandgap Eg by,Band gap and critical wavelength of common dielectrics at roomtemperature,Optical Properties of Dielectric Materials,Maxwell equations,At o

34、ptical frequencies, the relative permeability is taken normally to be unity. This condition substantially simplifies our description of optical materials transparent ones in particular by assigning a refractive index n=sqrt(epsilon) to each medium,At optical frequencies, the oscillation of the elect

35、ric field is so fast that the bound charges in atoms or molecules are unable to follow the electric field in time. Consequently, (2.2a) does not hold in the time domain for the high requencies of the optical range. Instead, the electromagnetic response of the medium described by D(t ) at time t depe

36、nds not only on the electric field E at that moment, but also on the value of E at all past times. Hence the constitutive relation has to involve time operators (convolution) as follows,Fortunately, the proportionality is still valid for the relationship between D and E in the frequency domain, as l

37、ong as the material being considered is a linear medium (which means the susceptibility is independent of the strength of the electric field). We therefore write the frequency-domain constitutive relationship as: The dielectric function can be expressed in a classical HelmholtzDrude model,Two resona

38、nces are included in the oscillator formula, with omega1 representing the phonon resonance in the mid-infrared, and omega2 corresponding to the electron transition in the UV range due to the bandgap of the crystal. The dielectric function exhibits a Lorentz line shape at each resonance along with a

39、distinct peak in the imaginary part of epsilon, which indicates the loss feature associated with the resonance,The dielectric function for a typical dielectric material with the lattice resonance and electron transition resonance,Between the two resonance frequencies, the permittivity curve is rathe

40、r flat with a negligible imaginary part. This explains why a common dielectric like quartz or alumina is transparent to the visible light. The real part of exhibits a Lorentz line shape around each resonance. The real part is large and positive at the low-frequency side of the resonance, and it has

41、a negative value when the frequency is slightly higher than that of the resonance. A negative value implies that the response is directed opposite to the electric field E,The dielectric function for a typical dielectric material with the lattice resonance and electron transition resonance,The positi

42、ve and negative electromagnetic responses around a resonance. The three spring-mass oscillators are used as a mechanic analogue of the scenario,The simple square-root relationship between the refractive index and the permittivity still holds in the frequency domain. Therefore the frequency-dependent

43、 refractive index n(omega), being a complex value in the general case, is related to the dielectric function by: n : refractive index or the index of refraction; n”: is referred to as the absorption index,Since the imaginary part n” is negligibly small (usually less than 1e-5) for common transparent

44、 dielectrics in the visible range, the refractive index of such materials can be modeled in a form similar to (2.5) without involving the imaginary part or the damping constants. In this situation, (2.5) reduces to the widely used Sellmeier dispersion formula: For weakly absorptive media, the absorp

45、tion coefficient alpha is routinely used to characterize the attenuation of light propagating in the material. The absorption coefficient is the exponential index appearing in Beers law. Since the electric field E changes along the propagation direction following the function exp(i2pi (n+in”)z/lambd

46、a_0), and the intensity is proportional to E2, so,Optical Properties of Metals,In optical metamaterials, however, most of the designs being studied incorporate metals in the unit structure of the metamaterial. The sharp contrast between the optical response of metals and that of dielectrics is essen

47、tial to making meta-atoms functional elements. In this section we briefly review the physical processes involved in light-metal interactions and emphasize the modification of metal behaviors at the nanoscale. Typically optical properties: opaque and high reflectivity. Origin: The Fermi level in meta

48、ls sits inside a continuous energy band, and there is no gap between the empty energy levels and the occupied ones. Consequently, the photon energy from any electromagnetic radiation is enough to excite an electron to a higher level. Since the empty electron states are continuously available, light

49、of all frequencies that enters into a metal can be absorbed within a tiny propagating length, usually less than 100 nanometers,From (2.11) and (2.2a), we obtain the frequency dependence of the dielectric function: where omega_p is the volume plasma frequency at which the density of the electron gas

50、oscillates,Note that the damping constant Gama , which represents the electron collision rate, is absolutely necessary to provide an imaginary part in epsilon. Sometimes the inverse of Gama the mean electron collision time tor is used in the Drude model. Hence the damping constant is related to the electron mean free path l and the Fermi velocity vF by,In fact, the influence of such transitions is still needed to supplement the Drude mode