File Name: physics and applications of negative refractive index materials .zip
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.
Click here to see what's new. The refractive index is a basic parameter of materials which it is essential to know for the manipulation of electromagnetic waves. However, there are no naturally occurring materials with negative refractive indices, and high-performance materials with negative refractive indices and low losses are demanded in the terahertz waveband. The terahertz metamaterial with these unprecedented properties can provide various attractive terahertz applications such as superlenses with resolutions beyond the diffraction limit in terahertz continuous wave imaging.
Terahertz metamaterials [ 1 ] are artificial materials with subwavelength structures and can manipulate terahertz waves such as absorber [ 2 ], antireflection coating [ 3 ], and polarization conversion [ 4 ]. Metamaterials have evolved into metadevices [ 5 ] for active control of terahertz waves with various external modulations such as optical pump [ 6—8 ], electric field [ 9,10 ], temperature [ 11 ], and Micro Electro Mechanical Systems MEMS [ 12 ].
Metamaterials can provide unprecedented refractive indices such as negative refractive indices due to the direct control of the relative permittivity and permeability. A material with a negative refractive index would make possible a perfect lens [ 13 ] and superlenses [ 14 ] with resolutions beyond the diffraction limit in imaging. The work in [ 15,16 ] was the first to report a negative refractive index utilizing the meta-atoms of split ring resonators and metal wires in the microwave band.
A steric structure consisting of metal rings and wires has demonstrated near perfect imaging beyond the diffraction limit in the microwave band [ 17 ]. A low-loss metamaterial with a negative refractive index would be essential, especially for high resolutions even though conductor and dielectric losses are in principle unavoidable.
However, it is not straightforward to demonstrate an ideal metamaterial in the terahertz waveband because the dimensions of the meta-atoms are of the order of ten to a hundred microns, and this considerably limits the design flexibility of steric structures. Further, substrates are commonly required to be able to fabricate metamaterials, but there are few materials with low losses in the terahertz waveband. Two-dimensional metamaterials, meta-surfaces, have a high potential utility in the terahertz waveband as the application of a lamination structure would make bulky metamaterials with a three-dimensional structure possible.
Some papers have reported measurements and simulations of meta-surfaces with a negative refractive index in the terahertz wave band which were composed of several meta-atoms, such as an I-shaped structure [ 18 ], a cross-shaped structure [ 19 ], and symmetrically aligned paired cut metal wires [ 20 ]. The simultaneous dielectric and magnetic resonances of two-dimensional meta-atoms here enable the achievement of negative refractive indices.
A high figure of merit FOM , the real part over the imaginary part in a complex refractive index, is a barometer of the utility in low-loss materials. Work on negative refractive indices has discussed FOMs able to obtain a desirable metamaterials with negative refractive indices and low losses: among these one [ 18 ] measures a FOM of 1. Various structures of negative refractive index metamaterials have also been reported in the terahertz waveband such as short-slab pair and wires [ 21 ], bi-layer S-strings [ 22 ], close-ring pair [ 23 ], Mie resonance [ 24 ], and fishnet [ 25—27 ].
A terahertz metamaterial with a negative refractive index enables terahertz imaging beyond the diffraction limit due to the restoration of a terahertz evanescent wave.
Terahertz imaging has the potential to evolve into game changing industrial applications because terahertz waves can be transmitted through objects that are opaque to visible light and enables visualization of inner structures. In [ 28 ] terahertz near-field imaging with a subwavelength resolution beyond the diffraction limit was reported with probe detection of terahertz evanescent waves.
Terahertz imaging with a resonant tunneling diode RTD in [ 29 ] has utilized a propagating continuous wave CW without an evanescent wave at 0.
A material with a negative refractive index can directly integrate various terahertz CW sources for terahertz near-field imaging. Semiconductor devices such as RTD are commonly planar structures, and the integration of a two-dimensional attached structure has been utilized to obtain high gains without a bulky Si lens [ 30 ].
Terahertz sources have also developed rapidly, and the oscillation frequency of RTD has reached 1. The manipulation of terahertz waves and the miniaturization of optical systems are challenges that have to be overcome, and an unprecedented material able to achieve this [ 32 ] would be a powerful tool for the exploration of game changing terahertz applications.
The impedance matching between a material and free space due to the simultaneous control of the relative permittivity and relative permeability would enable the design of a material with high transmission power, low reflection power, and low loss. The FOM of The other reported FOM [ 19,20 ] were simulated. The metamaterial with a negative refractive index in this paper consists of asymmetrically aligned paired cut metal wires on the front and back of a dielectric substrate.
The low-loss performance suggests the potential for a three-dimensional bulky metamaterial with a negative refractive index in the terahertz waveband as well as in the microwave band. In other published work [ 33,34 ], there are reports on the performance of asymmetrically aligned paired cut metal wires as a meta-atom, and a detailed discussion of material properties related to the permittivity and permeability suggested there is necessary.
In [ 34 ] a measured dispersion diagram rather than a negative refractive index is reported. Figure 1 a shows a full model of the metamaterial with negative refractive index consisting of the asymmetrically aligned paired cut metal wires on the front and back of a dielectric substrate. The metamaterial is a self-supporting structure and would be suitable as a three-dimensional laminated metamaterial. Figure 1 b shows the design model of one meta-atom with its periodic boundary conditions.
The design model is a one-unit cell model extracted from the full model assuming periodic boundary walls around the exterior. An incident terahertz wave propagates with an electric field parallel to the y -axis.
The full model of the metamaterial is periodic along the x and y -axes. The cut metal wires on the front and back are aligned asymmetrically with a half periodicity along the y -axis. A low-loss dielectric and metal should be chosen for the metamaterial. Conductivity losses cannot be avoided as there are no perfect electric conductors that do not give rise to losses. Further, the performance of this metamaterial utilizes the resonant phenomenon of the currents on the cut metal wires.
Dielectric resonance is caused by the current on the cut metal wires induced by the electric field of the terahertz waves. The permittivity and permeability can be designed with the parameters of the cut metal wires. Scattering matrices of the design model derive the effective optical constants, such as the relative permittivity, relative permeability, refractive index, and wave impedance [ 35 ].
Table 1 shows the parameters of the cut metal wires. The dielectric substrate is a cyclo-olefin polymer with a complex refractive index n dielectric of 1. The conductor is copper with a conductivity of 5. Figure 2 shows contour maps for the real and imaginary parts of the refractive indices, the transmission power, and reflection power. The design frequency is 0. The dielectric and magnetic properties resonate simultaneously at the optimized parameters.
Terahertz CW imaging has been developed in the frequency band near 0. The length l of the cut metal wires is approximately 0. The periodicities along the x and y -axes are approximately 0.
A high transmission power is obtained for impedance matching between the metamaterial and free space due to small variations in the permittivity and permeability.
The operating principle of a negative refractive index in the metamaterial is explained by the effective optical constants as well as the equivalent circuits. A negative refractive index is caused by both negative permittivity and permeability. Permittivity and permeability denote dielectric and magnetic properties, respectively. Permittivity and permeability have negative values around the resonant frequencies for a metamaterial consisting of paired cut metal wires.
Figures 3 a and 3 b show respectively the frequency characteristics of the refractive index, relative permittivity, and relative permeability for a symmetrical structure. Figure 3 a shows that the refractive index is positive for this metamaterial of symmetrically aligned paired cut metal wires.
Figure 3 b shows that the resonance frequency of the dielectric property is stronger than that of the magnetic property in this metamaterial. Figures 3 c —3 h directly show the overlap of the negative permittivity and negative permeability, which enables a negative refractive index.
The dashed curves in Figs. The half-wavelength inside the metamaterial is smaller than the unit-cell thickness in the Bragg regime, and the effective optical constants cannot be expected to be accurate [ 36 ]. An approximate equivalent circuit can effectively explain the differences between asymmetrically and symmetrically aligned paired cut metal wires.
The dielectric resonance properties for a symmetrical structure is determined by an inductance component L d at a cut metal wire and a capacitance component C d at a gap of the cut metal wires along the direction of the electric field. The capacitance component for an asymmetrical structure increases due to the addition of a parallel capacitance C d '. The shifted distance of the cut metal wires controls the capacitance C d '.
The resonant frequency f d a is decreased with the value of the shift, and the region with a negative permittivity shifts to lower frequencies as suggested by Figs. Here, the magnetic resonance properties for a symmetrical structure is determined by an inductance component L m at the cut metal wires on the front and back and a capacitance C m at the cut metal wires on the front and back.
The inductance component L m ' and capacitance component C m ' decrease for an asymmetrical structure as the parallel circuit becomes shorter.
The shifted distance of the cut metal wires control the inductance L m ' and the capacitance C m '. The resonant frequency f m a increases with the shifted value, and the region with negative permeability shifts to higher frequencies as in Figs. The dielectric substrate is a cyclo-olefin polymer which has a measured refractive index of 1.
A cyclo-olefin polymer film with copper layers on the front and back is etched for the fabrication of the metamaterial. The copper layer is 0. Figure 5 a shows the measurements and simulations of the refractive indices. The refractive index of the measurement at 0. The terahertz path lengths in optical systems for the transmission and reflection measurements are approximately mm and mm, respectively.
The terahertz wave radiated from a photoconductive antenna is focused at the sample and reference. The focused beam at the sample and reference has spot size of approximately 2. The angle of reflection is 0 degrees for the reflection measurements. The focused beam at the sample and reference has spot size of approximately 3. The deviations between the measurements and simulation could be caused by the accuracy of THz-TDS measurements [ 37 ].
The measurements also confirm the negative refractive indices from 0. Figure 5 b shows the measured values of the transmitted and reflected power. The transmitted and reflected power are The frequency difference between the measurements and simulations is small at 0. Figure 5 c shows the measurements of the relative permittivity. The relative permittivity of the measurement at 0. Figure 5 d shows that the measurements of the relative permeability at 0.
Figure 5 e shows that the relative wave impedance, the wave impedance of the metamaterial is divided by a wave impedance in free space.
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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. We perform the first experiments on nonlinear propagation in bulk zero and negative index optical metamaterials and demonstrate that a zero index material can phase match four wave mixing processes in ways not possible in finite index materials. In addition, we demonstrate the ability of nonlinear scattering theory to describe the geometry dependence of second and third harmonic generation in plasmonic nanostructures. As an application of nonlinear metamaterials, we propose a phase matching technique called "resonant phase matching" to increase the gain and bandwidth of Josephson junction traveling wave parametric amplifers.
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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: In the past few years, new developments in structured electromagnetic materials have given rise to negative refractive index materials which have both negative dielectric permittivity and negative magnetic permeability in some frequency ranges.
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