Being able to achieve a lower diffraction limit, the focusing of light is intellectually intriguing and important for application possibilities. It may be employed to manipulate and image biomolecules at a higher precision, resolution and depth of focus with propagating light, to sense the structure and dynamics of biological and physical systems at a smaller scale, to diagnose and modify material surfaces with greater precision. In addition, it allows to remove the limit on photolithography, which is the key issue preventing the further progress of the semiconductor industry according to Moore’s Law, to craft finer circuits, to produce and read smaller spots for optical storage, to focus light for optical detection/imaging and into photonic and plasmonic circuits [77],to connect optical
systems and finer electronic circuits, among many others. The physical mechanisms might be used in applications required for the processing of optical information and thus in communication and optical computing processes.
In summary, the physical mechanisms of the innovative approach using a miniature FAB lens are demonstrated to focus light to a single-line with its width smaller than the conventional diffraction limited value in the intermediate zone of 2 < kr < 4. It is quantitatively verified that the involvement of near-field in the focused fields is negligible. As of result of being able to propagate light, this scheme can be superior to those based on the involvement of the near-field.
Besides the academic interest generated by the physical mechanisms and the approach, the light focusing process is expected to open up a wide range of application possibilities, especially with regard to the capabilities of the focused light being able to propagate, tuning the focal point position and reducing the sizes of the focused light spot and the corresponding devices. The result has been accepted to be published [83]
3 Strategy for designing epsilon-near-zero nanostructured metamaterials over a frequency range
3.1 Introduction
Epsilon-near-zero (ENZ) materials may be used as optical “insulators” for the displacement currents in optical nanocircuits, improving the directivity of antennas and transmission efficiency of waveguides with sharp bends, far-field subdiffraction optical microscopy, tailoring the wave front of arbitrary light sources, the transmission of subwavelength Gaussian beams, etc [78].
3.2 Background and current conditions
Dealing with a single frequency limits the possibilities for a practical implementation of ENZ metamaterials. Nevertheless, so far nobody has designed such materials ensuring the low permittivity over a frequency range. It is well-!"#$"%&'(&%)&%)*%+(*,%&#%-./-)//%&'+%0#"1)&)#"%2 0 at a frequency of interest using a composite with layered or filament geometry. Using effective medium theory we show that the same condition can be fulfilled over a frequency range and develop our concept for designing broadband ENZ metamaterials.
3.3 Research purpose
Consider a composite made of parallel layers (see Figure 15). Each layer has its own permittivity i.The volume fraction of the ith layer is fi; the applied electric field is normal to the layer interfaces. Because the normal component of the displacement is continuous at the boundaries, the effective permittivity of the composite effmay be written as the harmonic average,
FIG. 15. Schematic of the composite: the unit cell consisting of 7 parallel layers.
1
eff i fi i
&' (
)
& . (3)If now i =0 for any layer then eff =0 for the whole composite. Having closely located zeros of iin a frequency range, we get the condition effeff 0 over the range.
How to obtain zeros of i? Many mixing rules allow it for two-phase composites with properly chosen parameters. So, we could design each layer in the form of metal cylinders with the permittivity m and filling factor fim inside a dielectric with the permittivity d and filling factor fid, or could consider parallel cylindrical holes inside a metal. In both cases the applied electric field is directed along the dielectric/metal interfaces, and the permittivity of each ith layer is the arithmetic average, layers and fi= 1/11 (the layers are of uniform thickness). To null the permittivity in the range 650 nm – 750 nm, we could design the layers with i =0 at regularly spaced wavelengths 650, 660, …, 750 nm, so that the interval !"between adjacent nulled wavelengths is 10 nm. To null the permittivity in the range 675 nm – 725 nm, the interval is 5 nm. To null the permittivity in the range 685 nm – 715 nm, the interval is 3 nm. Furthermore, let d=1.8 and silver with a frequency-dependent permittivity &m (&m+ *i&m++ be a metal phase. Having found fid and fim at the corresponding frequencies, one gets eff from Eqs. (3) and (4). Using the Drude model for silver, we calculated eff(see Figure 16). Actually, | eff | is small in the considered ranges, but Re( eff) passes through zero at the only wavelength close to the range center (700 nm). Thus, more complicated structure should be used to ensure the condition Re( eff)34%#5+6%&'+%6("7+8
FIG. 16. Spectra of | eff|, Re( eff), and Im( eff) for nanocomposites with different intervals between adjacent nulled frequencies.
Generally, Re( eff) may be arbitrarily close to zero over a frequency range.
Formally, the problem reduces to minimizing the objective function
,
-1
Re ;
M
eff fi d
.
. & . .
/
where the factors fi are fitting parameters. The objective function in the form of the mean square deviation from zero may be also chosen.The numerical solution of the problem is a standard mathematical procedure and presents few difficulties.
Schematically, two possible geometries of the composite can be represented as in Figure17.
FIG. 17. Possible geometries of composites under consideration.
The first geometry may be imagined as a forest of metal wires of varied width inside a dielectric or, alternatively, an array of dielectric channels of varied width inside a metal. For the circular wires, the metal filling factor in the ith layer, fim, may be related to the corresponding radius, ri, via fim=#$%i2, where N is the wire concentration.In the case of the circular channels, the dielectric filling factor in the ith layer fid = 1- fim= #$%i2
. The other geometry is an array of parallel channels of varied length. For cylindrical metal channels of equal width, the metal filling factor in the ith layer fim= Ni$%2. The thickness of the ith layer ti=fih, where h is the total thickness of the cell.
For demonstration, consider nulling Re eff9:;%)"%three ranges with the spectral
$)1&'*% <44=% >44% ("1% ?44% "@% 0+"&+6+1% (&% ABCC4% "@% 9*++% D)7.6+%18). For the narrowest range 500 nm – 600 nm, breaking the range into ten intervals (!A= 10 nm) and fitting the parameters fi yield |Re eff9:;EF4844C%)"*)1+%&'+%G("d 512-581 nm.
For the range 450 nm – 650 nm (!A= 20 nm) one gets oscillating Re eff9:;%$)&'%&'+%
oscillation amplitude less than 0.02 inside the band 475-625 nm. For the widest range 400 nm – 700 nm, breaking the range into twenty intervals (!A= 15 nm) and fitting the parameters fiyield oscillating Re eff9:;%$)&'%&'+%#*0)//(&)#"%(@H/)&.1+%"#&%
exceeding 0.008 inside the band 415-675 nm.
FIG. 188% IH+0&6(% J+92eff) for nanocomposites with different intervals between adjacent nulled frequencies.
Our results show how to improve the efficiency of nulling. As the effective medium approximation is valid, even for a range as wide as desired, it is possible to
get Re eff(&) arbitrarily close to zero by enlarging the number of the cell layers. The optimum number of the layers depends on how drastically the permittivity changes within the range.
3.5 Summary and conclusion
We have, for the first time, proposed a general technique for designing broadband ENZ metamaterials using the effective medium theory. Yet, it is a crude approximation, and we feel a need for a more sophisticated technique. If the losses are small, the dielectric response of ENZ metamaterials can become nonlocal [79];
we hope to address this issue in our future work. We have considered only one specific geometry and may not claim that it is the best one.
ENZ metamaterials considered above are anisotropic like single axis crystals.
In many cases, however, this is not a critical issue, for example, when dealing with far-field optical microscopy, directive emission in metamaterials, or cloaking techniques based on the scattering cancellation [80]. This result have been published [84]
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5 ीฝԋ݀Ծຑ
Relativistic cyclotron instabilities have received much attention and found applications in many research fields such as radiation sources, fusion plasmas and astronomy. In order to maintain the resonance between wave and particles, the uniformity of the external magnetic field is always an important issue. As a well-known requirement being consistent with all theoretical studies and experimental observations, the frequency mismatch between the wave and the harmonic gyro-frequency of particles must be positive for driving relativistic cyclotron instabilities. However, in this project, we demonstrated that the instabilities can survive even when the magnetic variation is much larger than the Lorentz factor minus one. The instability under sinusoidal nonuniform magnetic fields has been investigated via, respectively, a hybrid particle-in-cell simulation and analytic methods, adopting a parabolic magnetic field approximation. Both the simulation and the theory show that the wave mode can exist where its frequency is smaller than the local harmonic cyclotron frequency, violating the well-known requirement for driving relativistic cyclotron instabilities. In addition to possible applications to fusion plasmas, this study may also be helpful for electron cyclotron instability and application, especially for high harmonic and for tunability.
The diffraction limit concerns travelling light that can propagate freely in the free space, in contrast to the evanescent near-field that is electrostatic or magnetostatic, needs a preferred plane or surface for propagation and cannot propagate freely in the free space, such as occurs in a super lens. In this project, a new understanding and a different approach with the excitations of surface plasmon on metallic surfaces and surface-plasmon-like modes through subwavelength holes/slits were shown to produce a beyond-the-limit focusing of travelling light. The innovative approach and physical mechanisms of the focusing aperture beyond the conventional diffraction limited line width (FAB) of half the wavelength are demonstrated here with the FAB lens including a metallic film with a double-slit and a patterned exit structure. In this project, we have shown that a lower diffraction limit can be achieved using the FAB lens at the intermediate zone in which there is such a small single-line width occurring with regard to the focused light. Being able to achieve a lower diffraction limit, the focusing of light is intellectually intriguing and important for application possibilities. It may be employed to manipulate and image biomolecules at a higher precision, resolution and depth of focus with propagating light, to sense the structure and dynamics of biological and physical systems at a smaller scale, to diagnose and modify material surfaces with greater precision. In addition, it allows to remove the limit on photolithography, which is the key issue preventing the further progress of the semiconductor industry according to Moore’s Law, to craft finer circuits, to produce and read smaller spots for optical
storage, to focus light for optical detection/imaging and into photonic and plasmonic circuits, to connect optical systems and finer electronic circuits, among many others.
The physical mechanisms might be used in applications required for the processing of optical information and thus in communication and optical computing processes.
Epsilon-near-zero (ENZ) materials may be used as optical “insulators” for the displacement currents in optical nanocircuits, improving the directivity of antennas and transmission efficiency of waveguides with sharp bends, far-field subdiffraction optical microscopy, tailoring the wave front of arbitrary light sources, the transmission of subwavelength Gaussian beams, etc. Dealing with a single frequency limits the possibilities for a practical implementation of ENZ metamaterials. Nevertheless, so far nobody has designed such materials ensuring the low permittivity over a frequency range. In terms of the effective medium theory, we propose a general solution to such a fundamental problem as designing nanostructured materials with the very low permittivity (epsilon-near-zero metamaterials) over a frequency range. ENZ metamaterials considered above are anisotropic like single axis crystals. In many cases, however, this is not a critical issue, for example, when dealing with far-field optical microscopy, directive emission in metamaterials, or cloaking techniques based on the scattering cancellation.