Terahertz metamaterials

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Terahertz waves lie at the far end of the infrared band, just before the start of the microwave band. In this image, an array of gold structures on top of a semiconductor base. The metamaterial and the semiconductor together form a device that can modulate the intensity of the T-rays by up to 50 percent when a voltage is applied to the gold structures. The experimental demonstration of the device exceeds the performance of existing electrical terahertz modulators

Terahertz metamaterials are metamaterials which interact at terahertz frequencies.[1] For research or applications of the terahertz range for metamaterials and other materials the frequency range is usually defined as 0.1 to 10 THz. This corresponds to the submillimeter wavelengths between 1 mm (EHF band) and 0.1 mm (long-wavelength edge of far-infrared light).[1]

Because applications of frequencies in the terahertz radiation range hold the promise of efficient advancement in important technologies, it has been important to find natural materials, or else, develop artificially constructed materials that have the desired electromagnetic response. Currently, a fundamental lack in naturally occurring materials that allow for the desired electromagnetic response has led to constructing artificial materials.[2] These artificial materials are metamaterials – a new type of artificial composite with electromagnetic properties that are derived from their sub-wavelength structure. The resonant response can be efficiently controlled for applications in optical frequency metamaterials or other types of electromagnetic metamaterials. This has resulted in the creation of efficient THz metamaterial switches and modulators of potential importance for advancing numerous real world THz applications.[2]

Furthermore, research into technologies which utilize THz frequencies show the capabilities for advanced sensing techniques. In areas where other wavelengths are limited, THz frequencies appear to fill the near future gap for advancements in security, public health, biomedicine, defense, communication, and quality control in manufacturing. Terahertz frequencies show capabilities such as passing through and imaging the contents of a plastic container, penetrate a few millimeters of human skin tissue without ill effects, clothing to detect hidden objects on personnel, the detection of chemical and biological agents as novel approaches for counter-terrorism.[3] Terahertz metamaterials, because they interact at the appropriate THz frequencies, seem to be one answer in developing materials which use THz radiation.[3]

Contents

[edit] Terahertz material parameters

Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding zero crossings as shown.

Research has established that composite metamaterials scale to 1/10 the wavelength of a source of EM radiation. The source in this case is applied electromagnetic fields. Wavelength is commonly designated by the Greek letter lambda (λ). The concept can also be applied to periodic waves of non-sinusoidal shape.[4][5] The wavelength is derived from an inverse relationship to frequency. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by:[6]

\lambda = \frac{v}{f},

where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave's frequency. In the case of electromagnetic radiation such as light in free space, the speed is the speed of light, about 3×108 m/s. As an example, the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×108 m/s divided by 100×106 Hz = 3 meters. Theoretically then a composite metamaterial interacting with a radio wave source can scale the wavelength to 30 cm.

Terahertz radiation occurs between the extremely high frequency (EHF) band, and infrared bands of the electromagnetic spectrum. The term has been accepted for the region of the electromagnetic spectrum between 100 GHz (1×1011 Hz or 0.1 THz) and 30 THz (3×1013 Hz). However, 10 – 30 THz exceeds the far-infrared band, and enters into the mid-infrared band. Much research in optical materials has already been accomplished in this range, and established technologies exist. A more convenient definition of terahertz range is between 0.1 and 10 THz, which corresponds to the submillimeter wavelengths between 1 mm (EHF band) and 0.1 mm (long-wavelength edge of far-infrared light).[1]

A recurrent issue with conventional (non-magnetic) materials is the lack of desired magnetic response. Conversely, there are common conventional materials which have a pliable electrical response. These are any metal. Negative permittivity occurs in any metal with an applied frequency from zero to the plasma frequency. A magnetic response is far less common in nature, and it is particularly rare at THz and optical frequencies. A negative permeability at optical frequencies, in particular, does not occur in natural materials.[7]

With artificially constructed metamaterials this problem is overcome. Effective magnetic permeability μeff of metamaterials can be tuned to values not accessible in nature.[8]

There have been reports of some natural magnetic materials that have responded at microwave frequencies. However, the magnetic effects in these materials are typically weak and often exhibit narrow bands, which limits the scope of possible THz devices. It was noted that the realization of magnetism at THz and higher frequencies will substantially affect THz optics and their applications.[9]

Potential terahertz frequency applications are being researched globally. Two technologies, Terahertz time-domain spectroscopy and quantum cascade lasers, which have been developed only recently throughout the past two decades. These could possibly be part of a multitude of development platforms worldwide. However, the devices and components necessary to effectively manipulate terahertz radiation require substantial development beyond what has been accomplished to date (December 2009).[10]

[edit] Rare permeability at THz frequencies

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A recurrent issue with naturally occurring materials is the lack of the desired magnetic response.[7][11] Light or EM radiation is, very much ‘one-handed’ when interacting with conventional or naturally occurring materials. This is because the magnetic component of the source EM radiation remains relatively unused in naturally occurring materials. This has to do with magnetic coupling at the atomic level. This drawback can be overcome by using metamaterials that mirror atomic magnetic coupling, on a scale magnitudes larger than the atom.[11]

Materials which can couple magnetically are particularly rare at terahertz or optical frequencies.[7][9] However metamaterials are helping to fill this gap. Metamaterials which respond to terahertz frequencies are making it feasible to design and construct systems with desired magnetic (paramagnetic) and electrical properties.[9][11]

Magnetic response and electromagnetic coupling at terahertz frequencies was accomplished in 2004.[9] A type of metamaterial was constructed from a combination of split ring resonators and thin wires which are nonmagnetic conductive resonant elements. The magnetism, called paramagnetism, is induced but temporary because of the nature of the material.[7][9][11] However, researchers believe that artificial magnetic (paramagnetic) structures, or hybrid structures that combine natural and artificial magnetic materials, can play a key role in terahertz devices. Some THz metamaterial devices are compact cavities, adaptive optics and lenses, tunable mirrors, isolators, and converters.[2][7][9]

[edit] Magnetic response from metamaterials at 1 THz

Schematic setup of an ellipsometry experiment.

The Split-Ring Resonator (SRR) is a common metamaterial in use for a variety of experiments.[1]. Magnetic responses (permeability) at terahertz frequencies can be achieved with a structure composed of non-magnetic elements, such as SRRs, which demonstrate different responses at resonant frequencies and near resonant frequencies.[9] The desired, artificially fabricated, magnetic response is realized over a large bandwidth, and can be tuned throughout the terahertz frequency spectrum.[9] The periodic array allows the material to behave as a medium with an effective magnetic permeability µeff(ω), where ω is frequency. In other words, at resonance µeff is achieved.[9]

Effective permeability µeff is boosted from the inductance of the rings and the capacitance occurs at the gaps of the split rings. In prior microwave frequency experiments bulk metamaterial is used, such as waveguides to transmit the source of radiation. In this terahertz experiment ellipsometry is applied. In other words, a light source in free space, emits a polarized beam of radiation which is then reflected off the sample. The emitted polarization is intended and angle of polarization is known (see the section on chirality at the article entitled: Metamaterial). The change in polarization of the radiation reflected off the sample material is then measured. This is used to obtain phase information and the polarization state of the emitted and reflected radiation. This information is then is used to demonstrate the boost in effective magnetic permeability at terahertz frequencies.[9]

An external magnetic field is applied with the THz radiation. Then the radiation induces a current in the looped wire of the SRR cell. This current then induces a local magnetic field (a vector quantity). The local magnetic field can be understood as a magnetic response. Well below the resonance frequency ω0 the local magnetic field increases over time corresponding to increasing frequency. This magnetic response stays in phase with the electric field. Because the SRR cell is actually a non-magnetic material, this local magnetic response is temporary and will retain magnetic characteristics only so long as there is a an externally applied magnetic field. Thus the total magnetization will drop to zero when the applied field is removed. In addition, the local magnetic response is actually a fraction of the total magnetic field. This fraction is proportional to the field strength and this explains the linear dependency. All this has to do with alignments and spins at the atomic level.[9]

For more information see:Paramagnetism and Split-ring resonator

As the frequency continues to increase, approaching resonance, the induced currents in the looped wire can no longer keep up with the applied field and the local response begins to lag. Then as the frequency increases above ω0, the induced local field response lags further until it is completely out of phase with the excitation field. This results in a magnetic permeability that is falling below unity, over time - including values less than zero. The linear coupling between the induced local field and the fluctuating applied field is in contrast to the non-linear characteristics of ferromagnetism, hence no permanent magnetic effect is achieved.[9]

Three different SRR samples were compared. The wavelength of the resonant excited field is λ and the material is able to scale 1/7 λ. These are the necessary conditions for the metamaterial to become a medium with µeff. The sample was placed inside a vacuum produced inside a compartment. A mercury arc lamp was used as the electromagnetic source, and shined onto the sample, at an angle of 30°. The SRRs are expected to respond magnetically when the magnetic field penetrates the rings (S-polarization) and to exhibit no magnetic response when the magnetic field is parallel to the plane of the SRR (P-polarization). The frequency range of 0.6 THz to 1.8 THz was used for the measurements. The reflectance ratio of S- and P- polarizations was matched with strong magnetic responses of SRRs when the magnetic field penetrates the rings (S-polarization). Three different artificial magnetic structures are designated D1, D2, and D3. See the graphical representation of the magnetic responses here. D1 strong magnetic response at 1.25 THz, with a ratio of just below 1.5. To show that it is the material that is used to vary the effective permeability, two other samples are used to show that this resonance should scale with dimensions in accordance to Maxwell's equations. Therefore D2 has a strong magnetic response at peaks at 0.95 THz, and the D3 sample peaks at 0.8 THz. This demonstrates the scalability of these magnetic metamaterials throughout the THz range and potentially into optical frequencies. To further demonstrate verification of the results, a mathematical simulation was performed which repeated the demonstration. The results of the simulation were in good agreement with the actual results for materials D1, D2, and D3.[9]

[edit] Magnetic response of metamaterials at 100 terahertz

Illustration of the analogy between a conventional LC circuit (A), consisting of an inductance L, a capacitance C, and the single SRRs used here (B). l, length; w, width; d, gap width; t, thickness. (C) An electron micrograph of a typical SRR fabricated by electron-beam lithography.

To fulfill a need to achieve localized magnetic resonant responses for terahertz optical frequencies, an array of single nonmagnetic metallic split rings can be used to implement a magnetic resonance at 100 THz. The split-ring resonator mimicked an LC oscillator which generated waves with frequency ωLC = (LC)−1/2.[7]

See the image to the right:

An LC circuit is a resonant circuit or tuned circuit that consists of an inductor, and a capacitor. When connected together, an electric current can alternate between them at the circuit's resonant frequency. LC circuits are used either for generating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal. They are key components in many applications such as oscillators, filters, tuners and frequency mixers.

The radiated transmission is red. The response is graphed in blue. An etched picture of the sample is shown on right-hand side. Polarization configurations are shown on top of the two columns. Resonances of the three lattice constants are shown in the gray area of the graph at about 3-µm. first row (A and B), the lattice constant of the SRRs is a = 450 nm; in the second row (C and D), it is a = 600 nm; and in the third row (E and F), it is a = 900 nm. In the last row (G and H), results for closed-ring resonators with a = 600 nm are shown

To couple an incident light beam to the LC resonance one of two conditions must be met. The first condition is that electric field vector E of the incident light source has a component that is normal to the plates of the capacitor. The second condition is the magnetic field vector H of the incident light has a component normal to the plane of the coil. When the second condition is met, a localized magnetic field is created which counteracts the magnetic field of the light source and can result in a negative permeability. Such metamaterials were first realized at frequencies around 10 GHz (3-cm wavelengths) - and could be fabricated on stacked electronic circuit boards. In this case another two orders of magnitude, to 100 THz, had been achieved. This puts visible frequencies for negative refraction index much closer.[7]

The first responses are shown with a lattice constant of a = 450 nm. Additionally, this corresponds to a total number of 56 × 56 = 3136 SRR microstructures. Coupling is controlled through the polarization of the incident light - the interaction of the electric field components with the capacitor and the interaction of the magnetic field components with the inductor.[7]. Other lattice constants shown will have a different total number of SRR microstructures.

The LC resonance occurs at 3 µm. Resonant responses occur at lattice constants of 450 nm, 650 nm, and 900 nm. Two distinct resonant responses occur for all three of these lattice constants. Additionally, all three lattice constants are notably smaller than the LC resonant frequency. Coupling to the LC resonance can only occur if there is a component normal from the polarized electric field to the plates of the capacitance. If the electric field is rotated 90° then resonance around the 3-µm wavelength completely disappears.[7]

Next, closed rings rather than split rings are radiated to compare results. Linear polarization does not occur for either position of the metamaterial. Hence, unlike the split ring resonators, no resonance occurs at 3-µm. Finally, measurements are performed under an angle of up to 40° with respect to the surface normal, such that the magnetic field vector of the incident light acquires a component normal to the coils. As expected, the 3-µm resonance persists and does not shift.[7]

From this analysis and demonstration the electrical and magnetic parameters of normal materials is overturned. In normal materials, resonances fade away above gigahertz frequencies. Instead, orders of magnitude above gigahertz frequencies - with resonances at terahertz frequencies - applied to metamaterials has been effectively demonstrated. This now allows for interesting new effects in linear optics as well as in nonlinear optics. Furthermore, a negative magnetic permeability would allow for negative-index materials at optical frequencies, which seemed totally out of reach just a few years ago.[7]

Later, in 2005, resonant magnetic nanostructures were fabricated that experimentally exhibited a negative permeability in the mid-infrared range. This was the first practical demonstration to do so. This was seen as an important step toward achieving negative refractive index in the IR range.[12]

[edit] Negative index of refraction at 200 THz

The two previous sections discussed a magnetic response at terahertz frequencies, but not a negative index of refraction. These two studies are nevertheless important because a negative magnetic permeability is necessary to achieve negative refraction. In addition, these experiments demonstrated that optical negative index metamaterials are possible because of the acquired magnetic response (permeability). In 2005 experimental observation of a negative refractive index for the optical range, specifically, for the wavelengths close to 1.5 μm (200 THz frequency) was accomplished.[13]

This accomplishment was in agreement with prior theoretical predictions that a layer of pairs of parallel metal nanorods can produce a negative refractive index.[13]

[edit] Active terahertz metamaterials

Electromagnetic metamaterials show promise to fill the Terahertz gap (0.1 – 10 THz). The terahertz gap is caused by two general shortfalls. First, almost no naturally occurring materials are available for applications which would utilize terahertz frequency sources. Second is the inability to translate the successes with EM metamaterials in the microwave and optical domain, to the terahertz domain.[14][15]

Moreover, the majority of research has focused on the passive properties of artificial periodic THz transmission, e.g., the effects of metal film thickness, hole geometry, periodicity, etc. It has been shown that the resonance can also be affected by depositing a dielectric layer on the metal hole arrays and by doping a semiconductor substrate, both of which result in significant shifting of the resonance frequency. However, little work has focused on the "active" manipulation of the extraordinary optical transmission though it is essential to realize many applications.[16]

Answering this need, there are proposals for "active metamaterials" which can proactively control the proportion of transmission and reflection components of the source (EM) radiation. Strategies include illuminating the structure with laser light, varying an external static magnetic field where the current does not vary, and by using an external bias voltage supply (semiconductor controlled). These methods lead to the possibilities of high-sensitive spectroscopy, higher power terahertz generation, short-range secure THz communication, an even more sensitive detection through terahertz capabilities. Furthermore these include the development of techniques for, more sensitive terahertz detection, and more effective control and manipulation of terahertz waves.[14][15]

[edit] Electronic control of THz transmission properties

Electronic switching of the extraordinary THz transmission was demonstrated with subwavelength metal hole arrays fabricated on doped semiconductor substrates. The passive resonance properties are mainly determined by the geometry and dimensions of the metal holes as well as the array periodicity. By electronically altering the substrate conductivity via an external voltage bias, switching of the extraordinary THz transmission is accomplished in real time.[16]

[edit] Hybrid metamaterial modulation of terahertz radiation

Terahertz modulators based on semiconductor structures often require cryogenic temperatures. This particular modulator is electrically modulated at room temperature. The bandwidth of the hybrid structure is proactively controlled by semiconductor conduction.[14]

Semiconductor-SRR metamaterial-based terahertz electrical modulators will be useful for real-time terahertz imaging, fast sensing and identification, and even in short range secure terahertz communications.[14]

[edit] High-frequency modulation of terahertz radiation

In 2008, a metamaterial based modulator for THz radiation, was designed, fabricated and experimentally demonstrated. It was electrically tunable. The metamaterial is constructed with symmetric unit cell structures to ensure the material is not affected by the arbitrary polarizations of a radiated source.[15]

The metamaterial was composed of an array of gold crosses fabricated on top of an n-doped semiconductor (GaAs) layer.[15]

The crossbars were effectively electric dipoles. In the vicinity of the resonance frequency the crossbars create a negative effective permittivity for this metamaterial. Upon reaching negative permittivity, a major fraction of the electromagnetic wave is reflected from the metamaterial surface. The other part is of course transmitted, hence a stop band occurs around the dipole resonance frequency. Here is where the n-doped GaAs layer comes into play. The conductivity of the semiconductor layer is the tuning device for the transmitted part of the EM wave. And the semiconductor layer can be purposely tuned.[15]

[edit] Adaptive metamaterials (THz)

With adaptive metamaterials the unit cell's response is reorientation. Adaptive metamaterials offer significant potential to realize novel electromagnetic functionality ranging from thermal detection to reconfigurable electromagnetic radiation absorbers.

[edit] Reconfigurable terahertz metamaterials

The first demonstrations of negative refractive index with metamaterials were anisotropic metamaterials. Reconfigurable metamaterials at terahertz frequencies are anisotropic materials where the artificial dipole, which comprises the unit cell, is reoriented when responding to the external EM source field. The split ring resonators are designed in a cantilever configuration, which allows bending out of plane in response to stimulus. A distinctive capability to tune the electric and magnetic response as the split ring resonators reorient within their unit cells.[17]

[edit] Employing MEM technology

By combining metamaterial elements - specifically, split ring resonators - with MEMS technology - has enabled the creation of non-planar flexible composites and micromechanically active structures where the orientation of the electromagnetically resonant elements can be precisely controlled with respect to the incident field.[18]

[edit] Dynamic electric and magnetic metamaterial response at THz frequencies

The theory, simulation, and demonstration of a dynamic response of metamaterial parameters were shown for the first time with a planar array of split ring resonators (SRRs).[19]

[edit] Survey of terahertz metamaterial devices

The current trend of metamaterial research aims for design of nanostructures that are capable of manipulating electromagnetic waves at the visible frequency regime. A metamaterial mimicking the Drude-Lorentz model can be straightforwardly achieved by an array of wire elements into which cuts are periodically introduced. At frequencies above the resonant frequency and below plasma frequency, the permittivity is negative and, because the resonant frequency can be set to virtually any value in a metamaterial, phenomena usually associated with optical frequencies including negative ε can be reproduced at low frequencies.[20][21]

[edit] Terahertz amplifier design improved with metamaterial

2007 - The frequency range (0.3–3.0)×1012 Hz, or 0.3 to 3.0 THz has little use and is referred to as the “terahertz gap” of the electromagnetic spectrum because compact moderate power amplifiers are not available there. Improvements aim to increase the power and efficiency of terahertz amplification in two types of vacuum electronics slow-wave circuits. The first type of circuit has a folded waveguide geometry incorporating anisotropic dielectrics and holey metamaterials, which consist of arrays of subwavelength holes.

The second type of circuit has a flat rectangular geometry with a meandering zig-zag transmission line to carry the electromagnetic wave and a metamaterial structure embedded in the substrate. Preliminary computational results are more promising with this circuit. They suggest that the metamaterial structure is effective in decreasing the electric field magnitude in the substrate and increasing the magnitude in the region above the meander line, where it can interact with an electron sheet beam. In addition, the planar circuit is easier to fabricate and it can support a higher current.[22][23]

An optimization algorithm has been developed to design slow-wave circuits of high-frequency traveling-wave tubes. A simulated statistical performance test of a robust design for a 94-GHz folded-waveguide circuit shows significantly smaller sensitivity to dimensional tolerance variations.[22][23]

[edit] Tuned terahertz split-ring resonators for devices and sensors

Device design is quickly becoming a large part of metamaterial research. In the short half decade since its conception, understanding of the physics behind tailored electromagnetic responses in metamaterials has progressed far enough to where application demonstrations are surfacing.

A process is demonstrated for tuning the magnetic resonance frequency of a fixed split-ring resonator array, by way of adding material near the split-ring elements. The sensitivity of the fine tuning suggests possible applications as a sensor device. The resonant frequency responds to silicon nanospheres.[24]

Applying drops of a silicon-nanospheres/ethanol solution to the surface of the sample decreases the magnetic resonance frequency of the split-ring array in incremental steps of 0.03 THz. This fine tuning is done post fabrication and is demonstrated to be reversible. The exhibited sensitivity of the split-ring resonance frequency to the presence of silicon nanospheres also suggests further application possibilities as a sensor device.

[edit] A metamaterial solid-state terahertz phase modulator

The terahertz phase modulator uses a voltage-controlled metamaterial of a single unit cell layer. This new device achieves a voltage-controlled linear phase shift of π /6 radians at 16 V. Moreover, the causal relation between amplitude switching and phase shifting enables broadband modulation.[10]

[edit] THz metamaterial IR sensor

One of the most critical applications of such a filter is to block unwanted radiation from nearby military high-power laser, while still allowing the sensor to conduct necessary battlefield.[25]

[edit] Biomolecular sensing at THz frequencies

Recently, it has been proposed in a numerical study to use THz-FSS based on asymmetric split ring resonators as a sensor for detecting biomolecular sample films with a thickness of only 10 nm. Because large biomolecules, e.g. DNA, exhibit a multitude of inherent vibrational modes, terahertz radiation is ideal to excite and probe these modes and to detect DNA by its terahertz properties at a specific binding state. This is a proposal for a rapid processing and reading of up to 100 arrayed gene sensors for diagnostic applications.[26]

v • d • e
Spectroscopy

[edit] See also

[edit] Electromagnetic interactions

[edit] External links

[edit] References

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  2. ^ a b c Averitt, R. D. (2007). "Terahertz metamaterial devices". Proceedings of SPIE 6772: 677209. doi:10.1117/12.751613. 
  3. ^ a b Rainsforda, Tamath; Samuel P. Mickana,and Derek Abbotta (2005). "T-ray Sensing Applications: Review of Global Developments". Proceedings of SPIE 5649: 826–837. doi:10.1117/12.607746. http://augean.eleceng.adelaide.edu.au/thz/publications/rainsford_2005_spie.pdf. Retrieved 2009-09-08. 
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  7. ^ a b c d e f g h i j k Linden, Stefan; Christian Enkrich, Martin Wegener, Jiangfeng Zhou, Thomas Koschny, Costas M. Soukoulis (2004). "Magnetic Response of Metamaterials at 100 Terahertz". Science 306 (5700): 1351–1353. doi:10.1126/science.1105371. 
  8. ^ Pendry, J.B.; Holden, A.J. Robbins, D.J. Stewart, W.J. (1999). "Magnetism from conductors and enhanced nonlinear phenomena". Microwave Theory and Techniques (IEEE) 47 (11). doi:10.1109/22.798002. 
  9. ^ a b c d e f g h i j k l m Yen, T. J.; et. al. (2004). "Terahertz Magnetic Response from Artificial Materials". Science 303 (5663): 1494–1496. doi:10.1126/science.1094025. PMID 15001772. 
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  14. ^ a b c d Chen, Hou-Tong et al. (2008-09-04). "Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves". Applied Physics Letters 93: 091117 (2008). doi:10.1063/1.2978071. http://www2.bc.edu/~padillaw/PDF/APL_93_091117_2008.pdf. Retrieved 2009-11-12. 
  15. ^ a b c d e Paul, Oliver et al. (2009-09-2009). "Polarization-independent active metamaterial for high-frequency terahertz modulation" (Free PDF download. Published online 2009-01-19). Optics Express (OSA) 17 (02): 819–827. doi:10.1364/OE.17.000819. http://www.physik.uni-kl.de/fileadmin/beigang/PDF_zum_download/Paul2009.pdf. Retrieved 2009-11-12. 
  16. ^ a b Chen, Hou-Tong (2008-05-12). "Electronic control of extraordinary terahertz transmission through subwavelength metal hole arrays". Optics express 16 (11): 7641. doi:10.1364/OE.16.007641. http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.2942v2.pdf. Retrieved 2009-11-12. 
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  20. ^ Withayachumnankul1, Withawat; and Derek Abbot (2008-12). "Survey of terahertz metamaterial devices" (Free PDF download). Proceedings of SPIE 7268: 7268–1Z. doi:10.1117/12.823538. http://www.eleceng.adelaide.edu.au/thz/publications/withayachumnankul_2008_spie.pdf. Retrieved 2009-10-21. 
  21. ^ Pendry, John B.; and David R. Smith (2004-06). "Reversing Light: Negative Refraction" (Free PDF download. Cited by 185. Alternate copy here.). Physics Today 57: 37–44. doi:10.1063/1.1784272. http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/DRS&JBP_final_.pdf. Retrieved 2009-11-30. 
  22. ^ a b Wilson, J.D.; Chevalier, C.T. (2007-04-23). "Robust Optimization of High-Frequency Traveling-Wave Tube Slow-Wave Circuits". IEEE Transactions on Electron Devices (NASA Glenn Res. Cen. Cleveland,OH,USA & Lausanne, Switzerland: IEEE) 54 (5): 1232–1237. doi:10.1109/TED.2007.894613. ISSN 0018-9383. http://www.grc.nasa.gov/WWW/RT/2007/Comm/06-RCE-wilson1.html. Retrieved 2009-09-14. 
  23. ^ a b Chevalier, Christine T.; Jeffrey D. Wilson, Carol L. Kory (2007-08). "Comparing the Robustness of High-Frequency Traveling-Wave Tube Slow-Wave Circuits". NASA/TP (Cleveland, Ohio: NASA Glenn Research Center): 1–11. ISSN NASA/TP—2007-214700. http://gltrs.grc.nasa.gov/reports/2007/TP-2007-214700.pdf. Retrieved 2009-08-14. 
  24. ^ Driscoll, T.; G. O. Andreev, D. N. Basov,S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith (2007-08-07). "Tuned permeability in terahertz split-ring resonators for devices and sensors". Appl. Phys. Lett. 91 (06): 062511. doi:10.1063/1.2768300. http://infrared.ucsd.edu/basov_pubs/Driscoll_APL91_062511_2007.pdf. Retrieved 2009-10-02. 
  25. ^ CASSE, B. D. F. et al. "Novel infrared sensors using micro- and nano-electromagnetic metamaterials" (I will try to find DOI later. For now use PDF link). Singapore Synchrotron Light Source. http://metamaterials.googlepages.com/bdfc_APCOT2006_EM3_20060411.pdf. Retrieved 2009-10-21. 
  26. ^ Klatt, G. et al. (2009-03-12 Free PDF download). "Rapid and precise read-out of terahertz sensor by high-speed asynchronous optical sampling". Electron. Lett. / Instrumentation & measurement (Institution of Engineering and Technology) 45 (06): 310–311. doi:10.1049/el.2009.3249. http://kops.ub.uni-konstanz.de/volltexte/2009/8576/pdf/ElecLett4520096.pdf. Retrieved 2009-10-31. 
v • d • e
General subfields within physics
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