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This paper reviews recent advances in the research and development of graphene-based plasmonic metamaterials for terahertz (THz) laser transistors. The authors’ theoretical discovery on THz laser transistors in 2007 was realized as a distributed-feedback dual-gate graphene-channel field-effect transistor (DFB-DG-GFET) in 2018, demonstrating ∼0.1 µW single-mode emission at 5.2 THz and ∼80 µW amplified spontaneous 1–7.6 THz emission at 100 K. To realize room-temperature, dry-cell-battery operating intense THz lasing with fast direct modulation, various approaches based on graphene plasmonic metamaterials are investigated and introduced as real device implementations, including (i) replacement of the laser photonic cavity with plasmonic cavity enormously improving the THz photon field confinement with larger gain overlapping, (ii) introduction of THz amplification of stimulated emission via current-driven graphene Dirac plasmons (GDPs), and (iii) controlling the parity and time-reversal symmetry of GDPs enabling ultrafast direct gain-switch modulation. Possible real device structures and design constraints are discussed and addressed toward coherent light sources applicable to future 6G- and 7G-class THz wireless communication systems.

Terahertz (THz) waves have revealed a great potential for use in various fields and for a wide range of challenging applications. High-performance detectors are, however, vital for exploitation of THz technology. Graphene plasmonic THz detectors have proven to be promising optoelectronic devices, but improving their performance is still necessary. In this work, an asymmetric-dual-grating-gate graphene-terahertz-field-effect-transistor with a graphite back-gate was fabricated and characterized under illumination of 0.3 THz radiation in the temperature range from 4.5 K up to the room temperature. The device was fabricated as a sub-THz detector using a heterostructure of h-BN/Graphene/h-BN/Graphite to make a transistor with a double asymmetric-grating-top-gate and a continuous graphite back-gate. By biasing the metallic top-gates and the graphite back-gate, abrupt n+n (or p+p) or np (or pn) junctions with different potential barriers are formed along the graphene layer leading to enhancement of the THz rectified signal by about an order of magnitude. The plasmonic rectification for graphene containing np junctions is interpreted as due to the plasmonic electron-hole ratchet mechanism, whereas, for graphene with n+n junctions, rectification is attributed to the differential plasmonic drag effect. This work shows a new way of responsivity enhancement and paves the way towards new record performances of graphene THz nano-photodetectors.

The ferromagnetic resonance (FMR) spectra of epitaxial yttrium iron garnet films are experimentally studied. The field dependences of the FR frequency are used to determine the effective fields induced by the first and second anisotropy constants and the effective uniaxial anisotropy field. The FMR frequency and linewidth are found to increase in the fields lower than 8 Oe applied in the bismuth-containing film plane. This increase is related to the formation of a nonuniform magnetization distribution, which is supported by a direct magnetooptical observation. The FMR spectra are found to be modulated by a set of narrow lines, the amplitude of which is proportional to the FMR signal intensity. The frequency position of the lines is independent of the magnitude and direction of a dc magnetic field. This modulation is shown to be associated with the resonance excitation of transverse elastic vibration modes. The effective magnetoelastic coupling parameter and the linewidth of the elastic vibrations excited by resonance pumping are estimated.

The giant magnetoimpedance effect in a glass-coated Fe-based amorphous microwire annealed under stresses is theoretically studied. The magnetization distribution in a microwire is described within a model that takes into account the presence in the sample of two regions with different types of magnetic anisotropy. It is assumed that, in the central part of the microwire, the anisotropy is longitudinal and, in the surface region, an induced helicoidal anisotropy arises as a result of annealing. An expression for the impedance of the microwire with allowance for different permeabilities of the two regions is found. The obtained theoretical dependences of the impedance on an external field and frequency make it possible to qualitatively describe the results of experimental studies of the magnetoimpedance in glass-coated Fe-based amorphous microwires.

The magnetoimpedance effect in a stress-annealed Fe-rich amorphous microwire with induced magnetic anisotropy in a surface region is studied theoretically. The static magnetization distribution within the microwire is described in the framework of the core–shell magnetic structure. It is assumed that the microwire has an axial magnetic anisotropy in the inner core and a helical anisotropy in the external shell appearing due to the stress-annealing. Both the diagonal and off-diagonal magnetoimpedance responses are found in terms of the surface impedance tensor. The influence of the bias current on the magnetoimpedance is analyzed. The obtained theoretical dependences are shown to be in a qualitative agreement with the results of recent experimental studies of the magnetoimpedance effect in stress-annealed Fe-rich glass–coated amorphous microwires.

The intrinsic transverse-magnetic modes of graphene with spatial dispersion are investigated theoretically in the hydrodynamic regime in a terahertz frequency range. It is revealed that spatial dispersion is caused by the diffusion electron-transport mechanism due to the spreading of electron-concentration gradients under the effect of pressure in an electron liquid. The cases of a screened and unscreened plasmon as well as electron sound are considered.

As an example of application of the contemporary numerical-analytic methods to the solution of boundary-value problems in noncanonical domains, we consider the Dirichlet boundary-value problem of the potential theory in the domain bounded by a parallelogram. The simplicity and clarity of the procedure used for the construction of the solution enable us to clearly illustrate some specific features of the contemporary approaches to the solution of various problems of mathematical physics. For numerous types of regions including a broad range of noncanonical domains, the application of the notion of general solution of the boundary-value problem enables one to construct its numerical-analytic solution. In this case, the researchers use the well-known collections of partial solutions of the basic equations of mathematical physics. The main problem is to indicate efficient ways that can be used to determine arbitrary coefficients and functions appearing in the general solution. Note that the application of the traditional approach according to which the numerical-analytic solutions are obtained on the basis of minimization of standard deviations often leads to cumbersome calculations in the case of noncanonical domains. As an alternative to this method, we can mention the contemporary method of boundary integral equations. The present work is devoted to the development of the indicated two approaches to the solution of the boundary-value problems and their comparison.

We propose a concept of an electrically controllable plasmonic directional coupler of terahertz signal based on a periodical structure with an active (with inversion of the population of free charge carriers) graphene with a dual grating gate and numerically calculate its characteristics. Proposed concept of plasmon excitation by using the grating gate offers highly effective coupling of incident electromagnetic wave to plasmons as compared with the excitation of plasmons by a single diffraction element. The coefficient which characterizes the efficiency of transformation of the electromagnetic wave into the propagating plasmon has been calculated. This transformation coefficient substantially exceeds the unity (exceeding 6 in value) due to amplification of plasmons in the studied structure by using pumped active graphene. We have shown that applying different dc voltages to different subgratings of the dual grating gate allows for exciting the surface plasmon in graphene, which can propagate along or opposite the direction of the structure periodicity, or can be a standing plasma wave for the same frequency of the incident terahertz wave. The coefficient of unidirectionality, which is the ratio of the plasmon power flux propagating along (opposite) the direction of the structure periodicity to the sum of the absolute values of plasmon power fluxes propagating in both directions, could reach up to 80 percent. Two different methods of the plasmon propagation direction switching are studied and possible application of the found effects are suggested.

The possibility of excitation and amplification of terahertz plasmons in a structure containing a layer of graphene with charge-carrier drift and a layer of graphene without carrier drift is theoretically investigated. The plasmon excitation in the graphene structure by an incident terahertz electromagnetic wave is calculated in the attenuated total reflection geometry. It is shown that, in graphene with charge-carrier drift, it is possible to achieve negative values of the real part of graphene conductivity for the phase velocity of plasmons exceeding the charge carrier's drift velocities, which indicates a non-Cherenkov amplification of terahertz plasmons in the double-layer graphene structure for practically achievable direct electric current values. Terahertz amplification originates due to the variation of the carrier mass density in graphene with terahertz electric field. In the case of weak deceleration of terahertz wave incident onto graphene structure, the value of the negative conductivity of graphene does not depend on the direction of the direct current in graphene (only the codirectional and counterdirectional currents with respect to the direction of plasmon propagation are considered). This is due to the insignificant spatial dispersion of the hydrodynamic conductivity of graphene in the case of weak deceleration of terahertz waves. The results of this work can be used to create compact terahertz radiation amplifiers operating at room temperature.

We demonstrate that the periodic graphene structure with asymmetric unit cell can effectively transform the incident electromagnetic wave into propagating plasmon. Periodic graphene structure with asymmetric unit cell and active graphene transforms the incident electromagnetic wave into amplifying propagating plasmon.

Deceleration of terahertz plasma waves (plasmons) in tapered graphene-insulator-graphene heterostructure is studied. It is shown that the plasmon energy velocity can become several times smaller as compared to that near the taper apex.

We explore current-driven Dirac plasmon dynamics in monolayer graphene metasurfaces. DC-current-induced complete suppression of the graphene absorption is experimentally observed in a broad frequency range followed by a giant amplification (up to ∼ 9 % gain) of an incoming terahertz radiation at room temperature.

The plasmonic absorption / amplification spectrum of THz radiation in the periodically screened graphene with charge carrier drift is theoretically studied. It is shown that graphene exhibits strong plasmon resonances at THz frequencies. The threshold of the Cherenkov radiation is controlled by the graphene screening.

Switching of terahertz plasmon propagation direction in a periodic graphene structure with a double grating gate is studied theoretically. The coefficient of transformation of an incident electromagnetic wave into a propagating plasmon is numerically calculated. It is shown that near the “radiative” and “nonradiative” mode crosses plasmons propagating can be switched between forward and backward directions with respect to the x-axis by tuning voltage values applying to sub-grating gates. The absolute value of the transformation coefficient can exceed the unit value because of the gain provided by the active graphene.

The amplification of the terahertz electromagnetic wave incident on graphene with direct electric current which is located between two dielectric slabs is investigated theoretically. The expression of the graphene conductivity of in the hydrodynamic regime taking into account spatial dispersion is obtained. It was shown that the direct electric current in graphene leads to an amplification of terahertz radiation due to the real part of graphene conductivity becomes negative.

The terahertz absorption spectrum in a periodic array of graphene nanoribbons located on the surface of a dielectric substrate with a high refractive index (terahertz prism) is studied theoretically. The total absorption of terahertz radiation is shown to occur in the regime of total internal reflection of the terahertz wave from the periodic array of graphene nanoribbons, at the frequencies of plasma oscillations in graphene, in a wide range of incidence angles of the external terahertz wave even at room temperature.

Linear and gapless energy spectrum of graphene carriers enables population inversion under optical and electrical pumping. We first theoretically discovered this phenomenon and demonstrated experimental observation of single-mode THz lasing with rather weak intensity at 100K in current-injection pumped graphene-channel field-effect transistors (GFETs). We introduce graphene surface plasmon polariton (SPP) instability to substantially boost the THz gain. We demonstrate our experimental observation of giant amplification of THz radiation at 300K stimulated by graphene plasmon instabilities in asymmetric dual-grating gate (ADGG) GFETs. Integrating the graphene SPP amplifier into a GFET laser will be a promising solution towards room-temperature intense THz lasing.

Plasmon in two-dimensional electron gas (2DEG) has long been considered as a promising active medium for terahertz emitters and detectors. However, the efficiency of terahertz plasmonic devices is severely limited by the high damping rate of plasma wave in solid state. In addition to the enhancement of plasmon lifetime by using 2DEGs with higher carrier mobility, engineering on the boundary condition and electromagnetic environment of plasmon cavity helps to preserve the plasmon states. Here we report on terahertz reflection spectroscopy of plasmon states in a grating-coupled AlGaN/GaN-2DEG plasmonic device at 7 K in equilibrium with ambient blackbody irradiation. Localized plasmon states and plasmon-polariton states were observed when the core plasmonic device is integrated with a silicon lens and when it is embedded in a terahertz Fabry-Perot cavity, respectively. Simulation results including the reflection spectra and total reflection power agree well with the measured results. The Rabi splitting is found to be inversely proportional to the resonance frequency, and follows a linear relation with the square root of the sheet electron density. A normalized coupling ratio, ΩRω0≈0.13, is achieved between the Rabi splitting ΩR and the resonance frequency ω0. The coupling ratio could be further increased to allow for ultrastrong coupling between terahertz photons and plasmons.

It is shown theoretically that stimulated generation of terahertz radiation by plasmons in graphene with a planar distributed Bragg resonator is possible at two different frequencies for each plasmon mode. This behavior may be attributed to the superradiance of the collective plasmon mode, which is associated with superlinear increase in the radiative damping of the plasmons with increase in pumping power. As a result, the curves of the radiative damping and the plasmon gain as a function of the pumping power intersect at two points corresponding to different generation conditions.

We report on experimental studies of terahertz (THz) radiation transmission through grating-gate graphene-channel transistor nanostructures and demonstrate room temperature THz radiation amplification stimulated by current-driven plasmon excitations. Specifically, with increase of the direct current (dc) under periodic charge density modulation, we observe a strong red shift of the resonant THz plasmon absorption, its complete bleaching, followed by the amplification and blue shift of the resonant plasmon frequency. Our results are, to the best of our knowledge, the first experimental observation of energy transfer from dc current to plasmons leading to THz amplification. We present a simple model allowing for the phenomenological description of the observed amplification phenomena. This model shows that in the presence of dc current the radiation-induced correction to dissipation is sensitive to the phase shift between THz oscillations of carrier density and drift velocity, and with increase of the current becomes negative, leading to amplification. The experimental results of this work as all obtained at room temperature, pave the way towards the new 2D plasmons based, voltage tuneable THz radiation amplifiers., Comment: 17 pages with 15 figures, uses revtex4-2, additionally include 6 pages of supplementary materials with 6 figures

The excitation and amplification of the propagating plasmons in a periodic active (with population inversion of charge carriers) graphene-based structure with dual grating-gate with an asymmetric unit cell is studied theoretically. Such structure transforms the normally incident THz electromagnetic wave into sustained or amplified unidirectionally propagating plasmon. This effect is caused by simultaneous excitation of radiative and ‘non-radiative’ plasmon modes at the same frequency.

We report an attempt to improve the sensitivity of terahertz detection based on self-mixing in antenna-coupled field-effect transistors by enhancing the field-effect factor and the antenna factor with a reduced gate length and a reduced antenna-gate gap, respectively. An optical noise equivalent power (NEP) of 3.7 pW/Hz at 0.65 THz was achieved in a GaN/AlGaN high-electron-mobility transistor (HEMT) with a gate length of 300 nm and an antenna-gate gap of 200 nm at room temperature. It was found that the antenna factor was inversely proportional to the antenna-gate gap, and the responses upon coherent/incoherent terahertz irradiation were well described by the self-mixing model. To fill the NEP gap of 0.1−1 pW/Hz between room-temperature and cryogenic detectors by HEMT-based detectors at room temperature, impedance match needs to be carefully considered.

Terahertz plasma wave (plasmon) localization and velocity control in tapered heterostructure (taper) with double-layer graphene were numerically studied. We employ a simple rigorous theoretical model to find out the plasmon localization length and energy velocity values along the tapered structure. It is shown that the plasmon decelerates while moving from the taper apex and the deceleration process is accompanied with increase of the plasmon wave localization. While moving along the structure from the taper apex, the plasmon energy velocity as well as the plasmon localization length can become nearly an order of magnitude smaller as compared to the values near the taper apex.

We experimentally demonstrate terahertz light amplification by instability-driven stimulated emission of graphene plasmon polaritons in an asymmetric dual-grating-gate transistor structure. D.C. channel current driven by the drain bias voltage induces plasmon instability, alternating the electromagnetic response from the resonant absorption to the resonant amplification (up to ~ 9 % gain) beyond the threshold drain bias voltage at room temperature.

We analyze the pumping of the graphene-based laser heterostructures by infrared radiation using the numerical model. To enable the injection of sufficiently cooled carriers into the graphene layer (GL) leading to the interband population inversion, we propose to use the graded-gap black-PxAs1 − x absorption-cooling layers. Our calculations are based on the thermodiffusion-drift carrier transport model. We demonstrate that the proposed optical pumping method can provide an efficient injection of the cool electron–hole plasma into the GL and the interband population inversion in the GL. Since the energy gap in b-As layer can be smaller than the energy of optical phonons in the GL, the injected electron–hole plasma can be additionally cooled down to the temperatures lower than the lattice temperature. This promotes a stronger population inversion that is beneficial for realization of the GL-based optically pumped terahertz and far-infrared laser, plasmon emitters, and the superluminescent downconverters. We also compare the efficiency of optical pumping through the graded-gap and uniform absorbing-cooling layers.

The generation and amplification of terahertz (THz) electromagnetic waves by plasmonic instabilities in conventional two-dimensional (2D) electron systems (2DESs) have been actively investigated since 1980 [1]. However, after about forty years, we are still a long way from the realization of efficient emitters and amplifiers [2]. The rise of graphene and its extremely strong light-plasmon coupling and superior carrier transport properties make this work worth to be revisited [3]. We investigate dc current driven plasmonic instabilities in high mobility graphene-channel field-effect transistors (GFETs) working for tunable THz amplifier at room temperature (RT).

This paper reports on room-temperature frequency tunable terahertz light amplification by current-driven plasmon instabilities produced in a graphene metasurface implemented in an asymmetric dual-grating-gate graphene field effect transistor.

The electrical and galvanomagnetic properties of partially graphitized highly porous bioC(Ni) biocarbon matrices produced by pyrolysis (carbonization) of beech wood at temperatures T carb = 850–1600°C in the presence of a Ni-containing catalyst have been studied in comparison with their microstructural features. The temperature dependences of the resistivity, the magnetoresistance, and the Hall coefficient have been measured in the temperature range of 4.2–300 K in magnetic fields to 28 kOe. It has been shown that an additional graphite phase introduction into samples with T carb ≥ 1000°C results in an increase in the carrier mobility by a factor of 2–3, whereas the carrier (hole) concentration remains within ~1020 cm−3, as in biocarbons obtained without catalyst. An analysis of experimental data has demonstrated that the features of the conductivity and magnetoresistance of these samples are described by quantum corrections related to their structural features, i.e., the formation of a globular graphite phase of nano- and submicrometer sizes in the amorphous matrix. The quantum corrections to the conductivity decrease with increasing carbonization temperature, which indicates an increase in the degree of structure ordering and is in good agreement with microstructural data.

The dispersion and damping of the transverse plasmon mode in a screened two-dimensional (2D) electron system are theoretically studied. It is shown that the transverse plasmon mode has a much larger quality factor and a smaller retardation factor at terahertz (THz) frequencies in comparison with those known for the longitudinal plasmon mode. In addition, the electric dipole moment of the transverse plasmon mode in the screened 2D electron system can be comparable with the dipole moment of the longitudinal plasmon mode. These properties of the transverse plasmon mode make it attractive for use in plasmon devices of the THz frequency range.

A new type of ultra-broadband near-field antenna for terahertz frequencies is proposed. This antenna is a short-period planar metal array. It is theoretically shown that irradiation of the short-period array antenna by a plane homogeneous terahertz waves excite a highly inhomogeneous near electric field near the metal array. In this case, the amplitude of the excited inhomogeneous near electric field is almost independent of frequency in the entire terahertz frequency range. The excitation of plasma oscillations in a two-dimensional electron system using the antenna under study is numerically simulated in the resonant and non-resonant plasmonic response modes. This type of antenna can be used for developing ultra-broadband plasmonic detectors of terahertz radiation.

The problem of the rectification of terahertz radiation due to plasmonic nonlinearities in a periodic two-dimensional electron system upon the excitation of plasma oscillations by the attenuated total reflection method is solved. This model allows the independent study of different plasmonic rectification mechanisms, i.e., plasmonic electron drag and plasmonic ratchet effects.

Amplification of plasma waves in shielded graphene with inverted energy distribution of charge carriers is investigated theoretically. It is shown that graphene shielding allows one to increase an amplification factor of terahertz plasmons in several times compared to the case of amplification of unshielded plasmons due to strong field confinement of the shielded plasmons near graphene.

Performance of a detector based on AlGaAs/InGaAs/GaAs-material system was studied. The detector was comprised of large serpentine array of high-electron mobility transistors (HEMTs) connected in series. The floating drain contact of each transistor (except the last one) served as a source for the next one. Detection of terahertz (THz) radiation was based on the excitation of electron plasma oscillations in the HEMT's channel. The peculiarities of THz response of the detector in question including an enhanced noise-equivalent power were demonstrated.

This paper reports on the observation of the magnetic quantum ratchet effect in (Cd,Mn)Te- and CdTe-based quantum well structures with an asymmetric lateral dual grating gate superlattice subjected to an external magnetic field ($B$), applied normal to the quantum well plane. An electric current excited by terahertz laser radiation shows 1/$B$-periodic oscillations with amplitude much larger than the photocurrent at zero magnetic field. It is shown that the photocurrent generation is due to the combined action of a spatially periodic lateral potential and the spatially modulated radiation due to the near-field effects of light diffraction. The magnitude and direction of the photocurrent are determined by the degree of the lateral asymmetry controlled by the variation of voltages applied to the individual gates. The observed magneto-oscillations with enhanced photocurrent amplitude result from Landau quantization. For (Cd,Mn)Te-based structures at low temperatures, a beating-like pattern of the oscillations is observed, caused by the interplay of Zeeman and Landau splitting. A theoretical analysis, considering the magnetic quantum ratchet effect in the framework of a semiclassical approach, describes quite well the experimental results.

The effect of partial graphitization on electrical and galvanomagnetic properties of BE-C(Fe) biomorphic carbons produced by beech wood carbonization at temperatures of 850–1600°C in the presence of an iron-containing catalyst is studied. The use of an Fe catalyst at Т ≥ 1000°C leads to the formation of nanoscale graphite-phase inclusions; its total volume and nanocrystallite sizes increase with Т. The data on the carrier concentration and mobility are obtained. It was shown that partially graphitized BE-C(Fe) carbons with Т ≥ 1000°C in the conductivity type and magnetoresistance features relate to highly disordered metal systems whose conductivity can be described taking into account the contribution of quantum corrections, mainly the correction caused by the electron–electron interaction. It is shown that nonmonotonic dependences of the Hall constant R on the magnetic field are characteristic of BE-C(Fe) samples with 1000 ≤ Т < 1600°C, which is most probably caused by the contribution of various carrier groups, i.e., electrons and holes. In BE-C(Fe) samples with Т = 1600°C, the Hall coefficient corresponds to the metal state, which is associated with conducting medium homogenization resulting from the formation of a significant graphite phase volume., This study was supported in part by the Russian Foundation for Basic Research (project no. 14-03-00496) and the Presidium of the Russian Academy of Sciences (program P-20).

We study terahertz excitation of plasmons in a two-dimensional electron system with a periodic metal grating coupler. We assume that a negative electric potential is applied to one of the grating fingers, which results in forming a slit in an otherwise continuous two-dimensional plasmonic system. We analyze numerically the excitation of plasmons in such system and study plasmonic field near the slit. We predict a deep subwavelength localization of plasmons and a dramatic field enhancement at the slit edges.

We report an approach to make two-terminal antenna-coupled AlGaN/GaN high-electron-mobility-transistor self-mixing terahertz detectors. Fluorine ion implantation is used to increase the threshold voltage of the AlGaN/GaN two-dimensional electron gas. An optimal implantation dose can be reached so that the detector responsivity is maximized at zero gate voltage or with the gate floating. The relationship between the ion dosage and the threshold voltage, electron mobility, electron density, responsivity, and noise-equivalent power (NEP) is obtained. A minimum optical NEP of 47 p W / Hz is achieved from a two-terminal detector at 0.65 THz. The capability of two-terminal operation allows for the design of a large array of antenna-coupled high-electron-mobility transistor detectors without the demanding needs of routing negative gate voltage lines around the antenna array and minimizing the gate leakage current.

We have fabricated a grating-gate InGaAs/GaAs field-effect transistor structure with narrow slits between the grating gate fingers. The resonant photoconductive response of this structure has been measured in the sub-terahertz frequency range. The frequencies of the photoresponse peaks correspond to the excitation of the plasmon resonances in the structure channel. The obtained responsivity exceeds the responsivity reported previously for the grating-gate FET detector with wider slits of the grating-gate by two orders of magnitude due to enhanced coupling between incoming terahertz radiation and plasmon oscillations in the slit-grating-gate field-effect transistor structure.

The gapless energy spectra and linear dispersion relations of electrons and holes in graphene lead to nontrivial features such as a high carrier mobility and a flat, broadband optical response. This article reviews recent advances in graphene-based materials and devices for terahertz science and technology. After an introduction to the fundamental basis of the optoelectronic properties of graphene, the synthesis and crystallographic characterization of graphene materials are described, with a particular focus on the authors’ original heteroepitaxial graphene-on-silicon technology. The nonequilibrium dynamics of carrier relaxation and recombination in optically or electrically pumped graphene is discussed to introduce the possibility of negative dynamic conductivity over a wide terahertz range. Recent theoretical advances toward the creation of current-injection graphene terahertz lasers are described, followed by the unique terahertz dynamics of two-dimensional plasmons in graphene. Finally, the advantages of graphene materials and devices for terahertz applications are summarized.