太赫兹信号源Terahertzsources（二）

2. Terahertz sources

There are many sources of terahertz radiation. A small sampling is given in table 1.

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Table 1. Some sources of terahertz radiation.

Extraterrestrial thermal sources include the sun and the cosmic background radiation [40]. Common laboratory thermal source are the mercury lamp [41] and the globar, an electrically heated rod of carborundum (SiC). Various schemes are available to mount the globar [42, 43]. It typically operates at 1650 K with emissivity in the range 0.5–0.8 [44], so may be thought of as a 'grey-body'. It provides more power than the Nernst glower in the terahertz region [45].

Vacuum electronic sources include the backward-wave oscillator [46–50], extended-interaction klystrons [51–55], travelling-wave tubes [56], gyrotrons [57–62], free-electron lasers [63–66] and synchrotrons [67–76]. These sources are typically of high power [77]. Solid-state electronic sources include the Gunn diode [78–81] and high-frequency transistors [82–86]. Frequency multipliers are used to shift fundamentally sub-terahertz electronic oscillations into the terahertz range [87–89]. Josephson junctions serve as sources of terahertz and sub-terahertz radiation in superconductors [90, 91].

Terahertz lasers have been built from the archetypical elemental semiconductors, germanium and silicon [92, 93]. Semiconductor lasers include electrically pumped photonic-crystal lasers of low angular divergence [94]. Much interest is currently in the quantum cascade laser, a challenge being to raise the temperature of operation [95–97]. Gas lasers preceded the solid state lasers [98].

Visible or near-infrared lasers, either operating continuously or in pulsed mode, are widely-employed in various schemes to generate terahertz radiation by optical pumping. Two continuous laser sources may be mixed and the difference frequency lie in the terahertz range [99]. The laser sources exploited include diode lasers [100], dual-mode lasers [101], multi-mode lasers [101] and a dual-colour-VECSEL [102]. Photomixers are typically based on low-temperature grown GaAs. Difference frequency mixing occurs in a variety of materials, notably DAST [103]. Periodically inverted electro-optic crystals [104] and tilted fields increase efficiency [105]. Much work is at 780 nm, but there is also great interest at communications wavelengths of about 1.5 µm [106, 107]. These in practice use pulsed sources, but do not depend on them. Continuous stimulation of mesocrystal microspheres by a single laser produces mechanical resonance accompanied by terahertz emission [108, 109]. Pulsedlaser sources, the basis of time-domain spectroscopy, have been reviewed by Davies et al [110] and Kitaeva [111]. Pulsed lasers are used to excite photoconductive switches [112] or antennas [113]. Terahertz radiation also arises when a laser pulse pumps nothing more than air—the photoionization of the gas producing a plasma [114]. Other gases, including noble gases, may be used [115]. The radiation is very broad in its frequency range [116, 117]. As a diagnostic method, gas photoionization allows the measurement of the carrier-envelope phase of short laser pulses [118]. Solid targets may be used [119]. The polarization may be coherently controlled [120], and is enhanced by electric fields [121, 122]. In ferromagnetic films, magnetic, rather than electric, dipoles are employed [123]. Terahertz parametric oscillation in crystals such as LiNbO3 pumped by ns-Nd : YAG lasers produces coherent, tunable and unidirectional radiation; efficient output coupling is critical in realizing high power [124–126].

3. Terahertz surface emission—optical rectification

Experimentally, the principal signature of optical rectification is the strong geometrical dependence. As the emitting crystal is rotated around its surface normal perpendicular to the propagation direction of the pump beam an increase and decrease in the emitted terahertz radiation is observed. This phenomenon is usually referred to as 'azimuthal angle dependence'. Nanoporous InP (1 1 1) membranes, for example, show a marked azimuthal angle dependence, indicating optical rectification plays a major role [127]. Secondly, the terahertz emission remains directly proportional to the pump power, without evidencing saturation [127]. Thirdly, subjecting the crystal to a magnetic field has little or no effect.

3.1. Bulk effects

Optical rectification can occur in the bulk of a material. The bulk effect has been studied in detail in various crystals. Complete expressions have been given for zinc-blende (  3m) crystal faces of arbitrary orientation [128]. The terahertz generation in uniaxial birefringent crystals is similar in principle, but differs in the important respect that the polarization of the pump beam rotates as it traverses the crystal, as is illustrated in the case of ZnGeP2 (chalcopyrite) [129]. For ZnGeP2, it is found that {1 1 4} planes are more efficient than {0 1 2} and {1 1 0} planes for terahertz generation [129].

3.2. Surface effects

Not only the bulk of a crystal contributes to optical rectification. A surface contribution, induced by the electric field, may be important, and even dominate the bulk effect, at least at high excitation fluences. The surface electric-field-induced effect has been studied in detail in InAs, for (1 0 0), (1 1 0) and (1 1 1) faces, with second-harmonic (sum frequency) measurements made to supplement the terahertz (difference frequency) data, and the polarization of both measured [130]. It was found that bulk optical rectification was inadequate to explain the experimental results; an additional surface electric-field-induced contribution was also present. In fact, the surface field contribution was greater than the bulk contribution. Rotating the sample relative to the pump beam (azimuthal angle dependence of the terahertz emission) clarified this.

A surface electric-field-induced optical rectification has since been found in other materials. For example, the azimuthal angle dependence of terahertz emission from (1 0 0), (1 1 0) and (1 1 1) faces of Ge is consistent with a surface field effect and leads to an estimation of the third-order non-linear optical susceptibility of Ge [131]. In the case of (1 1 2) planes of InSb, both bulk and surface field-induced optical rectification are observed, with the latter approximately twice the strength of the former [132].

General expressions for surface optical rectification for arbitrary planes have been calculated [128]. In the accompanying experimental study of high-index planes of GaAs it was found that, while the bulk expressions gave a good agreement with the data, including the surface expressions gave an excellent agreement. Only a single parameter was needed to fit the data for the (1 1 2)A, (1 1 3)A, (1 1 4)A, (1 1 5)A, (1 1 2)B, (1 1 3)B, (1 1 4)B and (1 1 5)B faces of GaAs; moreover, the surface fields on the faces were estimated [128]. Those results applied to transmission geometry. The work has been extended to the more complicated situation of quasi-reflection geometry. Here transient currents, bulk optical rectification, and surface optical rectification all play a role, but the various contributions can be untangled [133].

The contribution of surface field-induced optical rectification is essential in explaining the terahertz emission from GaAsBi (3 1 1)B faces [134]. To explicate the mechanism, the effect of increasing optical fluence on the terahertz emission was investigated. The effect was linear, with no saturation (such as would indicate a transient current effect) being observed. Moreover, rotation of an in-plane magnetic field also had no effect on the produced terahertz radiation, again suggesting no role of transient currents. The azimuthal angle dependence of the substrate, with three peaks per rotation, was quite different to that of the GaBi0.035As0.965 epilayer, which exhibited only one peak per rotation. While bulk optical rectification could not account for the epilayer result, inclusion of the surface optical rectification term could [134]. More recently, a similar account has been given of terahertz emission from nanostructured (3 1 1) GaAs [135].