Anisotropy is ubiquitous in solids and enhanced in low-dimensional materials. In response to an electromagnetic wave, anisotropic absorptive and refractive properties result in dichroic and birefringent optical phenomena both in the linear and nonlin
ear optics regimes. Such material properties have led to a diverse array of useful polarization components in the visible and near-infrared, but mature technology is non-existent in the terahertz (THz). Here, we review several novel types of anisotropic material responses observed in the THz frequency range, including both linear and circular anisotropy, which have long-term implications for the development of THz polarization optics. We start with the extreme linear anisotropy of macroscopically aligned carbon nanotubes, arising from their intrinsically anisotropic dynamic conductivity. Magnetically induced anisotropy will then be reviewed, including the giant Faraday effects observed in semiconductors, semimetals, and two-dimensional electron systems.
We report the observation of strong third harmonic generation from a macroscopic array of aligned ultralong single-wall carbon nanotubes (SWCNTs) with intense midinfrared radiation. Through power-dependent experiments, we determined the absolute valu
e of the third-order nonlinear optical susceptibility, $chi^{(3)}$, of our SWCNT film to be 5.53 $times$ 10$^{-12}$ esu, three orders of magnitude larger than that of the fused silica reference we used. Taking account of the filling factor of 8.75% for our SWCNT film, we estimate a $chi^{(3)}$ of 6.32 $times$ 10$^{-11}$ esu for a fully dense film. Furthermore, through polarization-dependent experiments, we extracted all the nonzero elements of the $chi^{(3)}$ tensor, determining the magnitude of the weaker tensor elements to be $sim$1/6 of that of the dominant $chi^{(3)}_{zzzz}$ component.
We study macroscopically-aligned single-wall carbon nanotube arrays with uniform lengths via polarization-dependent terahertz and infrared transmission spectroscopy. Polarization anisotropy is extreme at frequencies less than $sim$3 THz with no sign
of attenuation when the polarization is perpendicular to the alignment direction. The attenuation for both parallel and perpendicular polarizations increases with increasing frequency, exhibiting a pronounced and broad peak around 10 THz in the parallel case. We model the electromagnetic response of the sample by taking into account both radiative scattering and absorption losses. We show that our sample acts as an effective antenna due to the high degree of alignment, exhibiting much larger radiative scattering than absorption in the mid/far-infrared range. Our calculated attenuation spectrum clearly shows a non-Drude peak at $sim$10 THz in agreement with the experiment.
We have used post-synthesis separation methods based on density gradient ultracentrifugation and DNA-based ion-exchange chromatography to produce aqueous suspensions strongly enriched in armchair nanotubes for spectroscopic studies. Through resonant
Raman spectroscopy of the radial breathing mode phonons, we provide macroscopic and unambiguous evidence that density gradient ultracentrifugation can enrich armchair nanotubes. Furthermore, using conventional, optical absorption spectroscopy in the near-infrared and visible range, we show that interband absorption in armchair nanotubes is strongly excitonic. Lastly, by examining the G-band mode in Raman spectra, we determine that observation of the broad, lower frequency (G^{-}) feature is a result of resonance with non-armchair metallic nanotubes. These findings regarding the fundamental optical absorption and scattering processes in metallic carbon nanotubes lay the foundation for further spectroscopic studies to probe many-body physical phenomena in one dimension.
We report on a giant Faraday effect in an electron plasma in n-InSb probed via polarization-resolved terahertz (THz) time-domain spectroscopy. Polarization rotation angles and ellipticities reach as large as {pi}/2 and 1, respectively, over a wide fr
equency range (0.3-2.5 THz) at magnetic fields of a few Tesla. The experimental results together with theoretical simulations show its promising ability to construct broadband and tunable THz polarization optics, such as a circular polarizer, half-wave plate, and polarization modulators.
We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in
SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.
We use terahertz pulses to induce resonant transitions between the eigenstates of optically generated exciton populations in a high-quality semiconductor quantum-well sample. Monitoring the excitonic photoluminescence, we observe transient quenching
of the $1s$ exciton emission, which we attribute to the terahertz-induced $1s$-to-$2p$ excitation. Simultaneously, a pronounced enhancement of the $2s$-exciton emission is observed, despite the $1s$-to-$2s$ transition being dipole forbidden. A microscopic many-body theory explains the experimental observations as a Coulomb-scattering mixing of the 2$s$ and 2$p$ states, yielding an effective terahertz transition between the 1$s$ and 2$s$ populations.
We have observed a nearly fourfold increase in the electron spin resonance (ESR) signal from an ensemble of single-walled carbon nanotubes (SWCNTs) due to oxygen desorption. By performing temperature-dependent ESR spectroscopy both before and after t
hermal annealing, we found that the ESR in SWCNTs can be reversibly altered via the molecular oxygen content in the samples. Independent of the presence of adsorbed oxygen, a Curie-law (spin susceptibility $propto 1/T$) is seen from $sim$4 K to 300 K, indicating that the probed spins are finite-level species. For both the pre-annealed and post-annealed sample conditions, the ESR linewidth decreased as the temperature was increased, a phenomenon we identify as motional narrowing. From the temperature dependence of the linewidth, we extracted an estimate of the intertube hopping frequency; for both sample conditions, we found this hopping frequency to be $sim$100 GHz. Since the spin hopping frequency changes only slightly when oxygen is desorbed, we conclude that only the spin susceptibility, not spin transport, is affected by the presence of physisorbed molecular oxygen in SWCNT ensembles. Surprisingly, no linewidth change is observed when the amount of oxygen in the SWCNT sample is altered, contrary to other carbonaceous systems and certain 1D conducting polymers. We hypothesize that physisorbed molecular oxygen acts as an acceptor ($p$-type), compensating the donor-like ($n$-type) defects that are responsible for the ESR signal in bulk SWCNTs.
Using ultrahigh magnetic fields up to 170 T and polarized midinfrared radiation with tunable wavelengths from 9.22 to 10.67 um, we studied cyclotron resonance in large-area graphene grown by chemical vapor deposition. Circular-polarization dependent
studies reveal strong p-type doping for as-grown graphene, and the dependence of the cyclotron resonance on radiation wavelength allows for a determination of the Fermi energy. Thermal annealing shifts the Fermi energy to near the Dirac point, resulting in the simultaneous appearance of hole and electron cyclotron resonance in the magnetic quantum limit, even though the sample is still p-type, due to graphenes linear dispersion and unique Landau level structure. These high-field studies therefore allow for a clear identification of cyclotron resonance features in large-area, low-mobility graphene samples.
We demonstrate coherent control of cyclotron resonance (CR) in a two-dimensional electron gas (2DEG). We use a sequence of terahertz pulses to control the amplitude of CR oscillations in an arbitrary fashion via phase-dependent coherent interactions.
We observe a self-interaction effect, where the 2DEG interacts with the terahertz field emitted by itself within the decoherence time, resulting in a revival and collapse of quantum coherence. These observations are accurately describable using {em single-particle} optical Bloch equations, showing no signatures of electron-electron interactions, which verifies the validity of Kohns theorem for CR in the coherent regime.
