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Graphene as a zero-bandgap two-dimensional semiconductor with a linear electron band dispersion near the Dirac points has the potential to exhibit very interesting nonlinear optical properties. In particular, third harmonic generation of terahertz radiation should occur due to the nonlinear relationship between the crystal momentum and the current density. In this work, we investigate the terahertz nonlinear response of graphene inside a parallel-plate waveguide. We optimize the plate separation and Fermi energy of the graphene to maximize third harmonic generation, by maximizing the nonlinear interaction while minimizing the loss and phase mismatch. The results obtained show an increase by more than a factor of 100 in the power efficiency relative to a normal-incidence configuration for a 2 terahertz incident field.

A density-matrix formalism within the length gauge is developed for the purpose of calculating the nonlinear response of intrinsic bilayer graphene at terahertz frequencies. Employing a tight-binding model, we find that interplay between the interband and intraband dynamics leads to strong harmonic generation at moderate field amplitudes. Specifically, we find that at low temperature (10 K), the reflected field of undoped suspended bilayer graphene exhibits a third harmonic amplitude that is 30% of the fundamental in the reflected field for an incident 1 THz single-cycle pulse with a field amplitude of 1.5 kV/cm. More interestingly, we find that as the central frequency of the incident radiation is increased, the third harmonic amplitude also increases; reaching a maximum of 53% for an incident frequency of 2 THz and amplitude of 2.5 kV/cm., Comment: 11 pages, 9 figures

We study the Fermi energy level dependence of nonlinear terahertz (THz) transmission of gated multi-layer and single-layer graphene transferred onto sapphire and quartz substrates. The two samples represent two limits of low-field impurity scattering: short-range neutral and long-range charged impurity scattering, respectively. We observe an increase in the transmission as the field amplitude is increased due to intraband absorption bleaching starting at fields above 8 kV/cm. This effect arises from a field-induced reduction in THz conductivity that depends strongly on the Fermi energy. We account for intraband absorption using a free carrier Drude model that includes neutral and charged impurity scattering as well as optical phonon scattering. We find that although the Fermi-level dependence in the monolayer and five-layer samples is quite different, both exhibit a strong dependence on the field amplitude that cannot be explained on the basis of an increase in the lattice temperature alone. Our results provide a deeper understanding of transport in graphene devices operating at THz frequencies and in modest kV/cm field strengths where nonlinearities exist., Comment: 10 pages, 8 figures

Random orientation of liquid-suspended magnetic nanoparticles (Ferrofluid) gives rise to zero net magnetic orientation. An external magnetic field tends to align them into clusters, leading to a strong linear dichroism on a propagating wave. Using 10 nm-sized Fe3O4, we experimentally realize a polarization-sensitive magnetic modulator operating at terahertz wavelengths. We reached a modulation depth of 66% using a field of 35 mT. The proposed concept offers a solution towards fundamental terahertz magnetic modulators.

We develop a density matrix formalism in the length gauge to calculate the nonlinear response of intrinsic monolayer graphene at terahertz frequencies. Employing a tight-binding model, we find that the interplay of the interband and intraband dynamics leads to strong harmonic generation at moderate field amplitudes. In particular, we find that at low temperature, the reflected field of undoped suspended graphene exhibits a third harmonic amplitude that is 32% of the fundamental for an incident field of 100 V/cm. Moreover, we find that up to the seventh harmonic and beyond are generated.

High quality factor resonances are extremely promising for designing ultra-sensitive refractive index label-free sensors since it allows intense interaction between electromagnetic waves and the analyte material. Metamaterial and plasmonic sensing has recently attracted a lot of attention due to subwavelength confinement of electromagnetic fields in the resonant structures. However, the excitation of high quality factor resonances in these systems has been a challenge. We excite an order of magnitude higher quality factor resonances in planar terahertz metamaterials that we exploit for ultrasensitive sensing. The low-loss quadrupole and Fano resonances with extremely narrow linewidths enable us to measure the minute spectral shift caused due to the smallest change in the refractive index of the surrounding media. We achieve sensitivity levels of 7.75 x 10^3 nm/ RIU with quadrupole and 5.7 x 10^4 nm/ RIU with the Fano resonances which could be further enhanced by using thinner substrates. These findings would facilitate the design of ultrasensitive real time chemical and biomolecular sensors in the fingerprint region of the terahertz regime., Comment: 10 pages, 6 figures

We report an experimental observation of three distinct resonances in split ring resonators (SRRs) for both vertical and horizontal electric field polarizations at normal incidence by use of terahertz time domain spectroscopy. Breaking the symmetry in SRRs by gradually displacing the capacitive gap from the center towards the corner of the ring allows for an 85% modulation of the fundamental inductive-capacitive resonance. Increasing asymmetry leads to the evolution of an otherwise inaccessible high quality factor electric quadrupole resonance that can be exploited for bio-sensing applications in the terahertz region., Comment: 8 pages, 5 figures