Photonic crystals and metamaterials have emerged as two classes of tailorable materials that enable precise control of light. Plasmonic crystals, which can be thought of as photonic crystals fabricated from plasmonic materials, Bragg scatter incident electromagnetic waves from a repeated unit cell. However, plasmonic crystals, like metamaterials, are composed of subwavelength unit cells. Here, we study terahertz plasmonic crystals of several periods in a two dimensional electron gas. This plasmonic medium is both extremely subwavelength (≈ λ/100) and reconfigurable through the application of voltages to metal electrodes. Weakly localized crystal surface states known as Tamm states are observed. By introducing an independently controlled plasmonic defect that interacts with the Tamm states, we demonstrate a frequency agile electromagnetically induced transparency phenomenon. The observed 50% in-situ tuning of the plasmonic crystal band edges should be realizable in materials such as graphene to actively control the plasmonic crystal dispersion in the infrared.Photonic band gaps 1 , strong light-matter interaction 2 , slow light 3 , and negative refractive index 4 arise in photonic crystal 5,6 structures due to Bragg scattering of electromagnetic waves from a repeated unit cell. However, the electromagnetic properties of photonic crystals engineered from bulk semiconductors, metals, and dielectrics generally are weakly tunable, if at all. Material systems such two dimensional electron gases (2DEGs) embedded in semiconductors 7,8 and graphene 9-11 offer a substantially more flexible electromagnetic medium. These plasmonic materials can both be lithographically patterned and electronically tuned, giving rise to a variety of subwavelength plasmonic devices that may be broadly controlled via an applied DC electric field. When a periodic structure is engineered from these systems, plasmonic band structure can be realized 12-15 . The 2DEG and graphene thus provide a platform for the exploration of widely tunable plasmonic band gap structures.Subwavelength plasmonic media that utilize a 2DEG formed at a GaAs/AlGaAs interface are the central focus of this article. Similar to the ω − q plasmon dispersion in graphene, the 2DEG plasmon dispersion depends explicitly upon both the plasmon wavevector and the AC conductivity of the medium. An effective methodology to describe plasma excitations in a 2DEG is that of an 'LC' plasmonic resonator 16 . Here L is the field effect tunable kinetic inductance of the 2DEG. The 2DEG capacitance can be introduced aswhere ef f is the effective permittivity of the embedded 2DEG and q is the plasmon wavevector 14,[17][18][19] . In high mobility 2DEG materials at microwave and THz frequencies, underdamped 'LC' plasma resonances are supported, allowing for propagation lengths on the order of tens of micrometers or plasmon wavelengths. The introduction of spatial periodicity to a 2DEG produces a plasmonic crystal (PC) where the 2DEG is a coherent plasmonic medium. Though a PC is physically more s...

We present a comprehensive theory of the one-dimensional plasmonic crystal formed in the grating gated two-dimensional electron gas (2DEG) in semiconductor heterostructures. To describe collective plasma excitations in the 2DEG, we develop a generalized transmission line theoretical formalism consistent with the plasma hydrodynamic model. We then apply this formalism to analyze the plasmonic spectra of 2DEG systems with step-like periodic changes of electron density and/or gate screening. We show that in a periodically modulated 2DEG, a plasmonic crystal is formed and derive closed-form analytical expressions describing its energy band spectrum for both infinite and finite size crystals. Our results demonstrate a non-monotonic dependence of the plasmonic band gap width on the electron density modulation. At so-called transparency points where the plasmon propagates through the periodic 2DEG in a resonant manner, the plasmonic band gaps vanish. In semi-infinite plasmonic crystals, we demonstrate the formation of plasmonic Tamm states and analytically derive their energy dispersion and spatial localization. Finally, we present detailed numerical analysis of the plasmonic band structure of a finite four-period plasmonic crystal terminated either by an Ohmic contact or by an infinite barrier on each side. We trace the evolution of the plasmonic band spectrum, including the Tamm states, with changing electron density modulation and analyze the boundary conditions necessary for formation of the Tamm states. We also analyze interaction between the Tamm states formed at the opposite edges of the short length plasmonic crystal. The validity of our theoretical approach was confirmed in experimental studies of plasmonic crystals in short modulated plasmonic cavities (G. C. Dyer et. al., Phys. Rev. Lett. 109, 126803 (2012)) which demonstrated excellent quantitative agreement between theory and experiment. * gregory.aizin@kbcc.cuny.edu † gcdyer@sandia.gov 2

We measured a change in the current transport of an antenna-coupled, multi-gate, GaAs/AlGaAs field-effect transistor when terahertz electromagnetic waves irradiated the transistor and attribute the change to bolometric heating of the electrons in the two-dimensional electron channel. The observed terahertz absorption spectrum indicates coherence between plasmons excited under adjacent biased device gates. The experimental results agree quantitatively with a theoretical model we developed that is based on a generalized plasmonic transmission line formalism and describes an evolution of the plasmonic spectrum with increasing electron density modulation from homogeneous to the crystal limit. These results demonstrate an electronically induced and dynamically tunable plasmonic band structure.

A multi-gate high electron mobility transistor coupled to a log-periodic antenna was engineered to detect sub-terahertz radiation through resonant excitation of plasmon modes in the channel. The device was integrated with a silicon hyper-hemispherical lens in order to enhance radiation collection and eliminate parasitic substrate modes. The continuous detector response spectrum from 185 GHz to 380 GHz indicates the presence of distinct collective plasmonic cavity modes resulting from the quantization of the plasmon wavevector. In a bolometric detection mode, a noise equivalent power of less than 50 pW/Hz 1/2 and a responsivity exceeding 100 kV/W have been measured at 11.5 K. V

Sensitivity of a plasmonic detector is enhanced by integrating a broadband log-periodic antenna with a two-dimensional plasma cavity that is defined by source, drain, and multiple gates of a GaAs/AlGaAs high electron mobility transistor. Both narrow-band terahertz detection and a rich harmonic spectrum are evident. With a bolometric sensor in the channel, we report responsivity, on resonance at 235–240 GHz and at 20 K, of up to 7 kV/W and a noise equivalent power of 5×10−10 W/Hz1/2.