Amir Ali Tavallaee

Zero-Index Terahertz Quantum-Cascade Metamaterial Lasers

We propose a new one-dimensional composite right/left-handed (CRLH) transmission line active metamaterial based upon a sub-wavelength metal waveguide loaded with quantum-cascade material that provides terahertz gain via stimulated emission. Finite element simulations were performed to design and characterize a one-dimensional CRLH metamaterial supporting ¿backward¿ waves in the range of 1-2 THz. The addition of capacitive gaps in the top metal and inductive virtual current paths from top contact to the ground plane of a metal-metal quantum-cascade waveguide introduces propagating negative index and zero-index modes. We evaluate the feasibility of a zero-index terahertz quantum-cascade laser, based on a CRLH resonator, which exhibits a uniform spatial mode that is immune to spatial hole burning. An alternate balanced design for traveling-wave applications is also discussed.

Terahertz quantum-cascade laser with active leaky-wave antenna

We report the demonstration of a one-dimensional waveguide for terahertz quantum-cascade (QC) lasers, which acts as a leaky-wave antenna and tailors laser radiation in one dimension to a directional beam. This scheme adapts microwave transmission-line metamaterial concepts to a planar structure realized in terahertz metal-metal waveguide technology. The active leaky-wave antenna is fed by a master oscillator QC-laser with a mode that propagates with an effective phase index smaller than unity, such that it radiates in the surface direction. The direction of emission of main beam is governed by the antenna dispersion characteristic. 25° of beam steering is observed as the lasing frequency of the QC-laser is varied from 2.65–2.81 THz.

Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers

We present the use of the cavity antenna model in predicting the radiative loss, far-field polarization and far-field beam patterns of terahertz quantum-cascade (QC) lasers. Metal-metal waveguide QC-lasers, transmission-line metamaterial QC-lasers, and leaky-wave metamaterial antennas are considered. Comparison of the fundamental and first higher order lateral mode in a metal-metal waveguide QC-laser shows distinct differences in the radiation characteristics. Full-wave finite-element simulations, cavity model predictions and measurements of far-field beam patterns are compared for a one-dimensional leaky-wave antenna. Lastly, an active leaky-wave metamaterial antenna with full backward to forward wave beam steering is proposed and analyzed using the cavity antenna model.

Terahertz composite right-left handed transmission-line metamaterial waveguides

We report terahertz metamaterial waveguides based on the concept of composite right/left-handed transmission-lines. The waveguides are implemented in a metal-insulator-metal geometry fabricated with spin-coated Benzocyclobutene and contact photolithography. Angle-resolved reflection spectroscopy shows strong resonant absorption features corresponding to both right-handed and left-handed (backward wave) propagating modes within the leaky-wave bandwidth. Tuning of the waveguide dispersion is achieved by varying the effective lumped element series capacitance. The experimental results are in good agreement with full-wave finite element method simulations as well as an intuitive transmission-line circuit model.

Finite-Element Modeling of Evanescent Modes in the Stopband of Periodic Structures

A novel implementation of periodic boundary conditions in the finite-element method is presented that is applicable to complex eigenmode analysis of the electromagnetic waves in infinite periodic media. A weighted residual finite-element (FE) model is employed to obtain the attenuation constant of evanescent/complex modes within bandgaps by analyzing only one unit cell of the structure. Plots of the imaginary and the real parts of the propagation constants versus frequency are shown which confirms the capability of the developed FE code in capturing complex modes.

A novel strategy for broadband and miniaturized EBG designs: hybrid MTL theory and PSO algorithm

Electromagnetic Bandgap (EBG) structures are increasingly utilized by a variety of microwave and optical devices as filters for unwanted signals. One such application is their incorporation in power distribution network (PDN) of electronic circuits where the EBG structure replaces one of the reference voltage planes thus forming a shielded EBG structure. The EBG induces a wide (on the order of few GHz) omni-directional stopband in the operating frequency range of the PDN which mitigates the so called simultaneous switching noise (SSN) on the power plane. The challenging aspect in designing an EBG for such applications is to achieve a wide stopband centered at low GHz frequencies while maintaining a reasonably small unit cell size and a low profile. Indeed, the dimensions of the unit cell of the EBG structure for low frequency designs can become relatively large with respect to the size of the host dielectric substrate. Therefore, availability of a systematic design approach that can provide a fast and accurate means of performance prediction to enable geometry tweaking and design optimization will be of critical importance in utilizing EBG structures in such applications.

Transmission-line metamaterial antennas for THz quantum-cascade lasers

We present a scheme for achieving active composite right/left handed (CRLH) transmission line metamaterial waveguides in the THz by loading THz QC-laser metal-metal waveguides with sub-wavelength capacitive and inductive structures. We discuss our progress in using transmission-line metamaterial concepts for the engineering of THz active leaky-wave antennas that provide amplification and exhibit beam steering.

Active terahertz waveguides based on transmission-line metamaterials

Electromagnetic metamaterials are artificial structures that can be engineered to exhibit customizable or conventionally unobtainable electromagnetic properties, such as propagation with near-zero or even negative refractive index. In a material with a negative index, the flow of energy is opposite to the movement of the wavefronts, an effect known as backward-wave or left-handed propagation (so named because the electric field, magnetic field, and wavevector form a left-handed triple). At IR and optical frequencies, left-handed materials can be made by incorporating plasmonic structures into a dielectric. Provided the size and periodicity of the structures is sufficiently small compared to the wavelength, waves propagate as if the medium were uniform with new values for the refractive index (or other bulk properties). Current research in this area investigates electromagnetic metamaterials for novel antenna concepts, sub-wavelength resonators and waveguides, superlenses that beat the diffraction limit, and even cloaking from electromagnetic radiation. Our research group has been working on methods to apply metamaterial concepts to the terahertz (THz) frequency range, where the wavelength is approximately a hundred times longer than in the visible. The novelty in our work is the combination of metamaterial-inspired waveguides with a THz quantumcascade laser-gain medium. In this way, stimulated emission of THz photons from intraband transitions in the galliumarsenide-based medium compensates for losses and allows active devices.1 To design and describe the metamaterial waveguide, we adopt the transmission-line formalism, where negative and Figure 1. Calculated dispersion relation for a balanced terahertz (THz) metamaterial waveguide exhibiting left-handed (LH) and right-handed (RH) propagation. GaAs: Gallium arsenide. AlGaAs: Aluminum gallium arsenide. p: Unit cell size.

Metamaterial concepts applied to terahertz-laser waveguides

Researchers have devoted considerable recent effort to development of ‘electromagnetic metamaterials.’ Such materials can be engineered to exhibit customizable or conventionally unobtainable electromagnetic properties, including propagation with near-zero or even negative refractive index (i.e., backward wave propagation). This is typically done by incorporating lumped inductive or capacitive elements (or, at optical frequencies, plasmonic or dielectric elements) on length scales that are sufficiently smaller than the wavelength so that the medium appears homogeneous. Electromagnetic metamaterials are currently being used to investigate and implement novel antenna concepts, subwavelength resonators and waveguides, superlenses that beat the diffraction limit, and even electromagnetic cloaking. A particular challenge is coping with the absorption that accompanies the various metallic inclusions. One approach offsets these losses by incorporating a source of gain into the metamaterial structure. For example, an active photonic material can provide gain through stimulated emission of photons.1 The terahertz frequency range is particularly well suited for investigation of active photonic metamaterials, since metal is still a relatively good conductor, inductor-capacitor circuit elements can be fabricated using contact photolithography, and photonic gain is available through intersubband transitions in terahertz quantum-cascade (QC)-laser material. Our group has proposed an approach to develop planar metamaterial waveguides that are suitable for integration with QC-laser material.2 It is adapted from the transmission-line formalism where negative and zero-index propagation can be modeled by introduction of additional lumped-element capacitance and inductance into the series and shunt branches of the transmission line (see Figure 1).3 Figure 2 shows the calculated dispersion relation for a typical balanced design. This can be readily Figure 1. (a) Schematic of a candidate quantum-cascade (QC)-laser double-metal metamaterial waveguide, where gold contacts and ground plane are indicated in yellow. (b) 1D transmission-line metamaterial obtained by incorporating both shunt and series inductors and capacitors. THz: Terahertz. GaAs: Gallium arsenide. AlGaAs: Aluminum GaAs. Cx , Lx : Capacitors, inductors (where x denotes R or L). h̄!LO : Stimulated emission energy.