Active terahertz waveguides based on transmission-line metamaterials

Benjamin S. Williams, Amir Ali Tavallaee, Philip Hon and Tatsuo Itoh The demonstration of a 1D left-handed metamaterial waveguide for terahertz quantum-cascade lasers opens the door to new techniques for beam steering and shaping. 22 August 2013, SPIE Newsroom. DOI: 10.1117/2.1201308.005081 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 quantum-cascade laser-gain medium. In this way, stimulated emission of THz photons from intraband transitions in the gallium-arsenide-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 zero-index propagation are modeled by the introduction of additional lumped element capacitance and inductance into the series and shunt branches of the transmission line.2Where a conventional transmission line has series inductance LR and shunt capacitance CR, a metamaterial line is modeled by adding series capacitance CL and shunt inductance LL (the subscripts L and R stand for left-handed and right-handed propagation, respectively). We can adapt this scheme to THz quantum-cascade devices, which are fabricated into a metal-dielectric-metal waveguide. Figure 1 shows the calculated dispersion relation for a typical design with left-handed propagation below about 2.6THz and right-handed propagation above 2.6THz: a composite right-/left-handed (CRLH) metamaterial waveguide. At 2.6THz, the dispersion relation crosses between the two types of propagation, without a stopband, while maintaining non-zero group velocity. Such a condition is referred to as balanced and results from proper engineering of the effective capacitance and inductance on the transmission line.   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. The key advance in this recent work is the inclusion of 200nm-size gaps in the top metallization of the waveguide: see Figure 2. These gaps play the role of a series capacitance in the transmission-line model for the waveguide, and are the key feature that enables left-handed propagation. We demonstrated the existence of left-handed propagation indirectly by using a section of the CRLH metamaterial waveguide as a leaky-wave coupling antenna for a THz quantum-cascade laser. The laser feeds the antenna with the THz signal, which is then radiated into the far-field at an angle that depends on the THz frequency and its location on the dispersion diagram. While propagation in the right-handed region will result in a beam angled in the forward direction, propagation in the left-handed region generates a beam angled in the backward direction (off normal). Propagation with a zero effective index (β=0) gives a beam directed in the surface normal direction. Therefore, by measuring the far-field beam pattern and the radiation frequency, we can reconstruct the dispersion relation: see Figure 1. We recently observed a backward-directed beam for the first time, demonstrating the existence of left-handed propagation.3   Figure 2. Image of a composite right-/left-handed metamaterial waveguide implemented in a THz quantum-cascade (QC) metal-metal waveguide. The dielectric of this ‘transmission line’ is made up of active THz QC gain material grown in GaAs/AlGaAs quantum wells. The inset image shows a close-up of 200nm gaps in the metallization that create the series capacitance CL and enable left-handed propagation. Cx, Lx: Capacitors, inductors (where x denotes R or L). Cu: Copper. Cr: Chromium. Au: Gold. Beyond this proof of principle, we now have access to a wide array of microwave circuit, antenna, and metamaterial design techniques that can be applied to THz lasers. For example, such a metamaterial antenna could be used to steer a beam between the forward and backward directions (depending on the exact frequency). Or, if we can develop dynamic control of the circuit elements, tunable resonators and phase shifters become possible. Our future work focuses on using these design techniques to create a new class of lasers with flexible and dynamic control of spectral and radiation properties, including beam shaping and steering, wavelength tuning, and polarization state. Benjamin S. Williams, Amir Ali Tavallaee, Philip Hon, Tatsuo Itoh University of California at Los Angeles Los Angeles, CA References: 1. B. S. Williams, Terahertz quantum-cascade lasers, Nat. Photon. 1, p. 517-525, 2007. 2. A. Lai, C. Caloz, T. Itoh, Composite right/left-handed transmission line metamaterials,IEEE Microw. Mag. 5, p. 34-50, 2004. 3. A. A. Tavallaee, P. W. C. Hon, Q.-S. Chen, T. Itoh, B. S. Williams, Active terahertz quantum-cascade composite right/left handed metamaterial, Appl. Phys. Lett. 102, p. 021103, 2013.

Metamaterial concepts applied to terahertz-laser waveguides

http://spie.org/x47667.xml?highlight=x2404&ArticleID=x47667

Benjamin S. Williams, Amir Ali Tavallaee, Philip Hon and Tatsuo Itoh

A terahertz quantum-cascade laser with a transmission-line metamaterial coupler antenna offers an intermediate step toward a zero-index laser.

11 April 2011, SPIE Newsroom. DOI: 10.1117/2.1201103.003597

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 applied to terahertz QC devices, which are typically fabricated into a double-metal waveguide that is similar in form to microstrip transmission line. Gallium arsenide (GaAs)/aluminum GaAs multiple quantum wells comprise the dielectric of the transmission line and provide amplification through stimulated emission of terahertz photons.⁴

 

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. C_x, L_x: Capacitors, inductors (where x denotes R or L). ℏω_LO: Stimulated emission energy.

 

Figure 2. Typical calculated dispersion relation for a balanced terahertz metamaterial waveguide exhibiting backward (at frequencies f < f₀) and forward wave propagation at (f > f₀), as well as zero-index propagation at f₀.

One device proposed by our group is a metamaterial ‘zero-index laser.’ This laser cavity is designed to oscillate in a mode with a zero phase index at frequency f₀ and, as such, exhibits a uniform mode in the longitudinal direction. Figure 3 shows the associated calculated electric-field pattern. This is very different from a conventional laser cavity in which the laser mode exhibits a sinusoidal standing-wave pattern and, hence, interacts nonuniformly with the gain medium. For this reason, a zero-index laser may be useful to suppress spatial-hole burning, a common phenomenon in lasers that can cause undesirable multimode oscillation. Other applications include traveling-wave metamaterial antennas that radiate with high efficiency and directivity in the forward and backward directions (depending on the exact frequency). The ability to engineer the beam and radiative coupling efficiencies would benefit terahertz QC-lasers in particular, since double-metal waveguides have notoriously poor beam patterns and coupling efficiencies.

 

Figure 3. Full-wave simulation of electric-field vectors and intensity in zero-index laser cavity oscillating at frequency f₀. Note the uniformity of the electric field in the longitudinal direction.

Since the amount of gain provided by the QC-laser material is limited, the success of this approach depends on designs that minimize losses. Our full-wave electromagnetic simulations indicate that while the ohmic and radiative losses are larger than in conventional terahertz QC lasers, they are not insurmountable. As an intermediate step toward a zero-index laser, we have demonstrated that a section of metamaterial waveguide can be used as a coupling antenna when fed by the signal from an adjacent, conventional terahertz QC-laser. The metamaterial section is active—i.e., gain is available to provide amplification to the signal injected from the master oscillator—and a directional beam (in one direction) is obtained in the forward direction.

Our next step is to demonstrate backward-wave operation from these antennas and optimize the designs to reduce losses so that a zero-index laser can be realized. However, in general, use of transmission-line metamaterial concepts is useful for designing laser waveguides and resonators with engineered phase characteristics. These techniques have the potential to allow design of lasers with flexible control of spectral and radiation properties, including beam shaping and steering, wavelength tuning, and polarization control.

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Benjamin S. Williams, Amir Ali Tavallaee, Philip Hon, Tatsuo Itoh

University of California at Los Angeles

Los Angeles, CA

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References:

1. T. A. Klar, A. V. Kildishev, V. P. Drachev, V. M. Shalaev, Negative-index metamaterials: going optical, IEEE J. Sel. Top. Quant. Electron. 12, pp. 1106-1115, 2006.

2. A. A. Tavallaee, P. Hon, K. Mehta, T. Itoh, B. S. Williams, Zero-index terahertz quantum-cascade metamaterial lasers, IEEE J. Quant. Electron. 46, pp. 1091-1098, 2010.

3. A. Lai, C. Caloz, T. Itoh, Composite right/left-handed transmission line metamaterials, IEEE Microw. Mag., pp. 34-50, 2004.

4. B. S. Williams, Terahertz quantum cascade lasers, Nat. Photon. 1, pp. 517-524, 2007.