General Impedance Matching via Doped Epsilon-Near-Zero Media

Ziheng Zhou, Yue Li, Ehsan Nahvi, Hao Li, Yijing He, Iñigo Liberal, and Nader Engheta

Phys. Rev. Applied 13, 034005 – Published 3 March 2020

Abstract

The emerging technique of photonic doping endows epsilon-near-zero (ENZ) media with a broadly tunable effective magnetic permeability. Here, we theoretically and experimentally demonstrate that a finite-size doped ENZ region counterintuitively behaves as a lumped circuit element, modeled as a controllable series reactance. Based on this concept, a general matching network is constructed to match a load with arbitrary complex impedance, while, interestingly, its operating bandwidth can also be modified by fine-tuning the dopants’ properties. To demonstrate the universality of the concept, different kinds of loads are matched, including microwave circuits, antennas, and absorbing particles. Since this general impedance matching technique is not limited to a specific type of load, nor a specific geometry, and can be readily transplanted from microwave to optical regimes, the proposed methodology facilitates impedance matching for maximum usage of power in quite general scenarios, and thus, exhibits promising potential for broad applications.

Received 11 November 2019
Accepted 22 January 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.034005

Physics Subject Headings (PhySH)

Dielectric properties Dopants Impedance Light-matter interaction Metamaterials Optoelectronics Photonics

Energy applications

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Ziheng Zhou¹, Yue Li^1,†, Ehsan Nahvi², Hao Li¹, Yijing He¹, Iñigo Liberal^3,‡, and Nader Engheta ^2,*

¹Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
²Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
³Department of Electrical and Electronic Engineering, Public University of Navarre, Pamplona 31006, Spain

^*engheta@ee.upenn.edu
^†lyee@tsinghua.edu.cn
^‡inigo.liberal@unavarra.es

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 13, Iss. 3 — March 2020

Subject Areas

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Conceptual sketch of general impedance matching using doped ENZ regions. (a) A 2D ENZ medium comprising dielectric dopants is introduced within a transmission line to match a load of arbitrary complex impedance Z_L, which can take on various forms in practice, such as circuits and waveguides, antennas, and absorbing particles. Heights of the input and output ports are denoted as h_i and h_o, respectively. Incident wave is polarized with the magnetic field along the out-of-plane axis. (b) Equivalent transmission line model, where the doped ENZ channel is modeled as a series reactance iX_s.
Reuse & Permissions
Figure 2
Bandwidth tailorability with general impedance matching. (a) Equivalent circuit and geometry of a two-ENZ channel-matching network based on photonic doping structures. Cross-section areas of the regions filled with ENZ hosts (denoted by Ch.1 and Ch.2) are $0.073 λ_{p}^{2}$ and $0.039 λ_{p}^{2}$ , where λ_p is the free-space wavelength at f_p = 5.5 GHz. The relative permittivity of all dopants is chosen as 88, while the quarter-wavelength transmission lines are filled by a material with relative permittivity ε_t = 1, e.g., air. The heights of port 1 and port 2 (denoted by h₁ and h₂), and parameter L₁ take values of 10, 1, and 12 mm, respectively. Here, guided wavelength, λ_g, in the transmission line is equal to λ_p. (b) Effective relative permeability of doped ENZ channel 2. (c) Effective relative permeability of channel 1 for different values of the radii of dopants. (d) Simulation results of the transmission coefficients of the two-ENZ channel-matching network. (e) Equivalent circuit and geometry of a three-ENZ channel-matching network based on photonic doping structures. Three ENZ channels comprising dopants (with radii denoted by $R_{1}^{'}$ , $R_{2}^{'}$ , and $R_{3}^{'}$ ) are designed with cross-section areas of $0.032 λ_{p}^{2}$ , $0.037 λ_{p}^{2}$ , and $0.048 λ_{p}^{2}$ . (f) Simulation results of transmission amplitudes in Case I, $(R_{1}^{'}, R_{2}^{'}, R_{3}^{'}) = (4.10, 4.28, 4.09) 0.01 λ_{p}$ , and Case II, $(R_{1}^{'}, R_{2}^{'}, R_{3}^{'}) = (4.18, 4.22, 4.11) 0.01 λ_{p}$ .
Reuse & Permissions
Figure 3
Experimental verification. (a) The single-ENZ-channel matching network and the distribution of magnetic field magnitude at f_p. The dopant is designed with relative permittivity of 40, loss tangent of 0.001, and a cross-section area of 12 mm × 2.4 mm (0.22λ_p × 0.044λ_p). The length L of the doped ENZ channel is 20 mm (0.37λ_p), the length L₁ of the load is set as 11 mm for the single-ENZ-channel matching, and the relative permittivity of the feeding waveguide ε_f is 1.5. The heights h₁ and h₂ of port 1 and port 2 are chosen as 10 and 1 mm, respectively. (b) Simulated transmission coefficients for the dopant placed in different locations and in the absence of the dopant. (c) Photograph of the prototype of the single-ENZ-channel matching network, where a channel with width W = 27.2 mm is designed to emulate the plasmonic material following Drude dispersion profile of ε_h_,eff with a effective plasma frequency at f_p = 5.5 GHz. (d) Measured transmission coefficients for the dopant placed in different positions and in the absence of the dopant.
Reuse & Permissions
Figure 4
Applications of general impedance matching. (a) Conceptual sketch of photonic doping to match an antenna. Several apertures are introduced into the walls of the doped cavity, through which an incident-guided wave is transformed into a radiating wave. (b) Photograph of the fabricated aperture antenna matched by a doped ENZ medium. Width W, height h, and length L₀ of the air-filled cavity are set as 27.2, 5, and 55 mm, respectively. Dopant is designed with a size of 27.2 × 12 × 2.45 mm³, relative permittivity of 40, and loss tangent of 0.001. Upper metallic plate of the cavity is not shown here. (c) Measured and simulated reflection coefficients of the antenna with dopant placed at different positions. (d) Conceptual sketch of delivering power to arbitrarily shaped absorbing particles via doped ENZ media. (e) Proposed configuration for matching an absorbing particle with complex permittivity ε_p = 10 + 0.1i; detailed geometry information of this absorbing particle is presented in Supplementary Note 4 within the Supplemental Material [38]. The dopant is chosen with permittivity of 40 and radius R of 3.3 mm (0.061λ_p). Other parameters are L_s= 53.5 mm (0.98λ_p), h_c= 10 mm, L_q = 4.3 mm, and ε_q = 11. (f) Simulated reflection coefficient for the absorbing particle located at different positions. Inset depicts equivalent circuit of the matching scheme.
Reuse & Permissions
Figure 5
Numerical investigation of the influence of material loss. (a) Geometry of a two-element matching network, similar to those in Fig. 2 (radii of dopants in Ch. 1 and Ch. 2 are 0.037λ_p and 0.045λ_p, respectively), but considering the influence of loss of dopants, ENZ media, or surrounding metallic walls, which are shown in (b)–(d), respectively.
Reuse & Permissions

Physical Review Applied