[Paper Review] 'Growing Evanescent Envelopes and Anomalous Tunneling' in Cascaded Sets of Frequency-Selective Surfaces in Their Stop Bands

Andrea Alù, Nader Engheta|arXiv (Cornell University)|Aug 17, 2004

Advanced Antenna and Metasurface Technologies3 references18 citations

TL;DR

This paper proposes a mechanism for anomalous tunneling and growing evanescent wave envelopes in cascaded frequency-selective surfaces (FSS) operating within their stop bands. Using a transmission-line model, it demonstrates that engineered periodicity and geometry can induce interface resonances analogous to those in left-handed metamaterials, enabling complete wave tunneling despite bandgap operation.

ABSTRACT

The presence of wave tunneling and the 'growing evanescent envelope' for field distributions in suitably designed, periodically layered stacks of frequency selective surfaces (FSS) is discussed in this paper. Here it is shown that a setup completely different completely different from the Pendry's lens allows an analogous buildup of evanescently modulated waves. In particular, it is shown how an interface resonance phenomenon similar to the one present at the interface between metamaterials with oppositely signed constitutive parameters may be induced by a proper choice of the periodicities of the FSS stacks and the geometrical properties of these surfaces. The analysis is performed through an equivalent transmission-line approach, and some physical insights into this phenomenon are presented. Salient features, such as the complete wave tunneling through the pair of cascaded FSS, each operating at its bandgap, are presented and discussed.

Motivation & Objective

• To investigate wave tunneling through cascaded frequency-selective surfaces (FSS) operating in their stop bands.
• To explore the emergence of growing evanescent wave envelopes in periodic FSS stacks.
• To identify conditions under which anomalous tunneling occurs without relying on Pendry's lens or left-handed materials.
• To establish a transmission-line model for analyzing wave behavior in FSS stacks with engineered periodicity and geometry.
• To demonstrate that interface resonances can be induced in FSS systems, mimicking phenomena seen in metamaterials with opposite-sign parameters.

Proposed method

• Employing an equivalent transmission-line model to represent the periodic FSS stack and analyze wave propagation.
• Designing the periodicity and geometric parameters of FSS layers to induce resonant conditions at the interfaces.
• Analyzing the dispersion and field distribution in the stop band to identify evanescent wave growth and tunneling.
• Using the transmission-line approach to derive effective impedance and propagation constants for the system.
• Comparing the behavior of the FSS stack to that of left-handed materials with oppositely signed constitutive parameters.
• Validating the theoretical findings through numerical analysis and field distribution plots.

Experimental results

Research questions

• RQ1 Can wave tunneling occur through cascaded FSS structures when each layer is in its stop band?
• RQ2 Under what conditions can evanescent waves grow in amplitude within a periodic FSS stack?
• RQ3 How can interface resonances be engineered in FSS systems to mimic metamaterial-like behavior?
• RQ4 What role does periodicity and geometric design play in enabling anomalous tunneling in stop-band media?
• RQ5 To what extent can the transmission-line model accurately predict wave behavior in such FSS configurations?

Key findings

• Complete wave tunneling is achieved through a pair of cascaded FSS, each operating in its stop band, due to resonant interface coupling.
• Evanescent wave envelopes grow exponentially within the FSS stack, contrary to typical exponential decay in bandgap materials.
• The phenomenon arises from engineered interface resonances that mimic the behavior of materials with oppositely signed constitutive parameters.
• The transmission-line model successfully predicts the emergence of growing evanescent modes and anomalous tunneling.
• The system exhibits a strong dependence on periodicity and geometric parameters to achieve resonant tunneling.
• The results are validated through field distribution analysis and are consistent with the theoretical framework of effective medium behavior in periodic structures.