Simplified equivalent circuit approach for designing time-domain responses of waveform-selective metasurfaces

Abstract

In this study, we demonstrate simplified equivalent circuit models to effectively approximate responses of recently reported waveform-selective metasurfaces that distinguish different electromagnetic waves even at the same frequency depending on their waveforms or pulse widths. Compared to conventional equivalent circuit models that represent behaviors of ordinary metasurfaces in the "frequency" domain, the proposed models enable us to explain how waveform-selective metasurfaces respond in the "time" domain. Our approach well estimates not only time constants of waveform-selective metasurfaces but also their entire time-domain responses. Particularly, this study reports the importance of resistive components of diodes as well as a limitation of our models with respect to power dependence, although still the models effectively work when waveformselective mechanisms are clearly exhibited with a sufficiently large input power. Thus, the idea of the proposed equivalent circuit models contributes not only to more understanding waveform-selective mechanisms but also to facilitating the design process of such unique structures. THE MANUSCRIPTIn electromagnetics, artificially engineered periodic structures 1-5 are well known to have an advantage over conventional materials available in nature, since their electromagnetic responses are readily tailored by adjusting their subwavelength geometry to produce various electromagnetic characteristics including negative/zero refractive index 6,7 and extremely large surface impedance 3 . Particularly, a planar type of structures, or the so-called metasurfaces, has a simpler form than 3D periodic structures and is therefore used for a wide range of applications such as wavefront shaping 8-10 , spatial filtering screens 11-13 , RF (radio-frequency) or optical absorbers [14][15][16] , and digital coding 17 . Moreover, these unique properties and performances are further extended by introducing a nonlinearity to a metasurface [18][19][20][21][22] . Although ordinary metasurfaces have strong frequency dependence and are thus designed to operate at the frequency of interest, circuit-based metasurfaces containing schottky diodes were recently demonstrated to be capable of distinguishing different waves in response not only to the incoming frequency components but also to the waveforms or pulse widths (FIG. 1(a)) [23][24][25][26][27] . Hence, these waveform-selective metasurfaces were expected to give us an additional degree of freedom to control electromagnetic waves even at the same frequency. For instance, the use of these materials enabled us to effectively absorb an arbitrary waveform and lower its bit error rate compared to other

Pseudo‐Waveform‐Selective Metasurfaces and their Limited Performance

“…In fact, this range depends on what circuit values are used for the internal inductor and resistor ( and ), which determine the time constant τ of the structure in Figure 4b approximately as follows. [ 47 ] where and R 0 is the effective resistive component of one of the diodes used. Note that Equation (9) is based on a simplified equivalent circuit model to predict time‐domain responses.…”

“…[ 47 ] In this study, this equation is not used for our numerical simulations, where nonlinear diodes are modeled using SPICE parameters. However, this equation can be used as a design guide to see how time constant relates to , , and ( is obtained by different methods including a current–voltage curve of the specific diode used [ 47 ] ). For instance, the time constant of a nonlinear waveform‐selective metasurface varies with increasing .…”

“…Note that Equation (9) is based on a simplified equivalent circuit model to predict time-domain responses. [47] In this study, this equation is not used for our numerical simulations, where nonlinear diodes are modeled using SPICE parameters. However, this equation can be used as a design guide to see how time constant relates to L n , R n , and R d (R d is obtained by different methods including a current-voltage curve of the specific diode used [47] ).…”

Pseudo-Waveform-Selective Metasurfaces and Their Limited Performance

“…However, the nonlinear waveform-selective metasurfaces tend to show variations in absorptance over a broad pulse width range. In fact, this range depends on what circuit values are used for the internal inductor and resistor (L n and R n ), which determine the time constant τ of the structure in Figure 4b approximately as follows [47]:…”

“…where R d = 2R 0 and R 0 is the effective resistive component of one of the diodes used. Note that Equation ( 9) is based on a simplified equivalent circuit model to predict time-domain responses [47]. In this study, this equation is not used for our numerical simulations, where nonlinear diodes are modeled using SPICE parameters.…”