Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

THE EQUIVALENT CIRCUIT IMITATING WAVE SCATTERING BY ARRAYS OF SPLIT-RING RESONATORS
Algirdas Matulis, Gediminas Šlekas, Dalius Seliuta, and Žilvinas Kancleris
Semiconductor Physics Institute, Center for Physical Sciences and Technology, Saulėtekio 3, 10222 Vilnius, Lithuania
E-mail: algirdas.matulis@ftmc.lt

Received 7 March 2019; accepted 2 April 2019

The scattering of waves by a periodic chain of series resonant LC circuits in a two-dimensional lattice of lumped elements is considered, that imitates the scattering of electromagnetic waves by a periodic lattice of split-ring resonators. Using the translation symmetry of this chain we transformed the scattering problem into the problem of wave propagation along the strip with a single LC circuit. This problem was solved analytically presenting the transmittance as a sum of partial transmittances, corresponding to the frequency mini-bands of the strip. It is shown that the transmittance as a function of the incident wave frequency demonstrates two types of resonances with different resonant frequency dependence on the distance between neighbouring LC circuits.

Keywords: wave scattering, split-ring resonator, 2D model of lumped elements

EKVIVALENTINĖ GRANDINĖ, IMITUOJANTI BANGOS SKLAIDĄ ŽIEDINIŲ REZONATORIŲ MASYVU
Algirdas Matulis, Gediminas Šlekas, Dalius Seliuta, Žilvinas Kancleris

Fizinių ir technologijų mokslų centro Puslaidininkių fizikos institutas, Vilnius, Lietuva

Išanalizuota bangų sklaida dvimačiame radiotechniniame sutelktų parametrų modelyje su išilgai tiesės periodiškai išdėstytais nuosekliais rezonansiniais LC kontūrais. Tai imituoja elektromagnetinės bangos sklaidą dvimate periodine perpjautų žiedinių rezonatorių gardele. Panaudojus tiriamo darinio transliacinę simetriją šis difrakcinis uždavinys transformuotas į bangos plitimo juostele uždavinį ir jos sklaidą vieninteliu LC kontūru. Surastas sprendinys išreiškiant bangos pralaidumą ir atspindį dalinių pralaidumų bei atspindžių sumomis, atitinkančiomis juostelės minijuostas. Parodoma, kad tokioje sklaidoje stebimi dviejų tipų rezonansai su skirtingais rezonansiniais dažniais. Vienas jų yra susijęs su rezonansiniu LC kontūro dažniu, silpnai priklausančiu nuo nuotolio tarp gretimų LC kontūrų (plazmoninių modų analogas minėtame perpjautų žiedelių darinyje), o kito tipo svyravimų rezonansinis dažnis priklauso nuo nuotolio tarp gretimų LC kontūrų ir gali būti siejamas su gardelės modomis tuose periodiniuose dariniuose.

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