We investigate theoretically and experimentally light dynamics in plane-mirror Fabry-Pérot resonators filled with two- and three-dimensional photonic crystals. It has been predicted that the diffraction of such resonators can be manipulated [20] and used to control the linear and nonlinear light pattern formation there. Here we study the phenomenon in detail. We show the hyperbolic shape angular transmission profiles in case of a two-dimensional photonic structure (obtained by the one-dimensional modulation of the surface of the mirrors) and study the sub- and superdiffractive regimes in such resonators. We also summarize and review the previous results [21] of a resonator filled by a three-dimensional photonic structure (obtained by the two-dimensional modulation of the mirrors).

Keywords: photonic crystals, resonators, diffraction
PACS: 42.55.Tv, 42.25.Fx, 42.79.-e

FOTONINIAIS KRISTALAIS UŽPILDYTI REZONATORIAI
M. Peckus^a,b, R. Rogalskis^a, V. Sirutkaitis^a , K. Staliūnas^c,d
aVilniaus universiteto Lazerinių tyrimų centras, Vilnius, Lietuva
^bFizinių ir technologijos mokslų centras, Vilnius, Lietuva
^cKatalonų politechnikos universiteto Fizikos ir branduolinės inžinerijos katedra, Terasa, Ispanija
^dKatalonų tyrimų ir aukštųjų studijų institutas (ICREA), Barselona, Ispanija

Darbe tiriami plokščiųjų veidrodžių Fabri ir Pero rezonatoriai su vidine lūžio rodiklio moduliacija, atitinkančia vieną išilginį fotoninio kristalo periodą. Tokie rezonatoriai realizuojami sukuriant periodinę lūžio rodiklio moduliaciją vieno arba abiejų veidrodžių paviršiuje (t. y. suformuojant vienmates arba dvimates fazines difrakcines gardeles). Fotoninių kristalų rezonatoriaus formuojamų pluoštų difrakcinės savybės gali būti apibūdinamos subdifrakciniu (kai kampinis pralaidumo spektras platesnis už homogeninio rezonatoriaus) ir superdifrakciniu (kai kampinis pralaidumo spektras siauresnis už homogeninio rezonatoriaus) režimais. Rezonatorius su vienmate veidrodžių moduliacija išsiskiria hiperbolinio pavidalo erdviniu spektru, o dvimatės veidrodžių moduliacijos atveju – kvadratinio pavidalo erdviniu spektru. Rezonatoriaus analizei sukurtas sklaidos matricų teorija paremtas modelis. Analizuojamas pagrindinių rezonatoriaus parametrų (veidrodžių pralaidumo, gardelių difrakcinio efektyvumo, rezonatoriaus ilgio) įtaka rezonatoriaus erdvinės dispersijos charakteristikoms. Skirtingai nuo ankstesnių darbų ([20, 21]), šiame darbe pagrindinis dėmesys skiriamas rezonatoriui su vienu moduliuotu veidrodžiu. Tokio rezonatoriaus eksperimentiškai išmatuoti erdviniai skirstiniai labai gerai atitinka teoriškai sumodeliuotus, o sistema yra patogi netiesiniams šviesos dariniams fotoninių kristalų rezonatoriuose tirti.

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