Doubly Resonant Optical Periodic Structure

Abstract

Periodic structures are well known in various branches of physics for their ability to provide a stopband. In this article, using optical periodic structures we showed that, when a second periodicity – very closed to the original periodicity is introduced, large number of states appears in the stopband corresponding to the first periodicity. In the limit where the two periods matches, we have a continuum of states, and the original stopband completely disappears. This intriguing phenomena is uncovered by noticing that, regardless of the proximities of the two periodicities, there is an array of spatial points where the dielectric functions corresponding to the two periodicities interfere destructively. These spatial points mimic photonic atoms by satisfying the standards equations of quantum harmonic oscillators, and exhibit lossless, atom-like dispersions.

Center mode of a doubly resonant optical periodic structure

“…s Therefore, for a very large R, using a small angle approximation (i.e., assuming a small, x , is large [14]. Equation ( 9) is also in perfect agreement with the results of harmonic oscillator theory for the DPSs [7]. Equation (9) shows that when R is large the slowly varying envelop is essentially a Gaussian envelope.…”

“…Typical dielectric periodic structures such as conventional gratings and photonic crystals [1][2][3] can be characterized by a single period a. The dielectric profile of a single-period structure (SPS) can be modified periodically on a spatial scale much larger than a to form a dual periodic structure [4][5][6][7]. If we Fourier transform the dielectric function of the dual periodic structure it will consist a group of closely spaced peaks around the fundamental frequency, G=2π/a.…”

“…If a dielectric structure has only two such closely spaced frequency peaks [6,7], then interesting interference effects, like those observed in electromagnetic induced transparency and coupled resonator induced transparency systems [8][9][10] take place. The dielectric function of doubly resonant periodic structure (DPS)-dielectric periodic structure with two closely spaced harmonic peaks its Fourier spectra, with a weak dielectric modulation can be written as [7] sposition where the two cosine waves in equation (1) destructively interfere. A DPS in principle exhibits a dense number of slow modes [6,7].…”

“…The dielectric function of doubly resonant periodic structure (DPS)-dielectric periodic structure with two closely spaced harmonic peaks its Fourier spectra, with a weak dielectric modulation can be written as [7] sposition where the two cosine waves in equation (1) destructively interfere. A DPS in principle exhibits a dense number of slow modes [6,7]. The density of the slow modes increases as R increases.…”