Optical Demonstration of a Crystal Band Structure Formation

Abstract

The optical modes of chains of coupled micron sized semiconductor cavities have been studied using photoluminescence spectroscopy and detailed calculations. With an increasing number of cavities, the chains exhibit photon band gaps at several Brillouin zone boundaries. The sizes of the band gaps are shown to depend on the coupling between the microcavities and also on the order of the Brillouin zone involved. PACS numbers: 78.55.Cr, 42.70.Qs Systems which exhibit photon band gaps analogous to the band gaps in the electronic states of periodic solids have been the subject of intense investigations in the past decade [1][2][3]. In the photonic case, the forbidden energy gaps in the frequency spectrum result from a periodic modulation of the refractive index. These systems are called "photonic crystals" and calculations of their properties for a number of structures have been made [1,2,4]. They permit the coupling between photons and electronic excitations to be studied and controlled in powerful ways, including the introduction of highly localized defect modes in the band gaps.Experimentally, to date photonic crystals have been realized over several parts of the electromagnetic spectrum [5][6][7][8][9][10][11][12][13][14]. The near infrared and the visible range is particularly important for potential applications as well as for fundamental studies [15,16]. Photonic crystals could be used, for example, to obtain semiconductor lasers with zero, or low, threshold due to the possibility of suppressing the spontaneous emission by photonic energy gaps. Defect modes in band gaps are of interest in connection with waveguides for ultrasmall integration.Recently it has been shown that micron sized semiconductor resonator cavities exhibit sharp photonic resonances resulting from the strong optical confinement in all three directions [17][18][19]. The vertical confinement of the photon modes is effected by Bragg mirrors, and the lateral confinement is caused by etching of the cavity. In this way, strong photonic resonances are created in the cavities whose energies are controlled by the cavity size. These modes are analogous to the sharp electronic states of atoms or quantum dots.In the present work we have created a photonic band gap system for frequencies in the near infrared by putting together microcavities in chains. We are able to construct a system by adding individual building blocks ("photonic atoms") one by one. Angle-resolved photoluminescence spectroscopy is used to study the emergence of a photonic band structure: In chains formed from an increasing number of cavities we observe a transition from discrete atomiclike modes to the photonic band structure of a solid with band gaps at several Brillouin zone boundaries. We are able to modify the modulation of the refractive index by varying the coupling between the cavities, and the energy gaps are found to increase with increasing modulation. We show that the experimental results are in quantitative agreement with numerical calculations of the photonic band struct...

Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures

“…This is analogous to the transition from atomic-like discrete states to the continuous spectrum in solid-state physics. Recently, Bayer et al observed formation of a photonic band due to coupling between the optical molecules [18].In this communication, we demonstrate the guiding of light through localized coupled optical cavity modes in 1D PBG structures which are fabricated from siliconoxide/silicon-nitride (SiO 2 /Si 3 N 4 ) pairs with λ/2 SiO 2 cavity layers. It is observed that nearly 100% transmission can be achieved throughout the waveguiding band.…”

Engineering the spatial confinement of exciton polaritons in semiconductors

“…The polaritons resulting from the strong coupling of these photon modes with the quantum well exciton will also display a mixed spectrum containing both confined and extended states. In addition to an easier fabrication approach, this kind of structure features a considerable difference with respect to micropillars, 18,19,22 where photon confinement is obtained by etching the whole cavity body, thus resulting exclusively in confined modes.…”

“…Moreover, the discrete spectrum is the key feature 14 to overcome the effect of quantum fluctuations that dominate a two-dimensional interacting Bose gas, and opens the way to the observation of collective many-body effects. [15][16][17] Attempts to produce spatially confined polariton states, in the past, have been made by etching micropillars 18,19 of a few m in diameter from an initially planar MC. [20][21][22][23] These structures have in general proved able of producing lateral confinement of polariton modes.…”

Coupled resonator optical waveguides

“…The optical modes of a linear array of GaAs cavities with InGaAs quantum wells as the optically active material, were measured by angle-resolved photoluminescence spectroscopy, demonstrating the creation of a continuum of mode energy distributions from a discrete family as the number of resonators increases [23]. Narrowing the width of the GaAs channels connecting the cavities resulted in a larger bandgap at the Brillouin zone boundaries, in accordance with the increased modulation of the dielectric function along the waveguide.…”

“…The formation, when the number of resonators is increased, of a continuous dispersion relationship such as (5) from a discrete spectrum by reduction of the mode energy splitting of the individual resonators has been discussed elsewhere [22], [23]. In the limit of nearest-neighbor coupling, as applicable to waveguides formed by coupling high-Q resonators, the parameter in (3) is given in terms of the spatial variation of the dielectric constant by .…”