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Europhysics Letters (EPL)

Tunable ultra-narrow band-gap of anomalous dispersion photonic crystals

Jiangtao Liu, Yun‐Song Zhou, Dongfeng Chen, Qingmei Chen

Published May 15, 2007• 6 citations
Publisher

Abstract

We use the transfer-matrix method to research the band structures in one-dimensional photonic crystals composed of anomalous dispersion material (saturated atomic cesium vapor). Our calculations show that that type of photonic crystal possesses an ultra-narrow photonic band gap and this band gap is tunable when altering the electron population in the atomic ground state of the anomalous dispersion material by the optical pumping method.

DOI
10.1209/0295-5075/78/54001

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•Jun 24, 2013•0 citations
We use the transfer-matrix method to research the band structures in one-dimensional photonic crystals composed of anomalous dispersion material (saturated atomic cesium vapor). Our calculations show that that type of photonic crystal possesses an ultra-narrow photonic band gap and this band gap is tunable when altering the electron population in the atomic ground state of the anomalous dispersion material by the optical pumping method.
The influence of laser beam on the transmittance properties of anomalous dispersion photonic crystals （PCs） is investigated. Our calculations show that the pass band of anomalous dispersion PCs is tunable when altering the electron population in the atomic ground state of the anomalous dispersion material by the optical pumping method. With circularly polarized pump light, a huge Faraday rotation can be achieved under weak light intensity. Tunable pass band of anomalous dispersion PCs may lead to important technological applications in the optically controlled optical switch.
Using the Transfer matrix method to reserch the one-dimensional photonic crystal bandgap structure which is made of electromagnetically induced transparency atomic vapor.The results show that the photonic crystal bandgap can be manipulated by varying the refractive index of electromagnetically induced transparency atomic vapor.The EIT atomic vapor relative refractive index gradually increasing with the Rabi frequency.With the Rabi frequency gradually increasing,the band gap of the photonic crystal becomes more and more narrow,but the change is becoming slower.
We study a hybrid system consisting of a narrow-band atomic optical resonance and the long-range periodic order of an opaline photonic nanostructure. To this end, we have infiltrated atomic cesium vapor in a thin silica opal photonic crystal. With increasing temperature, the frequencies of the opal's reflectivity peaks shift down by >20>20%>20 due to chemical reduction of the silica. Simultaneously, the photonic bands and gaps shift relative to the fixed near-infrared cesium D1{D}_{1}D1​ transitions. As a result the narrow atomic resonances with high finesse $(\ensuremath{\omega}/\ensuremath{\Delta}\ensuremath{\omega}=8\ifmmode\times\else\texttimes\fi{}{10}^{5})$ dramatically change shape from a usual dispersive shape at the blue edge of a stop gap, to an inverted dispersion line shape at the red edge of a stop gap. The line shape, amplitude, and off-resonance reflectivity are well modeled with a transfer-matrix model that includes the dispersion and absorption of Cs hyperfine transitions and the chemically reduced opal. An ensemble of atoms in a photonic crystal is an intriguing hybrid system that features narrow defectlike resonances with a strong dispersion, with potential applications in slow light, sensing, and optical memory.
The photonic band gap is a spectral range which cannot propagate in a periodic optical nanostructure, that is, the structure itself has a “forbidden band”. It has been successfully applied to the filters, amplifiers, mixers, etc. As is well known, dynamically tunable photonic band gaps in cold atomic lattices are of great importance in various research fields. However, the photonic band gaps of a traditional photonic crystal are non-tunable because the periodic structure is determined once the photonic crystal is grown. On the other hand, a majority of previous researches focused on improving the reflectivity of photonic band gap, which can only keep approaching to 1. Due to the action of the vacuum of the radiation field, near-degenerate lower level has an additional coherence term, the spontaneously generated coherence term. In this paper, we consider a three-level ∧-type atomic system driven by a strong coherent field, a weak coherent field and an incoherent pump, in which the two ground states are of hyperfine structure. The one-dimensional photonic band gaps are formed by cold atoms trapped in a one-dimensional-ordered optical lattice and this system may create two photonic band gaps (PBGs). The trapped cold atoms have a Gaussian density distribution in each period as determined by the optical potential depth and the average atomic temperature. We investigate in detail how the reflectivities of the two PBGs are influenced by the coherent effect of spontaneously generated coherence. Then, we find that the reflectivities of the two band gaps can be significantly improved by the spontaneously generated coherence. The reflectivities of such two band gaps can be dynamically manipulated by varying the intensity of incoherent driving field and the relative phase between the probe field and the coupling field, which cannot be realized in a conventional ∧-type atomic system. Besides, by adjusting the parameters appropriately, the reflectivities of these two band gaps can be higher than 1, which is because probe field gain stems from the spontaneously generated coherence. In the future, photonic transport properties can be investigated in the three-dimensional atomic lattices and this work is meaningful for the optical routing, photodiode and transistor.
Modern demands for high speed telecommunication and data processing have created the need for advanced materials that allow active manipulation of light waves. Subsequent research has shown that photonic crystals provide excellent candidates to accommodate these needs. Photonic crystals are a relatively new class of materials in which the refractive index is periodic in 1, 2 or 3 dimensions. This periodicity gives rise to a photonic band gap which in turn provides selective reflection of certain wavelengths of light. Another interesting property of photonic crystals is the anomalous dispersion that occurs close to the photonic band gap (i.e. at the band edge). The anomalous dispersion causes the group velocity of light to decrease considerably, allowing stronger interactions between the travelling light and the material of which the photonic crystal consists