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Optics Express

Coupled resonator optical waveguide structures with highly dispersive media

Curtis W. Neff, L. Mauritz Andersson, Min Qiu

Published Jan 1, 2007• 5 citations
Publisher

Abstract

Analysis of photonic crystal coupled resonator optical waveguide (CROW) structures with a highly dispersive background medium is presented. A finite-difference time-domain algorithm was employed which contains an exact representation of the permittivity of a three-level atomic system which exhibits electromagnetically induced transparency (EIT). We find that the coupling strength between nearestneighbor cavities in the CROW decreases with increasing steepness of the background dispersion, which is continuously tunable as it is directly related to the control field Rabi frequency. The weaker coupling decreases the speed of pulse propagation through the waveguide. In addition, due to the dispersive nature of the EIT background, the CROW band shape is tuned around a fixed k-point. Thus, the EIT background enables dynamic tunability of the CROW band shape and the group velocity in the structure at a fixed operating point in momentum space.

DOI
10.1364/oe.15.010362

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Analysis of photonic crystal coupled resonator optical waveguide (CROW) structures with a highly dispersive background medium is presented. A finite-difference time-domain algorithm was employed which contains an exact representation of the permittivity of a three-level atomic system which exhibits electromagnetically induced transparency (EIT). We find that the coupling strength between nearestneighbor cavities in the CROW decreases with increasing steepness of the background dispersion, which is continuously tunable as it is directly related to the control field Rabi frequency. The weaker coupling decreases the speed of pulse propagation through the waveguide. In addition, due to the dispersive nature of the EIT background, the CROW band shape is tuned around a fixed k-point. Thus, the EIT background enables dynamic tunability of the CROW band shape and the group velocity in the structure at a fixed operating point in momentum space.
In this paper, we propose and study a hybrid mechanism for coherent transmission of photons in the coupled resonator optical waveguide (CROW) by incorporating the electromagnetically induced transparency (EIT) effect into the controllable band gap structure of the CROW. Here, the configuration setup of system consists of a CROW with homogeneous couplings and the artificial atoms with $\ensuremath{\Lambda}$-type three levels doped in each cavity. The roles of three levels are completely considered based on a mean field approach where the collection of three-level atoms collectively behave as two-mode spin waves. We show that the dynamics of low excitations of atomic ensemble can be effectively described by a coupling boson model. The exact solutions show that the light pulses can be stopped and stored coherently by adiabatically controlling the classical field.
In the first paper of our series of articles on photon transmission in the coupled resonator optical waveguide (CROW), we used the two time Green function approach to study the physical mechanism for the coherent control by doping two-level atoms. In present paper, we propose and study a hybrid mechanism for photon transmission in the CROW by incorporating the electromagnetically induced transparency (EIT) effect in the doping artificial atoms and the band structure of the CROW. Here, the configuration setup of system, similar to that in the first paper, consists of a CROW with homogeneous couplings and the artificial atoms with Lambda\\LambdaLambda-type three levels doped in each cavity. Unlike the stimulated Raman process used in the first paper to reduce the three level systems into the two level ones, the roles of three levels are completely considered based on a kind of mean field approach where the collection of three-level atoms collectively behave as two-mode spin waves. Then the total system is reduced into an exactly solvable coupling boson model. We show that the light pulses can be stopped and stored coherently by controlling the classical field.
Ability to tune the group velocity of a light pulse is of great importance for optical communication applications and realization of quantum information processing. Tunability of group velocity can be achieved by using either optical or electronic resonances. Tunability of an optical resonance depends on the change in refractive index of the cavity material. However, since electro-optical coefficients of non-engineered materials are quite small, the tuning range of optical resonances by electric field is narrow. This makes tuning by electric field impractical for most applications. Quantum dot (QD) coupled to a photonic crystal cavity is a useful hybrid system exhibiting nonlinear features. In this work, we analyze the use of quantum dot - optical cavity hybrid systems to engineer nonlinear waveguides susceptible to electric fields. We start by theoretically analyzing the optical pulse propagation at low-photon number excitation limit in a periodically arranged strongly coupled quantum dot - photonic crystal system. A one dimensional periodic array of evanescently coupled photonic cavities (coupled resonator optical waveguides, CROWs) containing non-interacting quantum dots allows us to tune the group velocity and the bandwidth of the pulse by adjusting the cavity/QD coupling. Tunable group velocity can be achieved by applying an external electric field which will result in a significant decrease in the cavity/QD coupling because of DC Stark effect. We also show that, using this approach, light pulses can be slowed down or stored by compressing the pulse bandwidth adiabatically and reversibly. Adiabatic bandwidth compression can be achieved by slowly decreasing the coupling strength when the light pulse is inside the coupled resonator optical waveguide. The energy splitting and the coupling constant after applying electric field is calculated by using perturbation theory for two level systems. With our approach, nonlinear materials highly susceptible to electric fields can be engineered in low-excitation regime.
Quantum logic gates are basic blocks to construct quantum computing and quantum information processing systems. Quantum logic gates based on coupled-resonator optical waveguide (CROW) are analyzed with the advantage of integration with other devices. Photonic crystal CROW (PhC CROW) structure with different dimension and background medium exhibits electromagnetically induced transparency (EIT), which is used as single quantum bit (qubit) phase gate. Quantum Hadamard gate can also be realized by coupling element. Two qubit conditional quantum phase gate is achieved by concatenating two Hadamard gates and a phase gate doped with dopant. The simplicity and dynamic tunability of the device…
This paper theoretically studies the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms in hybrid structures. We provide several approaches correspondingly based on the mean field method and spin wave theory. In the present paper, we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weak-coupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.