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Applied Physics Letters

Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme

Sheng Lan, Xiongwen Chen, Jing-Dong Chen, Xu-Sheng Lin, Venu Gopal Achanta

Published Mar 24, 2005• 3 citations
Publisher

Abstract

We investigate the dynamics of nonlinear photonic crystal (PC) atoms by use of numerical simulations in a pump-probe scheme based on a finite-difference time-domain technique. A two-dimensional nonlinear PC atom with multimode is intentionally employed for the numerical simulations. The use of the multimode PC atom makes it possible that the pump and probe waves are set at different frequencies, ensuring the clear identification of the dynamics of the nonlinear PC atom. The physical model for the dynamics of nonlinear PC atoms has been established and very good agreement between the analytical and simulation results has been achieved.

DOI
10.1063/1.1894612

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We investigate the dynamics of nonlinear photonic crystal (PC) atoms by use of numerical simulations in a pump-probe scheme based on a finite-difference time-domain technique. A two-dimensional nonlinear PC atom with multimode is intentionally employed for the numerical simulations. The use of the multimode PC atom makes it possible that the pump and probe waves are set at different frequencies, ensuring the clear identification of the dynamics of the nonlinear PC atom. The physical model for the dynamics of nonlinear PC atoms has been established and very good agreement between the analytical and simulation results has been achieved.
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In this paper, we report the numerical simulation of an atom-cavity interaction within photonic crystal nano-cavities. The numerical model is based on a damping oscillator description of a dipole current and it is implemented with a finite-difference time-domain method. Using the method, we successfully simulate the atom-cavity mode field interactions of a two-level system embedded in a photonic crystal cavity under several coupling strength conditions. We show that enhancement and suppression of optical emission rate from a two-level system are also shown by this model.
We report experimental and theoretical investigations of ultrafast coherent dynamics in a photonic-crystal point-defect nanocavity. The experimental investigations are carried out using a versatile heterodyne pump-probe setup giving access to wavelength and time-resolved dynamics. We find that parametric processes originating from coherent interactions between the pump and the probe lead to characteristic and clearly distinguishable features in the time-resolved dynamics. The parametric process is caused by fast oscillations of spatially trapped carriers, with the nanocavity acting to enhance the optical fields and thereby the strength of these processes. This interpretation is confirmed by the good agreement that is obtained with a theoretical model, which extends previous works by taking into account wave-mixing effects among the probe and pump pulse. The physics behind the parametric process is explained in detail and a simple expression is derived for the conditions under which coherent interactions lead to high-transmission bands for the probe pulses. These results are important for understanding how coherent effects can be used to improve the dynamical properties of nanocavity switches.
We demonstrate the existence of self-consistent Bloch modes in resonant nonlinear photonic crystals with a complex, intensity-dependent, and frequency-dependent dielectric function. Such a dielectric response may arise by "doping" the photonic crystal with resonant quantum dots, atomic impurities, or other two-level light emitters. These exact solutions of the nonlinear electromagnetic wave equation exhibit Bloch periodicity and describe fundamental eigenmodes of an active photonic crystal under incoherent pumping. In a simple model two-dimensional photonic crystal, doped with active two-level atoms, the optical field intensity of these waves shows a laserlike threshold behavior with pumping. This appears to be a universal property of active, nonlinear photonic crystals and photonic band gap materials, arising from multidirectional distributed feedback. We describe an iterative technique for computing the detailed properties of these exact, self-consistent nonlinear waves in strongly scattering photonic crystal architectures with regions of gain and loss.
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