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Acta Physica Sinica

Analysis of lasing in gain medium based on four-energy level atomic model

Sun Bing-Bing, Wu Bo, Wang Hui, Zhixiang Huang, Xianliang Wu

Published Jan 1, 2012• 1 citation
Publisher

Abstract

With the present interest in metamaterial, gain medium shows promise for complex system due to their amplification effect and wide potential application area. In this paper we present a model that simulates lasing in gain medium by using a model of four-energy level atomic system based on the finite-difference time-domain method.Meanwhile we propose a new pump mechanism, i.e., Gaussian Pump. It is found that results of the spectra, lasing threshold and population dynamics of the new pump mechanism are in good agreement with theoretical results. The results can also provide reference for caculating more complex metamaterial system.

DOI
10.7498/aps.61.220206

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•Jan 1, 1992•1 citation
With the present interest in metamaterial, gain medium shows promise for complex system due to their amplification effect and wide potential application area. In this paper we present a model that simulates lasing in gain medium by using a model of four-energy level atomic system based on the finite-difference time-domain method.Meanwhile we propose a new pump mechanism, i.e., Gaussian Pump. It is found that results of the spectra, lasing threshold and population dynamics of the new pump mechanism are in good agreement with theoretical results. The results can also provide reference for caculating more complex metamaterial system.
A faster numerical method based on FDTD for the four energy level atomic system is present here. The initial conditions for the electrons of each level are achieving while the fields are in steady state. Polarization equation, rate equations of electronic population and Maxwell’s equations were used to describe the coupling between the atoms and electromagnetic wave. Numerical simulations, based on a finite-difference time-domain (FDTD) method, were utilized to obtain the population inversion and lasing threshold. The validity of the model and its theory is confirmed. The time, which we can observe the lasing phenomenon, is much shorter in our new model. Our model can be put into using in large scale simulations in mutiphysics to reduce the total simulated time.
We establish a new approach for pump-probe simulations of metallic metamaterials coupled to the gain materials. It is of vital importance to understand the mechanism of the coupling of metamaterials with the gain medium. Using a four-level gain system, we have studied light amplification of arrays of metallic split-ring resonators with a gain layer underneath. We find that the differential transmittance ΔT/T can be negative for split-ring resonators on the top of the gain substrate, which is not expected, and ΔT/T is positive for the gain substrate alone. These simulations agree with pump-probe experiments and can help to design new experiments to compensate for the losses of metamaterials.
We derive and test a generalization of the steady-state ab initio laser theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient finite difference time domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over between the regime of strong spatial hole burning with multimode lasing to a regime of negligible spatial hole burning, leading to gain-clamping, and single mode lasing. The effect of spatially inhomogeneous pumping combined with diffusion is also studied and a relevant length scale for spatial inhomogeneity to persist under these conditions is determined. For the semiconductor gain model, we demonstrate the frequency shift due to Pauli blocking as the pumping strength changes.
Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.
Theoretical model of an open four-level atomic system driven by two fields was presented. The density matrix equations of motion were obtained by the electric dipole and the rotating wave approximations. Under resonance of corresponding fields, the physical mechanism of lasing without inversion (LWI) was discussed and its linear analytical solution was obtained. By numerical results, we studied the effects of the spontaneous decay rates between atomic levels, incoherent pump rate, the injection rates, and the exit rate on the gain without inversion and the population difference of the system. The difference between the linear and nonlinear gain and the population difference of the system were discussed. A LWI gain was got during the region of the spontaneous decay rates between atomic levels. The LWI gain can obtain by adjusting suitably incoherent pump rate, the atomic injection ratio and the exit rate. The curves of the linear gain and the nonlinear gain were similar with the Rabi frequencies of the driving fields. The curves of the linear population difference and the nonlinear population difference were similar too. The linear stable value of the gain was larger than the nonlinear stable value of the gain.
This thesis is concerned with the amplification of coherent radiation from an active medium under conditions which require no population inversion between the energy levels. Gain without population inversion may be obtained by creating a sufficiently strong correlation between pairs of atomic states, usually with the help of external sources of resonant electromagnetic radiation. Our main objective is to investigate two possible selections for the active medium: a three level atom in a lambda configuration and a Raman-driven four level model. For both we identify the conditions that lead to inversionless laser action, we calculate the small signal gain and investigate the physical mechanisms which are responsible for the emergence of gain. While the ultimate cause of the gain is quantum interference, we propose attractive alternative pictures based on the dressed states of the coupled atom-driving field systems. We address the important practical issue of the effect of atomic motion and related Doppler broadening on the inversionless gain profile and we also analyze the transient response of each laser model with the help of the appropriate Maxwell-Bloch equations. Finally we develop a fully quantum mechanical description of the lambda model and find that the radiated field can display unique quantum features which manifest themselves with sub-Poissonian photon fluctuations.