Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse

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Abstract

A semi-empirical model capable of predicting the rate of tunnel ionization of N2 and O2 molecules interacting with strong Ti:sapphire laser pulses is derived.

Introduction

The interaction of two major ingredients of the atmosphere, N2 and O2, with a strong femtosecond laser pulse determines the dynamics of its propagation in the atmosphere. Owing to the nonlinear index, the laser pulse self-focuses first. The contribution of the plasma generated from tunnel ionization (TI) counteracts self-focusing. The competition between these two processes results in filaments according to the moving focus model 1, 2, 3. Therefore, any meaningful simulation of the propagation needs a predictive model for the rate of TI of the atmospheric gases. For this purpose, in the past, different analytical models such as ADK model 4, 5, barrier suppression ionization model (BSI Model) [6], Szöke's model [7] or a simple IN model [8] have been used in various types of application, such as propagation 1, 2, 3, 9, plasma interaction [10], etc. The recent findings of Larochelle et al. [11] showed that none of these models is capable of providing a satisfactory result for the rate of TI of species as simple as rare gas atoms. Instead, they verified that two equivalent models, Perelemov, Popov, and Trent'ev's model (PPT model) [12] and Krainov's model [13], correctly predicted the TI rate of atoms. Based on this work, Talebpour et al. [14] were able to model the TI rate of D2 molecule. The remarkable finding of this work is that instead of a pure Coulomb barrier 1/r which is used in the calculation of the TI rate of atoms, the rate of TI of diatomic molecule can be calculated using the PPT model by assuming that the electron tunnels through a barrier is given by Zeff/r (Zeff<1, here, Zeff is a fitting parameter to simulate the effective Coulomb potential felt by the electron that tunnels out. This parameter depends principally on the random orientation of the ground state neutral molecule). This finding is translated to a simple recipe—to calculate the rate of TI of a diatomic molecule one has to find a single parameter Zeff, and use this parameter in the PPT model. To find Zeff from calculation is not simple for molecules other than H2, but this is barely needed. For practical uses Zeff can be found from experimental results. In this article, we attempt to find Zeff for N2 and O2 by comparing the experimentally measured ion vs. intensity curves with the theoretical curves. These are obtained by integrating over the pulse duration and the interaction volume of the TI rate using the PPT model with different values of Zeff. The result is immediately applicable in the modeling of the propagation and filamentation of intense femtosecond laser pulses in the atmosphere for different application such as LIDAR. Appendix Agives the formula of the PPT model.

Section snippets

Experimental results and discussion

The experimental ion vs. intensity curves of N2 and O2 (presented in Fig. 1Fig. 2, respectively) have been obtained using a Ti:sapphire laser, with a pulse duration of 200 fs and wavelength of 800 nm. A detailed description of the experimental technique can be found in Talebpour et al. [15]. In Fig. 1, the ion vs. intensity curve of Xe (IP=12.130 eV [16], which is similar to that of O2, 12.063 eV [16]) and in Fig. 2 the ion vs. intensity curve of Ar (IP=15.759 eV [16], which is similar to that

Conclusion

In the light of the theoretical analysis of the TI of D2 molecule, we have been able to offer a semi-empirical analytical model capable of correctly predicting the rate of TI of O2 and N2.

Acknowledgements

It is our pleasure to acknowledge the technical assistance of S. Lagace and fruitful discussions with S. Larochelle. This work is supported in part by NSERC, Le fonds-FCAR and US Army Research Office (Grant number: DAAG55-97-1-0404).

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