Elsevier

Optics Communications

Volume 328, 1 October 2014, Pages 41-48
Optics Communications

Measuring high-order Kerr effects of noble gases based on spectral analysis

https://doi.org/10.1016/j.optcom.2014.04.045Get rights and content

Abstract

A method for measuring high-order Kerr effects of noble gases is proposed. It is based on analyzing spectral characteristics of the optical pulse after propagation through a hollow-core fiber which is filled with noble gas whose Kerr effects are to be measured. This method is further investigated through numerical experiments, and the retrieved Kerr refractive indexes agree well with the coefficients used in the model simulating the propagation dynamics. This method uses single beam geometry which is easy to implement and avoids the spurious interfering effects in multi-beam methods originally used for measuring these effects.

Introduction

The past few years have witnessed tremendous progress in the research of ultrafast optical pulse propagation over long distance, i.e. filamentation [1], [2], [3], since its first identification in 1995 [4]. While the phenomenon of filamentation is rich in physics [5] which involves various nonlinear responses of materials to the optical field, it also finds a lot of exciting applications, ranging from generation of secondary coherent sources like supercontinuum or THz fields to remote sensing and atmosphere pollution detection, from micromachining on bulk materials to weather control [3]. Study on filamentation has become a unique research field in physics.

Even though the filamentation has been studied a lot experimentally and theoretically by groups around the world, the understanding of its dynamical mechanism has yet reached a consensus. Previously, it was well accepted that the dynamic balance between cubic Kerr self-focusing and plasma defocusing [3] leads to filamentation. Later, it was shown that including higher order nonlinear defocusing term n4I2 in the model will improve the quality of numerical results compared with experiments [6], [7]. In this case, the plasma effect is also necessary for defocusing despite of existence of n4I2 term. Recently the high-order Kerr (HOK) effect model is introduced in which the saturation or even the inversion of Kerr effect can be responsible for the defocusing without the need of plasma [8]. This new perspective raised a lot of debates regarding which model is right [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. These debates are important because the understanding of the mechanism underlies all the studies and applications of filamentation. Besides, as the debates go on, the understanding of the physics goes deeper.

In retrospect, part of this debate originates from the measuring method of HOK coefficients. While the original work performed the measurement through a polarization technique and interpreted the results as HOK effects [22], [23], another possible explanation of the work is a laser-induced transient grating [17]. Although this pump-probe method is further analyzed in detail experimentally and theoretically by the two sides [18], [19], both have their own supportive evidence. Therefore, an independent experimental method would be beneficial to obtain more insight into this problem.

In this paper, under the paradigm of HOK model, we propose a method for measuring HOK effects of noble gases. It is based on spectral analysis of the optical pulse after propagation through the medium, which was first proposed and demonstrated in [24] and later extended in [25], [26]. This method was formerly implemented through free-space propagation in medium. Recently, we further improved this method by combining it with hollow-core fiber (HCF) structure to measure the 3rd order Kerr nonlinear refractive indexes of argon at 800 nm and 1800 nm [27]. The use of HCF has several advantages over free-space propagation such as a uniform spectral broadening, a lower input energy and a shorter propagation distance, etc. In this work, we extend this method to measure HOK effects of noble gases. It should be noted that this work is NOT meant to justify the HOK model, but to provide an independent method of studying HOK effects. Therefore, this method can check the experimental results of the original work and contribute to the settlement of the debate. The rest of the paper is organized as follows. Section 2 describes the principles of the method. Section 3 numerically investigates the application of this method. Section 4 discusses the reliability of this method, and the paper ends with a conclusion in Section 5.

Section snippets

Method

It is assumed that in this method a Fourier-transform-limited (FTL) input pulse is focused and coupled into a standard 1 m-long HCF compressor. The gas tube where the HCF is placed is filled with inert gas whose (high-order) Kerr refractive indexes are to be measured. The inner diameter of HCF is several hundred micrometers and the input pulse energy is around 1 mJ level. At the output of the tube, the spectra are recorded with a spectrometer.

In order to establish the connection between Kerr

Numerical simulations

The spectral broadening factors are obtained through numerical integration of the nonlinear Schrödinger equation [30](∂ξ−iD^)E=iT^[ω0c(∑j=15n2jhj|E|2j)E]−σ2dE−iqe22meε0cω0T^−1[dE]−12fIE,where the envelope E is normalized to intensity I. Linear operator D^=iα(0)−α(1)∂τ+∑m=2∞(i∂τ)m[β(m)+iα(m)]/m! describes the waveguide mode attenuation α and dispersion β [31] where β(m)=dmβ/dωm|ω=ω0 and α(m)=dmα/dωm|ω=ω0. The retard frame moving at the group velocity of the fundamental mode is introduced. The

Discussions

To further show that the proposed method is capable of measuring the HOK effects, this method is also applied to measure Kerr effects of different models to see whether it can discriminate these models. Two extra models are used here, i.e., the cubic Kerr model (using only n2 with value in Table 2 in Eq. (6)) and the perturbative high-order Kerr model [6] (using n2 with value in Table 2 and n4 with value 10 times of that in Table 2 in Eq. (6)).

Fig. 6 shows the retrieved results of the cubic

Conclusions

In conclusion, we propose a new method for measuring HOK effects of noble gases. It is based on spectral analysis of the optical pulse after propagation through a gas-filled HCF. The application of this method is further demonstrated through numerical experiments, and the retrieved Kerr refractive indexes agree well with the coefficients used in the simulating model. This method uses single beam geometry which is easy to implement and avoids the spurious interfering effects in multi-beam

Acknowledgments

This work is supported by the National Natural Science Foundation of China Nos. 11204328, 10734080, 60908008, 60921004 and 61078037, the National Basic Research Program of China under Grant no. 2011CB808101.

References (36)

  • A. Couairon et al.

    Phys. Rep.

    (2007)
  • E.T.J. Nibbering et al.

    Opt. Commun.

    (1995)
  • J.-F. Ripoche et al.

    Opt. Commun.

    (1997)
  • Ding Wang et al.

    Opt. Commun.

    (2013)
  • Ding Wang et al.

    Opt. Commun.

    (2012)
  • S.L. Chin et al.

    Can. J. Phys.

    (2005)
  • L. Berge et al.

    Rep. Prog. Phys.

    (2007)
  • A. Braun et al.

    Opt. Lett.

    (1995)
  • S.L. Chin

    Femtosecond Laser Filamentation

    (2010)
  • A. Vincotte et al.

    Phys. Rev. A

    (2004)
  • S. Champeaux et al.

    Phys. Rev. E

    (2008)
  • P. Bejot et al.

    Phys. Rev. Lett.

    (2010)
  • J.K. Wahlstrand et al.

    Phys. Rev. Lett.

    (2011)
  • P. Polynkin et al.

    Phys. Rev. Lett.

    (2011)
  • P. Bejot et al.

    Phys. Rev. Lett.

    (2011)
  • V. Loriot et al.

    Laser Phys.

    (2011)
  • A. Teleki et al.

    Phys. Rev. A

    (2010)
  • C. Bree et al.

    Phys. Rev. Lett.

    (2011)
    • View full text
    Copyright © 2014 Elsevier B.V. All rights reserved.