Effect of plasma generation on the performance of the crystalline lens R.P. Sharma n , D. Strickland, M.C.W. Campbell Department of Physics and Astronomy, Guelph-Waterloo Physics Institute, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 article info Article history: Received 12 January 2012 Received in revised form 8 April 2013 Accepted 10 April 2013 Available online 3 May 2013 Keywords: Crystalline lens Nonlinearity due to Kerr effect Gradient index (GRIN) structure abstract This paper presents the dynamic equation of a laser pulse in the human crystalline lens when plasma generation by a laser, the nonlinearity due to Kerr effect and the gradient index (GRIN) structure are simultaneously taken into account. Plasma generation affects beam propagation mainly on account of two factors. Firstly, because of the electron heavy particles collisions in the plasma, laser energy is absorbed and hence the laser beam gets attenuated. Secondly, plasma electrons also contribute to the nonlinearity. Therefore, laser beam propagation in the crystalline lens with plasma becomes a complex process. For typical lens and laser parameters, the effect of changing the plasma parameters on beam dynamics is studied here. It is found that the laser power has to be increased by a factor around 3 as compared to without plasma, to cause self-focusing of the laser beam in the lens. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Moderate powered short pulse lasers are being used for non- invasive intratissue ablation [1,2]. The surgical effects are expected to be due to the localized plasma formation in a very narrow region which leaves the surrounding tissue unaffected. Similarly, in the crystalline lenses of animals a safety study of femtosecond laser photo-disruption has been reported [3] and the importance of the dense electron cloud dominated plasma was pointed out. Photo-disruption in a specific visible pattern has been shown to increase the elasticity of the crystalline lenses of pigs [4]. The small increases in elasticity of human donor lenses [5] suggests that less disruptive fs laser microsurgery [6] could be a viable method to reverse presbyopia, the loss of the ability of the crystalline lens to change focus (accommodate) due to a loss in elasticity [7]. The role of plasma creation in microsurgery and micromanipulation by pulsed lasers and measurements of plasma dimension and its variation with laser pulse energy has also been studied [8,2]. Interaction of short pulsed, moderate power laser beams in the human eye and the resulting nonlinear effects, including plasma formation, have been studied in detail in the past [9,10]. But to the best of our knowledge plasma formation in the human crystalline lens and the interaction of the laser beam with the laser created plasma have not been theoretically investigated [11]. These studies may play an important role in refractive surgery for determining the minimum laser pulse energy required for laser modification of the crystalline lens, within the safety limit. Recently, self-focusing in the human crystalline lens, having a gradient index (GRIN) structure has been theoretically investi- gated [12], where it was estimated that the laser power required for self-focusing in the presence of the crystalline lens would be one thousandth of the critical power for self-focusing of a laser pulse in homogeneous water. This result agrees with a previous study by Pare and Belanger [13] on self-focusing in GRIN media. They showed that while beam collapse occurs at the same critical power as in a homogeneous medium, the value of the critical power (P cr ) corresponding to the preservation of the initial beam waist gets reduced in comparison to the homogeneous case. Our previous theoretical results [12], which use GRIN values specific for the human crystalline lens, are consistent with this model [13]. But in both studies, the effects of plasma formation on laser pulse dynamics are ignored. However, these theoretical studies show that even at these greatly reduced powers, the focal position moves throughout the pulse elongating the focal volume. Plasma generation affects the laser pulse propagation in a number of ways. Firstly, the laser energy is reduced by the amount of energy required to generate the electrons through multi-photon ionization. Secondly, the electrons are generated preferentially on axis where the beam intensity is maximum, thereby creating a negative lens effect. The beam would then be defocused by the electrons. Although these effects dominate the pulse propagation, they do not account for the observed formation of microcavities in transparent media such as the crystalline lens. To better under- stand the plasma heating effects, we will investigate the interac- tion of the laser beam with plasma electrons. The collisions of electrons with heavy particles will further attenuate the laser, hence the laser power has to be increased to observe self-focusing. Interaction with the laser beam may lead to heating of electrons, in contrast to the background plasma, if the energy relaxation time Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/optcom Optics Communications 0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.04.025 n Corresponding author. E-mail address: rpsharma@ces.iitd.ernet.in (R.P. Sharma). Optics Communications 304 (2013) 23–28