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M. C. W. Campbell, R. P. Sharma, D. Strickland; Modeling Nonlinear Optical Interactions in the Crystalline Lens- Defining the Light Required for a Presbyopia Cure. Invest. Ophthalmol. Vis. Sci. 2007;48(13):6007.
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Femtosecond laser pulses are used to micromachine corneal flaps. Micromachining the crystalline lens of the eye has been proposed as a method of improving the elasticity of the lens by creating microbubbles within the lens. This would provide a potential "cure" for presbyopia. We wished to investigate the underlying physical mechanisms that might currently generate the cavitationbubbles observed in vitro. We assess the role of self-focusing (which is due to the intensity dependence of the refractive index), and multi-photon and avalanche ionization on micro-cavity bubble formation within the crystalline lens. It is important that these bubbles remain as small as possible to avoid excessive light scatter.
We created a model of nonlinear pulse propagation in the crystalline lens. We developed the paraxial wave equations for Gaussian beams that include both the nonlinear Kerr effect and the gradient refractive index (GRIN) of the crystalline lens.
Because of the GRIN structure, self-focusing occurs in the crystalline lens at powers that are three orders of magnitude lower than in homogeneous media. The model predicts the required input beam diameter and radius of curvature for self-focusing within the crystalline lens. The theoretical modeling showed that, at powers above the critical power for self-focusing, the focal spot moved over the duration of the pulse, resulting in a line array of foci known as filamentation. Filamentation could result in closely spaced microbubbles along the propagation direction that could then coalesce and cause light scatter.
To the best of our knowledge, self-focusing within a GRIN structure has not previously been theoretically modeled. A remaining question is whether bubble formation requires avalanche ionization and therefore a threshold energy as well as a threshold intensity for multi-photon ionization. Answers to these questions will define the pulse and beam profiles required for a presbyopia cure.
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