Document Type : Research
Authors
jahrom university
Abstract
ransformation optics describes light propagation, in the geometrical-optics limit, as geodesic motion in an effective optical geometry determined by the refractive-index distribution. In Kerr media, the refractive index depends on the optical intensity; however, the consequences of this dependence for the intrinsic curvature of optical space have rarely been examined in a systematic way. In this work, the Gaussian curvature corresponding to the Fermat metric in a Kerr medium is analytically derived, and its behavior is investigated for a Gaussian beam. It is shown that the central curvature, contrary to a simple perturbative expectation, is a non-monotonic function of intensity: it increases at low intensities, reaches a unique maximum at the point where the nonlinear contribution to the refractive index becomes comparable in order to the background refractive index, and decreases at higher intensities due to metric normalization. This behavior leads to the existence of an intrinsic upper bound for optical curvature and, consequently, yields a lower bound for the nonlinear focusing length within the framework of geometrical optics. Moreover, by comparing the geometrical convergence index with the wave-diffraction length, the classical dependence of the critical self-focusing power is recovered. Therefore, the self-focusing threshold can be interpreted as the point at which curvature-induced geometrical focusing and wave diffraction spreading become comparable. This framework provides a quantitative link between nonlinear optics, optical geometry, and the phenomenon of self-focusing.
Keywords
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