Based on the following paragraph. An initially parallel...

Based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index, $\mu(I)=\mu_{e}+\mu_{2} I$, where $\mu_{0}$ and $\mu_{2}$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The initial shape of the wavefront of the beam is (a) comvex IAIFEE 2010] (b) concave (c) comvex near the axis and concave near the periphery (d) planar

Based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index, $\mu(I)=\mu_{e}+\mu_{2} I$, where $\mu_{0}$ and $\mu_{2}$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.
The initial shape of the wavefront of the beam is
(a) comvex IAIFEE 2010]
(b) concave
(c) comvex near the axis and concave near the periphery
(d) planar

Key Concepts

Intensity-Dependent Refractive Index

This concept deals with how the refractive index of a medium can vary as a function of the light intensity passing through it. In many nonlinear optical materials, the index of refraction is not constant but changes with the beam’s intensity, leading to a situation where different parts of the beam experience different optical paths. This is crucial for understanding phenomena such as self-focusing and defocusing in nonlinear media.

Spatial Distribution of Intensity

The beam’s intensity profile—how brightness changes across the cross-section—directly influences the refractive index in intensity-dependent media. When the intensity is highest at the center and decreases toward the edges, the refractive index will similarly be highest at the center, causing variations in the phase velocity of light across the beam. This spatial inhomogeneity is central to the problem at hand.

Wavefront Curvature

Wavefront curvature is a measure of how the phase of a light wave varies spatially as it propagates. When different parts of the beam travel at different speeds due to a spatially varying refractive index, the initially planar wavefront can acquire a curvature. The part of the beam experiencing a higher refractive index will lag, which can result in a concave or convex wavefront depending on the exact profile of the refractive index variation.

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