Gaussian beam propagation and imaging in hyperbolic secant profile media

The propagation of Gaussian beams in GRIN media characterized by the hyperbolic secant (HS) index profile is studied. It is shown that the profile can contract, expand or maintain the width of a beam incident with the beam waist at the input end of the medium. We derive an accurate analytical expression for the mode width of the fundamental mode of a HS medium. The imaging characteristics of the medium are also studied and compared to selfoc media. It is shown that, in the appropriate limit, the expressions for the HS profile reduce to those of a selfoc medium.