Abstract

A gradient index medium is a medium with a parabolic refractive index distribution: Here G is the index gradient constant and the axis is in the z-direction. A recent analysis^[1] by one of the authors (J. Wang) and his student has shown that continuously adjustable negative group-velocity dispersion up to hundreds of square femtoseconds can be produced by propagating the optical beam off the axis of a gradient index medium (see Figure 1). The idea is that the dispersion caused by the frequency dependence of G(ω) (the index gradient dispersion) is of a different sign compared to the dispersion caused by the frequency dependence of n_o(ω) (the material dispersion, usually positive). The net effect of index gradient dispersion is proportional to the square of the offset distance from the beam center to the axis, as can be guessed from the form of equation (1). Therefore, by off-axis propagating the light with a big enough offset, the net dispersion can be made negative. In a subsequent paper^[2] they further show that optical solitons in a broad spectral range can be produced by such off-axis propagation after taking into account the Kerr nonlinearity. In the present paper we develop a variational approach to study the general off-axis pulse propagation problem in a gradient index medium with Kerr nonlinearity. Compared to the method used in Ref[1,2], our variational approach has the advantages of being more general and more physically clear. Simple expressions that describe the existence criteria and properties of this new type of solitons are obtained.

© 1993 Optical Society of America