Optics of General Guilding Media

Weakly focusing transparent media, exemplified by the gas lens,1 provide a possible means for guided transmission of coherent light beams with relatively small loss. The optics of a medium whose refractive index decreases quadratically away from some spatial axis (the z axis, say) has been the subject of much discussion in the literature. 2 In this paper, we would like to examine the properties of more general guiding media. Some work on this problem has been carried out recently by S. E. Miller. 3 Consider a light beam traveling paraxially in the z direction in space, guided in a weakly focusing transparent medium. For simplicity, we shall consider focusing only in one of the two transverse dimensions. Thus, the refractive index of the medium and the electromagnetic field will be assumed to be dependent only on the x dimension, and to be independent of y. Our concern is with transparent media whose index of refraction has the form n = n,,(l - %f(x)). 321 322 THE BELL SYSTEM TECHNICAL JOURNAL,