TE and TM families of self-trapped beams

TE and TM families of self-trapped light beams with circular cross section are examined. First, trapped TE/sub 0m/ modes with rotational symmetry are investigated analytically using a variational technique to obtain approximate analytical expressions for the field profiles and modal propagation constants. It is shown that trapped TE/sub 0m/ modes are unstable; they diffract below the critical trapping powers and focus to thin rings above the critical trapping powers. It is demonstrated that there exists a class of self-trapped beams with rotational symmetry, TM/sub 0m/ modes which can be trapped in the self-induced circular waveguides over a continuous range of power values, in contrast to TE/sub 0m/ modes trapped only at critical powers. Furthermore, the lowest order TM type of beam is found to be stable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>