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_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 _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_0m modes which can be trapped in the self-induced circular waveguides over a continuous range of power values, in contrast to TE_0m modes trapped only at critical powers. Furthermore, the lowest order TM type of beam is found to be stable