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Propagation of Doughnut Mode in Nonlinear Media
Ram Krishna Sarkar and S. Medhekar

In this paper we have carried out a detailed investigation on the propagation of central part (core) of doughnut mode considering Kerr and saturable nonlinear media. Equation governing beam width parameter with the propagation distance is obtained using standard parabolic equation approach and has been solved numerically. It is shown that the core always diverges in a positive nonlinear medium (PNM) and focuses in a negative nonlinear medium (NNM) (when power is above a threshold value). This is in contrast to the propagation of a Gaussian beam that focuses in a PNM and diverges in a NNM. Our main finding is that collapse of the core (in NNM) can not be avoided even by using a saturable nonlinear medium (when power is above a threshold value) and saturation only increases the distance of the collapse. Exactly at threshold level, stationary self trapped propagation of the core in absence of absorption is expected but such propagation is extremely delicate in nature and ultimately leads to either collapse or divergence of the core. One very important finding of our investigation is that with arbitrary initial power, stable core propagation up to an appreciable distance can be obtained by incorporating appropriate absorption. Physical explanation for unavoidable collapse of the core in zero absorption and stable propagation with appropriate absorption is also given.

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