Mathematical and diffractive modeling of self-healing

To analyze the self-healing of a partially obstructed optical beam, we represent it by two orthogonal field components. The first component is an exact copy of the unobstructed beam, attenuated by a factor that is computed by a simple formula. The second component represents a pure distortion field, due to its orthogonality respect to the first one. This approach provides a natural measure of the beam damage, due to the obstruction, and the degree of self-healing, during propagation of the obstructed beam. As interesting results, derived in our approach, we obtain that the self-healing reaches a limit degree at the far field propagation domain, and that certain relatively small phase obstructions may produce a total damage on the beam. The theory is illustrated considering a Gaussian beam, distorted by different amplitude and phase obstructions. In the case of a soft Gaussian obstruction we obtain simple formulas for the far field limit values of the beam damage and the self-healing degree.