A New Diffraction Integral

For the first time, it has been shown that the propagation of linearly polarized, circularly symmetric laser beams through an arbitrary optical system representable by complex ABCD matrices enclosed by a circular metal waveguide is

$$\mathbf{E_{out}^\prime}(r^\prime ,\phi) = E_0^\prime (r^\prime) \... ...me )] \mathbf{u_x} + sin(2 \phi )E_2^\prime (r^\prime ) \mathbf{u_y} \right\}$$ (1)

where

$$E_0^\prime (r^\prime) \equiv i2 \frac{\hat{z}_0}{B} exp(-i\beta_0 z) exp \left( -i \frac{\hat{z}_0}{B} Dr^{\prime 2} \right)$$ (2)

$$E_1^\prime (r^\prime) \equiv \int_0^\infty E_{x,in}^\prime (r_0^\... ...ft( 2 \frac{\hat{z}_0}{B} r_0^\prime r^\prime \right) r_0^\prime dr_0^\prime$$ (3)

$$E_2^\prime (r^\prime) \equiv \int_0^\infty E_{x,in}^\prime (1-r_0... ...eft( 2 \frac{\hat{z}_0}{B} r_0^\prime r^\prime \right) r_0^\prime dr_0^\prime$$ (4)