FF_node_polar_angle

ofiber.cylinder_step.FF_node_polar_angle(V, ell, em)

Calculate the smallest nonzero polar angle for V, ell, and em.

Calculate the smallest nonzero polar angle Θ_N for which the far-field field pattern has a node (zero), for LP mode (ell,em) in a circular step-index fiber. The polar angle-dependent factor in the far-field pattern is given by eq. (10.13) in Chen, and here by the function _FF_polar_x. This angle is a standard metric of the angular spread of an optical fiber’s output radiation. Note however that the higher the radial mode number m, the smaller the fraction of the irradiance is contained within the first node. The use of this function is demonstrated in 9-Far-field-irradiance.ipynb.

b is the normalized propagation constant. Each guided mode in an optical fiber has a specific value of b that depends on the fiber parameter V and the mode numbers ell and em.

If no mode exists, a value of np.nan is returned.

The LP_lm is specified by (ell,em) to avoid confusion between the number 1 and the letter l.

For cylindrical fibers, em is a positive integer: thus there are modes LP_01, LP_02, but not LP_10. If em <= 0 or V <= 0, None is returned.

This is a wrapper function that handles V, ell, or em being possible arrays. The private function _FF_node_polar_angle contains the details of the calculation itself.

Parameters:

• V – generalized frequency V for optical fiber (real number) [-]

• ell – azimuthal mode number ℓ (nonnegative integer) [-]

• em – radial mode number m (positive integer) [-]

Returns:

polar angle Θ_N of first far-field zero for mode (ℓ,m) [-]