def esi_radius(a, q):
    """
    Calculate equivalent step index (esi) radius for a graded-index fiber.

    Args:
        a :   radius of the fiber                  [m]
        q :   parameter for graded index fiber     [-]

    Returns:
        equivalent step index radius               [m]
    """
    return a * (1 + q) / (2 + q)