def electric_field_amplitude_gaussian(P, sigmax, sigmay=None, Omega=1.0e6,
                                      units="ad-hoc"):
    """Return the amplitude of the electric field for a Gaussian beam.

    This the amplitude at the center of a laser beam of power P (in Watts) and\
 a Gaussian intensity distribution of standard deviations sigmax, sigmay\
 (in meters). The value of E0 is given in rescaled units according to the\
 frequency scale  Omega (in Hertz) understood as absolute frequency\
 (as opposed to angular frequency).

    >>> print(electric_field_amplitude_gaussian(0.001, 0.001))
    19.6861467587

    """
    e0 = hbar*Omega/(e*a0)  # This is the electric field scale.

    if sigmay is None: sigmay = sigmax
    E0 = sqrt((c*mu0*P)/(2*Pi))/sqrt(sigmax*sigmay)
    if units == "ad-hoc":
        E0 = E0/e0
    return E0