  To study the effects of focusing distance on the characteristics of copper
plasma, a picosecond laser was utilized to ablate a pure copper plate to
generate a plasma spectrum. Following numerous experiments on the subject,
three significant factors have been determined: lens focal length, pulse energy
and the lens-to-sample distance. These factors were employed to analyze the
spectral intensity, plasma temperature and electron density in the local
thermodynamic equilibrium (LTE) and optically thin condition. Due to the
shielding effects of mixed plasma, the strongest spectral intensity can be
obtained in the pre-focused case rather than on the focus, no matter how much
beam irradiance was employed. The more intensive the beam irradiance is, the
more the optimal position is distant from the focal point. Similarly, the
evolution of plasma temperature and electron density was shown a peak in the
pre-focused case, which is consistent with the trend of spectral intensity. For
the case of extremely high irradiance (on the focus), the shielding effects
become more apparent and the resultant above three factors decreased sharply.
When a longer-focal-length lens was employed, the spectral intensity exhibited
an obvious bimodal trend. In the pre-focused case, a longer-focal-length lens
is helpful to eliminate the effects of the roughness of the target surface
compared with a shorter one. Finally, the assumed LTE was validated by
McWhirter relation, plasma relaxation time and diffusion length, and the
optically thin condition also validated by spectral intensity ratio. We hope
this work could be an important reference for the future design of highly
optimized experiments for Calibration-Free Laser-Induced Breakdown Spectroscopy
(CF-LIBS).
