Is it okay to ground one side of my laser diode?

It’s important that you NOT ground either the anode or the cathode of your laser diode for several reasons:

A closed-loop laser diode driver needs to measure the output current accurately. A path to ground diverts a portion of the current, making the measurement (and thus the output current) inaccurate.

A ground path reduces the effectiveness of the stripline cable. The increased inductance distorts the pulse waveform.

It’s unsafe. We don’t want current flowing from the laser fixture and table through a person or conductive object to ground!

If either terminal of the laser diode is unavoidably connected to the package, consider using nylon hardware to mount the laser package or placing other insulation between the laser package and the table.