There is nothing New Age or occult-based about a pocket diode. It supposedly protects a person from low frequency electromagnetic fields (EMF) which are emitted from objects such as power lines, microwave towers, television and computer screens, cell phones, etc. Pocket diodes supposedly neutralize these fields.
"Personal diodes have become a must for many people eager to deter as many sources of Chronic Stress as possible," writes this site which sells diodes. "These Personal Diodes come in different strengths from digital to analog frequencies. The diode is worn on the left side or center of the body. Quadrant energy enters the left side of the body as positive and exits the right side as negative. When the diode is worn on the left side of the body, the diode formula frequencies are picked up by the quadrant energies and sent throughout the body’s electrical system. The diode holds the electrical system in balance so the body is helped towards balance and health."
Some websites mention "subtle energies" and how these devices can balance "energy fields" such as those espoused by New Ager; however, the devices are not New Age or occult-based.
Whether or not they work is a different story. As this article explains, it's next to impossible to prove that an EMF device actually works which is why many consider them to be useless.
Speaking of scientific backing, there is little or no science proving the health risks of EMFs. This article contains valuable links to the current science on whether or not EMFs are harmful to humans and/or the environment.