The fiber optic modem-router doesn't produce a modulated electric voltage for transmitting data to the network station. This avoids completely the EMF due to the carrier and the modulation. However the fiber optic device could have some EM emissions nevertheless, see the Cons section about this.
The external fiber optic cable is not made of metal so it doesn't carry voltage spikes due to lightings during storms.
This may be very important in houses that are located in areas where storms with lots of lighting strikes happen frequently.
Since the fiber optic cable does not have any electric or magnetic field, it can be installed inside the house too. The same cable that comes from the outside can also be used inside the house to reach the room or corner where the computer and the other electronic devices are placed. If the external cable cannot be installed directly inside the house then a fiber optic coupler can be used so the fiber optic cable inside the house is connected to the fiber optic cable that comes from outside with negligible losses. This allows us to put the fiber optic modem-router in the best position inside the house to minimize our exposure to the EMF generated by the modem-router itself, or just to arrange the system in a more convenient way.
The fiber optic network terminal is still a pretty large electronic board, which surely generates some EM emissions. The optical part could have some high frequency emissions. Products made for the large public do not have any metal shielding around these parts. This could be a problem. At this moment we haven't done enough tests about this and anyway this problem may be of different intensity for different models of the fiber optic device.
The fiber optic network device surely needs a soure of DC voltage to work and the device provided for this is surely a small power adapter, which may generate a non negligible amount of EM noise. Also the power adapter may add EM noise into the mains wires, and can let the EM noise of the fiber optic device pass into the mains. This problem can be minimized by using a small linear power supply and some filters for powering the fiber optic device.
Office cable study with 3D model
Measured electric field around a power cord
Shielded power cords