Why can a copper Ethernet switch port auto-negotiate between 10, 100 and 1000 Mbps speeds, when fiber ports can only transmit at one speed?

The reason that fiber Ethernet ports can only transmit at one speed is that different light sources are utilized for each of the Ethernet configurations. 10Mbps Ethernet over fiber uses an 850nm LED (Light Emitting Diode), 100Mbps uses a 1300nm LED and 1000Mbps (1Gbps) uses a VCSEL (vertical Surface Emitting LASER).

If a fiber port was capable of transmitting at all of these speeds each port would require three separate light sources which is not feasibly economic. Make sure that the port speeds are the same when connecting fiber switch ports.

Also note it is recommended to always use LASER optimized Multimode fiber even when using LED light sources; this will ensure that your link will be able to support 1000Mbps speeds. When at all possible use a minimum of OM3 standard multimode and your link will be future-proof up to 10Gbps.