Why the eSATA port?
I had to transfer around 3 TByte of data from one external RAID to another. Both have been connected at the only FireWire 800 port in a daisy chain configuration. The transfer took more than 24 hours due to the fact that the 800 MBit/s the port could handle is cut into half the speed shared between both RAID systems. The 800 MBit/s are unrealistic and optimally I got around 80 MByte/s which is around 640 MBit/s. Over the full 3 TBytes I had an average of 34 MBytes/s per device.
This painful situation brought me to the idea of using the Optical SATA port to connect one of the Lacie 4big devices.
Coverting the Mac mini Slimline Port to Standard SATA
The first step is to convert the optical connector (slimline), which is slightly different to a standard SATA port. To get this done, I used a converter cable like the one in the second picture. There’s a how-to available at ifixit.com how to create such a cable.
The slimline connector looks like this:

The cable from the other side needs to be connected like this:

Converting the SATA connector to a eSATA port
I wanted to be able to have a real eSATA port on the backside of the Mac mini. To make this possible, I had to cut (actually mold) a hole into the backside plastic and let the standard SATA cable look to the outside.
To be able to close the case again, I also cut off the security cable connector. Once the case is closed I only needed to get the right adapter to change the SATA male port to a female eSATA port. The connector I used is the following:
InLine®, eSATA female to SATA female
The completed eSATA modification looks like this:

Transfer speeds connected via eSATA

The top speed is more than 120 MB/s, from FireWire 800 to eSATA I have more than 80 MBytes/s, which is more than double the speed I had before.
Here’s a screenshot of the LaCie 4big quadra connected via eSATA to the Mac mini:
