Combined threads as these are addressing the same basic question.
You have to address a couple issues to make this work: power and data.
You can certainly connect a SATA device to an eSATA port, with the proper cable. However, you also need to power your optical drive.
Something like this would do the trick (not free), but would use a USB connection vice the eSATA connection:
https://www.newegg.com/Product/Product.aspx?Item=N82E16827993013
This more expensive option provides the eSATA interface:
https://www.newegg.com/Product/Product.aspx?Item=9SIA6ZP3KF0899
This cheaper option can be used for a more temporary solution:
https://www.newegg.com/Product/Product.aspx?Item=N82E16812311004