Like I specify in the title, I want to know that one fiber can be used to transmit and receive signals. Whether it can or not, why?
Normally, you would use a separate fibre for transmit and receive, so two fibres for bi-directional transmission. You can purchase BiDi transceivers, which allow you to use a single fibre for both transit and receive. These transceivers use Wave Division Multiplexing and modulate the transmit and receive onto different wavelengths so that they do not interfere which each-other. An example of this would be Cisco SFP-10G-BXD-I or SFP-10G-BXU-I transceivers, which both allow for 10GBASE over a single strand of fibre.
A Passive Optical Network (PON) is used by a lot of Fiber to the Home (FTTH) Internet Service Providers (ISP) to provide network access over a single fiber to multiple end points (homes).
Here is a link to the Wikipedia Page on PON's.
Can one fiber be used to transmit and receive signals?
Yes, one fiber can be used to transmit and receive signals. Have you heard of the WDM technology? This technology can multiplexe a number of optical carrier signals onto a single optical fiber by using different wavelengths of laser light. There are two common types of the WDM technology—CWDM and DWDM.
Let's take CWDM as an example, a typical 8-channel CWDM system offers 8 times the amount of bandwidth that can be achieved using a SONET/SDH system, for a given transmission line speed and using the same optical fibers. For more, please have a look at this blog.
For you own network, you can use the CWDM/DWDM optical transceivers, or BiDi transceiver.