I believe I found a solution!
I doubt you are still having issues at this point, since it has been some time since the last person posted. However, I encountered the same issues you described, and was bummed to see no one posted a fix. To recap, we are both using a TP-Link router using wireless N, and every device in our home is capable of connecting to the router wireless, except our Mac computer. The mac is capable of seeing our neighbors wireless networks, and connect to those that are not secured, but our mac doesn't even see our routers SSID. AS a note, I am using OSX Yosemite 10.10.3, but other users have noted they have encountered the issue also using older apple operating systems.
Here is what worked for me:
In short, the "WPA Algorithms" on my router was set to "AES," but we are going to change it to "TKIP+AES." You can change it back to AES once we are done (if you would like) and the mac should now be able to detect the wireless network. That doesn't neccesarily explain why our macs don't using.
1. Wirelessly connect to your router via another computer. One that is able to see and connect.
2. Login to the routers backend. Likely you router will still have the default IP address 192.168.1.1 (open a browser, e.g., firefox, google chrome, and type in 192.168.1.1, press enter)
3. Type in the uersname and password. Hopefully you still know it, otherwise, it might be the default username and password for TPLink. Username: admin Password: admin
4. Select "wireless" or "wireless Security"
5. Change the "WPA Algorithms to either "TKIP+AES" or "AES" (the one you don't already have selected)
6. Apply Setting - At this point, you will be disconnected from your network for about 30 seconds. Reconnect to your wireless network.
7. Check to see if you Mac computer is now able to see your wireless network. Connect to it, and enjoy!
8. Optional: repeat this process, but change the WPA algorithm back to what it was before, (likely TKIP+AES for increased compatibility with devices)