I've got a Linksys E4200 connected to my modem. I have a spare Linksys E3000 which I want to use as a range extender. Full bandwidth is required, so putting the E3000 (DD WRT firmware) in Repeater/Repeater Bridge mode is not possible. I need to use a wired connection, as you can see on the diagram.

Is a wired connection between both routers a requirement? I can connect both routers to the modem, but not between each other. I'm not willing to pull a Ethernet line between them. Bare in mind that the modem can also act as a switch/router.