A TAMR (Thermal Assisted Magnetic Recording) write head uses the energy of optical-laser generated plasmons in a magnetic core plasmon antenna to locally heat a magnetic recording medium and reduce its coercivity and magnetic anisotropy. To enable the TAMR head to operate most effectively, the maximum gradient and value of the magnetic recording field should be at a point of the magnetic medium that is as close as possible to the point being heated. In addition, the coupling between the optical mode and the plasmon mode should be efficient so that maximum energy is transmitted to the medium. The present invention achieves both these objects by surrounding the magnetic core of a plasmon antenna by a variable thickness plasmon generating layer, whose thinnest and shortest portion is at the ABS end of the TAMR head and whose thickest and longest portion efficiently couples to the optical mode of a waveguide to produce a plasmon.