Inversionless amplification with standing-wave drive

We study amplification without inversion in closed Doppler-broadened
three-level systems driven by a standing-wave (SW) laser field. Our
results are compared to those of the well-known case of a traveling-wave
drive. A distinguishing feature of the SW case is the contribution to
probe the gain of multiphoton processes involving one probe photon and
several pump photons, with alternating absorption and emission from the
two counterpropagating pump components. These processes are only weakly
affected by Doppler broadening for probe to drive frequency ratios R
equal to integer numbers. Examples of inversionless amplification with
frequency up-conversion ratios R = 3 and R = 4 are presented.