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Resonant second harmonic generation of a relativistic self-focusing laser in plasma with density ramp profile has been investigated. A high intense Gaussian laser beam generates resonant second harmonic beam in plasma with density ramp profile. The second harmonic undergoes periodic focusing in the plasma channel created by the fundamental wave. The normalized second harmonic amplitude varies periodically with distance and attains maximum value in the focal region. Enhancement in the second harmonic amplitude on account of relativistic self-focusing of laser based on plasma density transition is seen. Plasma density ramp plays an important role to make self-focusing stronger which leads to enhance the second harmonic generation in plasma

Enhanced resonant second harmonic generation in plasma based on density transition