Phase matching for third-harmonic generation in collisional magnetoplasmas

Abstract

This paper presents a derivation of the phase-matching conditions for generation of the third-harmonic (3ω1) and combination frequencies (ω1+2ω2), by two fundamental electromagnetic waves of frequencies ω1 and ω2, propagating in the extraordinary mode along a magnetic field in a collisional plasma. Expressions for the corresponding optimum distance of propagation for maximum output and the associated values of the phase functions have been derived. In the case of the third-harmonic generation phase matching occurs when the gyrofrequency of the electrons is twice the wave frequency (for all values of plasma frequency). In the case of the combination frequencies, the phase-matching condition is represented by an expression for plasma frequency ωp in terms of the wave frequencies ω1, ω2 and the gyrofrequency ωc of electrons. Furthermore, it is seen that in the (ωc∕ω1)−(ω2∕ω1) plane, phase matching occurs in a narrow region; for every point in this region, there is a corresponding value of (ωp∕ω1). The dependence of optimum distance of propagation and the corresponding value of the phase function on electron collision frequency νav∕ω1 have been graphically illustrated for a specific case. An estimate of the maximum value of the third-harmonic conversion efficiency has also been made.