Nonlinear magnetooptics of vacuum: second harmonic generation

Abstract

Photon-photon scattering in vacuum1 is perhaps one of the most fundamental mechanisms which can give rise to nonlinear optical effects.2 Here, we demonstrate the feasibility of new nonlinear magnetooptic effects in vacuum giving rise to optical second harmonic (SH) generation of the fundamental wave under the action of both strong dc magnetic field H0 and optical laser radiation. The strongest interaction between the fundamental wave and SH occurs when both of them propagate along the direction normal to H0. In the case of an elliptically polarized wave with the ratio between amplitudes of two decomposed components along H0 and the direction normal to it being 2/√7 ≃ 0.76, SH is linearly polarized. In the case of a linearly polarized wave, SH is also linearly polarized. The ratio of maximal intensity of SH (which occurs at the polarization angle of the fundamental wave with respect to H0, θ1 = 0°) to minimal intensity (which occurs at θ1= 90°) is equal to (7/4)2 ≃ 3. A minimal angle between the polarization of SH and H0 is (θ2)min ≃ 74° and θ1 ≃ 53°. In the case of a circularly polarized wave, SH is still circularly polarized with the same rotation as the fundamental wave. The ratio of maximal intensity of SH for linear polarization to that for circular polarization is ( 7 2 / 3 ) 2 ≃ 10.9 . Assuming H0 ~ 105 G, interaction length ~ 50 cm, radiation wavelength ~ 1 µm (Nd:glass laser), pulse duration ~10−9 s, and the laser focal area ~2.5 × 10−3 cm2, we estimate that the intensity ~4.1 × 1017 W/cm2 is required to observe 30 averaged photons for a single pulse at SH frequency (wavelength ~ 0.5 µm) for the parallel polarization (θ1 = 0°, θ2 = 90°) and ~10 averaged photons for the normal polarization (θ1 = θ2 = 90°). An even lower number of photons per pulse can be used if the averaging over a large number of pulses is used; e.g., at a 10-Hz repetition rate, only laser intensity ~2.2 × 1015 W/cm2 is required to observe 30 averaged photons within an hour.