Abstract

Relativistic nonlinear optics¹ of free electrons in a magnetic field predicts the existence of strong nonlinear effects with very low power of driving radiation. Even small relativistic effects may result in a hysteretic resonance either at the main cyclotron frequency Ω, predicted in Ref. ² and experimentally observed in Ref. ³, or at the optical frequencies ω₁ and ω₂ when ω₁ − ω₁, = Ω or ω₁ − ω₁ = 2Ω (multiphoton resonances¹ of different orders). Here we show theoretically that yet another nonlinear optical effect in such a system is feasible; this effect consists in the generation of higher-order subharmonics Ω of optical field with frequency ω when ω = nΩ where n ≥ 2 is the integer. The critical amplitude of the laser field required for the subharmonic excitation of the nth order is E_cr= E₀ρ(n), where E₀ = 2eΩ²/3c² and ρ(n) is a slowly increasing function of n; ρ(2) = 1. For λ₀ = c/2πΩ = 1 mm, the amplitude E₀ corresponds to an intensity as low as ~2 × 10⁻¹⁰ W/cm². Therefore, the cyclotron motion of electrons in a microwave range can be excited at a very high-order subharmonic of a driving laser radiation in infrared or even visible ranges with a very low driving power. This phenomenon may prove to be very important in establishing coherent links between optical lasers and atomic or molecular microwave clocks.

© 1986 Optical Society of America