Nonlinear absorption and dispersion in a two-level system with permanent dipole moments

We calculate the third-order nonlinear absorption and dispersion (self-phase-modulation and cross-phase modulation) of a homogeneously broadened two-level molecular system with permanent dipole moments interacting with (1) an optical field of frequency {ω}, and (2) two optical fields of frequency ω₁ and ω₂, i.e., the susceptibilities χ⁽³⁾(-{ω};{ω},-{ω},{ω}) and χ⁽³⁾(-ω₁;ω₁,-ω₂,ω₂). Sharp features in the nonlinear absorption and dispersion appear whenever one- or two-photon resonance conditions are met. Only features corresponding to one-photon resonance arise if the difference between the permanent dipole moments of the levels, {Δ}{μ}, vanishes. The χ⁽³⁾(-{ω};{ω},-{ω},{ω}) spectrum has two features, one at frequency ωba dominated by contributions proportional to μab⁴, where μab is the transition dipole moment of the two levels with transition frequency ωba, and the other at frequency ωba/2 dominated by contributions proportional to ({Δ}{μ})²{{{μ}}}ab²$. Sharp features in ${{{χ}}}⁽³⁾$(-${{{ω}}}₁$;${{{ω}}}₂$,-${{{ω}}}₂$,${{{ω}}}₁$) appear when ${{{ω}}}₂$ is near ${{{ω}}}ba$,${{{ω}}}₁$,${{{ω}}}₁$+${{{ω}}}ba, and{{{ω}}}₁$-${{{ω}}}ba${}.