Normal mode splitting due to quadratic reactive coupling in a microdisk-waveguide optomechanical system

We study the effects of quadratic reactive coupling on normal mode splitting in a microdisk-waveguide optomechanical system, whose stability can be determined by the Routh–Hurwitz criterion. We find that the quadratic reactive coupling is important for the mode splitting of a Stokes field only in the presence of a strong pump field. For a large enough pump power, the quadratic reactive coupling will lead to larger and asymmetric frequency shifts for the two Stokes modes, which are however smaller and symmetric when only the linear reactive coupling is considered. Such a unique normal mode splitting happens in an efficient four-wave-mixing process of optomechanical interaction. This is why an anti-Stokes field is seen to arise in the presence of an excited waveguide oscillation. The anti-Stokes field has a much stronger interaction with the lower-frequency Stokes mode because their frequencies and amplitudes change remarkably in a similar way when the quadratic coupling constant is gradually increased.

► Quadratic reactive coupling may have an important influence on normal mode splitting in a microdisk-waveguide optomechanical system.
► Quadratic reactive coupling is essential to be considered only when the pump is strong enough.
► Quadratic reactive coupling can result in larger and asymmetric frequency shifts for the two split Stokes modes.
► Normal mode splitting due to quadratic coupling happens in an efficient four-wave-mixing process of optomechanical interaction.