Linear negative dispersion with a gain doublet via optomechanical interactions

Optical cavities containing a negative dispersion medium have been proposed as a means of improving the sensitivity of laser interferometric gravitational wave (GW) detectors through the creation of white light signal recycling cavities. Here we classically demonstrate that negative dispersion can be realized using an optomechanical cavity pumped by a blue detuned doublet. We used an 85mm cavity with an intra-cavity silicon nitride membrane. Tunable negative dispersion is demonstrated, with a phase derivative $d\phi \mathrm{/}df$ from $-0.14$ Deg$\cdot$Hz${}^{-1}$ to $-4.2\times {10}^{-3}$ Deg$\cdot$Hz${}^{-1}$.