Optomechanically induced transparency in a Laguerre-Gaussian rotational-cavity system and its application to the detection of orbital angular momentum of light fields

In this paper, we investigate the optomechanically induced transparency (OMIT) phenomenon in the Laguerre-Gaussian (L-G) rotational-cavity optomechanical system, which can be regarded as an analog of the OMIT in a cavity optomechanical system with a vibrational mirror. We find that the window width of OMIT is dependent on the orbital angular momentum of the L-G light, which can be used to detect the orbital angular momentum of L-G light. We then accordingly propose a scheme to measure the orbital angular momentum of L-G light with OMIT, and its feasibility is justified by numerical simulation.

Figure 1

Schematic diagram of the system consists of an optomechanical cavity with a rigidly fixed mirror FM and a rotational one RM, the cavity mode is the L-G mode and is driven by a strong pumping field ${\varepsilon }_l$. A weak field ${\varepsilon }_p$ acts as probe to detect response of the system. The output field is represented by ${\varepsilon }_{\text{out}}$. The equilibrium position of the rotational mirror is ${\varphi }_0$, and the angular displacement is indicated by angle $\varphi$ under the action of the torsion. The charge on the beams at various points has been indicated.

Figure 2

The absorption curves (a) and dispersion curves (b) as functions of the normalized optical detuning when the orbital angular momentum of L-G light is 35, mass of the rotational mirror is $m=2\mathrm{mg}$, and the powers of the pumping field are $p_l=0$, $p_l=1\mathrm{mw}$, and $p_l=5\mathrm{mw}$, respectively.

Figure 3

The absorption curve as a function of the normalized optical detuning with the orbital angular momentum of L-G light being 35 and the mass of the rotational mirror being $m=2\mathrm{mg}$, $m=4\mathrm{mg}$, and $m=8\mathrm{mg}$, respectively.

Figure 4

The absorption curve as a function of the normalized optical detuning in the case of $m=1\mathrm{mg}$, $p_l=10\mathrm{mw}$, and different orbital angular momentum: $l=5,l=12$, and $l=19$, respectively.

Figure 5

(a) $(l=0\sim 21)$ and (b) $(l=21\sim 42)$ plot the dependence of ${\tau }_{-}$ on the orbital angular momentum of L-G light where the topological charge $l$ changes in a unit of half integer.