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Multimode Cavity Optomechanics^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Theory

#### 2.2. Estimation of the Optomechanical Coupling Strength

**Figure 2.**Experimental setup for the measurements reported in Figure 3. The light of a laser at 1064 nm wavelength transmitted by an optical cavity of length L = 90 mm containing the membrane sandwich of thickness ${L}_{m}$ = 104 nm, and distance ${L}_{c}=24\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$m at rest, is revealed by a PIN photodiode (${\mathcal{I}}_{\mathrm{tr}}^{\mathcal{N}}$), while the frequency is scanned by applying a ramp signal (RAMP) to the piezo control of the laser. The positions of the two membranes are controlled by applying high-voltage (HV) to the piezos, which move the CoM, Q, and the cavity length, ${q}_{1}$.

**Figure 3.**Mode frequency shift normalized to the FSR as a function of the CoM, Q, normalized to the wavelength, for different values of the membrane sandwich length q (panels A–F) and indicated by the lines A–F in Figure 1b. Panel D shows the positions for the highest achievable coupling ${G}_{Q}^{\mathrm{max}}$ indicated by the solid blue line. The panels I–VI represents the mode frequency shift normalized to the FSR, as a function of the membrane position ${q}_{1}$, normalized to the wavelength, for different values of the position ${q}_{2}$. Panel V shows the highest achievable coupling ${G}_{1}^{\mathrm{max}}$. For comparison the single membrane result is added as a dotted black line in panels V and D which represents the maximum achievable coupling ${G}_{\mathrm{sing}}^{\mathrm{max}}$, shown in the panel on the top right.

## 3. Conclusions

## Acknowledgments

## References

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**Figure 1.**(

**a**) Schematic diagram of the system. (

**b**) Contour plot of the frequency shift function $\delta \omega $ normalized to the free–spectral–range of the cavity, FSR = $\pi c/L$, as a function of the membrane positions ${q}_{1}$ and ${q}_{2}$ normalized to the wavelength, due to the presence of the two–membrane cavity. The parameters used for the numerical analysis are: $\lambda $ = 1064 nm, $\mathcal{R}=0.99994$, L = 90 mm, ${L}_{\mathrm{m}}$ = 104 nm, and $n=2.17$. Superimposed the vector plot of the gradient field of the frequency shift, whose components give the two optomechanical couplings, with the unit indicated on the top–right of the panel. The oblique blue lines (A–F) and the horizontal red lines (I–VI) indicate the experimental spectra reported in Figure 3 (A–F). The red and blue dots represent the points where the optomechanical coupling was estimated.

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## Share and Cite

**MDPI and ACS Style**

Piergentili, P.; Catalini, L.; Bawaj, M.; Zippili, S.; Malossi, N.; Natali, R.; Vitali, D.; Giuseppe, G.D.
Multimode Cavity Optomechanics. *Proceedings* **2019**, *12*, 54.
https://doi.org/10.3390/proceedings2019012054

**AMA Style**

Piergentili P, Catalini L, Bawaj M, Zippili S, Malossi N, Natali R, Vitali D, Giuseppe GD.
Multimode Cavity Optomechanics. *Proceedings*. 2019; 12(1):54.
https://doi.org/10.3390/proceedings2019012054

**Chicago/Turabian Style**

Piergentili, Paolo, Letizia Catalini, Mateusz Bawaj, Stefano Zippili, Nicola Malossi, Riccardo Natali, David Vitali, and Giovanni Di Giuseppe.
2019. "Multimode Cavity Optomechanics" *Proceedings* 12, no. 1: 54.
https://doi.org/10.3390/proceedings2019012054