## 1 Fabry-Perot Etalon (Non-Dispersive)

A Fabry-Perot (FP) resonator is composed of a slab of material with high refractive index or a pair of parallel reflecting surfaces with some distance (L). The surfaces can either be mirrors or an interface between two regions of differing refractive index. The mechanism of resonance is based on the multiple beam interference as a result of successive reflections from the two parallel interfaces, see Fig. 1.## 2 Theory

The resulting transmitted (\(E_{t}\)) and reflected (\(E_{r}\)) electric fields from an FP resonator can be obtained as \[\begin{eqnarray} E_{t}&=&E_{i}t_{1}t_{2}\left(1+r_{2}^{2}e^{i\phi}+r_{2}^{4}e^{i2\phi}+...\right)\\ E_{r}&=&E_{i}\left[r_{1}+t_{1}t_{2}r_{2}e^{i\phi}\left(1+r_{2}^{2}e^{i\phi}+r_{2}^{4}e^{i2\phi}+...\right)\right] \end{eqnarray}\] where \(E_{i}\) is the incident electric field [1-2]. The coefficients \(r_{1}\) (\(r_{2}\)) and \(t_{1}\)(\(t_{2}\)) are the amplitude reflection and transmission coefficients from the medium \(n_{1}\)(\(n_{2}\)) to \(n_{2}\)(\(n_{1}\)), respectively. The parameter \(\phi=\frac{4\pi n_{2}L}{\lambda}\) is the phase difference as a result of a round-trip between two successive outgoing waves. The reflectivity of each interface (\(R=r_{1}r_{2}\)) for the normal angle of incidence is calculated as \[\begin{equation}R=\left(\frac{n_{2}-n_{1}}{n_{2}+n_{1}}\right)^{2}\end{equation}\] and the transmittance (the superposition all transmitted waves) (\(T\)) and reflectance (the superposition of all reflected waves) (\(\mathcal{R}\)) can be obtained as \[\begin{eqnarray} T&=&\frac{\left|E_{t}\right|^{2}}{\left|E_{i}\right|^{2}}=\frac{1}{1+F\:\mathrm{sin^{2}}\left(\frac{\phi}{2}\right)}\\ \mathcal{R}&=&\frac{\left|E_{r}\right|^{2}}{\left|E_{i}\right|^{2}}=F\frac{\mathrm{sin^{2}}\left(\frac{\phi}{2}\right)} {1+\mathrm{sin^{2}}\left(\frac{\phi}{2}\right)}\\ F&=&\frac{4R}{\left(1-R\right)^{2}} \end{eqnarray}\] where \(F\) is the finesse parameter indicating how sharp a resonance seems in comparison with the spectral distance between two consecutive resonances (FSR) [1-2]. For the case of a lossless resonator, the conservation of energy implies the relation \[\begin{equation}\mathcal{R}+T=1\end{equation}\] The reflectance spectrum of an FP etalon composed of a pair of parallel mirrors can be obtained analytically, see Fig. 2.## 3 Design

The simulation is performed using a 2D design consisting of a waveguide centered in the domain.Wafer properties | Value |
---|---|

Length along x ( \(\mu\) m ) | 1 \(\mu\) m |

Length along z ( \(\mu\) m ) | 16 \(\mu\) m |

Boundary conditions ( z = 0 and z = 16 \(\mu\) m | Anisotropic perfectly matched layer (APML) |

Boundary conditions ( x = 0 and z = 1 \(\mu\) m | Periodic boundary condition (PBC) |

Optical source features | Value |
---|---|

Wavelength ( \(\mu\)m ) | 1.55 |

Half Width ( \(\mu\)m ) | 0.5 |

Direction of propagation | z |

Time domain shape | Sine-Modulated Gaussian Pulse |