Fabry-Perot Optical Cavity Simulation

A Fabry–Perot cavity is formed by two mirrors facing one another so that light bouncing between them interferes with itself. When the round-trip distance matches an integer number of wavelengths, the fields build up coherently and the cavity stores far more light than the input beam alone. LIGO utilizes several cavities, including four-kilometer-long arm cavities to amplify the main laser power, recycling cavities to feed more light back into the interferometer, and tiny reference cavities to stabilize the laser frequency, each tuned to keep the interferometer on resonance for passing gravitational waves.

 

This simulation lets you explore those ideas interactively. The physics engine under the hood solves the standard Fabry–Perot transfer functions with complex amplitudes, so every parameter change immediately updates the amplified fields and readouts you see.

Fabry-Perot Optical Cavity
Cavity Visualization
$m_1$ $m_2$
Parameters
Mirror reflectivities›
Mirror losses›
How to use the simulation›

Drag either mirror to change the cavity length, set reflectivities $r_1$ and $r_2$, and add losses in parts per million to see how imperfect coatings sap energy. The canvas shows the incident, reflected, and circulating fields in real time, highlighting the standing wave that appears when the cavity is locked.

Use the “Lock Cavity” button to snap mirror $m_2$ onto the nearest resonance, then experiment with different reflectivity and loss combinations to mimic LIGO's arm (high $r$, ppm-level loss) or signal-recycling (asymmetric mirrors) cavities. Monitor optical gain, finesse, phase, and coupling regime as you tune the system, exactly as cavity physicists do when aligning LIGO.

Relative Power vs. Cavity Length
Formulas

Cavity length $L$ where $L = x_2 - x_1$ =

Wavenumber $k = \dfrac{2\pi}{\lambda}$ =

Phase $\phi = (kL) \bmod 2\pi$ =

Mirror $m_1$ transmission $t_1 = \sqrt{(1 - r_1^2)(1 - \ell_1)}$ =

Mirror $m_2$ transmission $t_2 = \sqrt{(1 - r_2^2)(1 - \ell_2)}$ =

Define effective (loss-including) reflectivities: $\; r_{1,\mathrm{eff}} = r_1\sqrt{1-\ell_1},\quad r_{2,\mathrm{eff}} = r_2\sqrt{1-\ell_2}$.

Optical gain $\left|\dfrac{E_\mathrm{circ}}{E_\mathrm{inc}}\right| = \left|\dfrac{t_1}{1 - r_{1,\mathrm{eff}}\, r_{2,\mathrm{eff}}\, e^{-2 i k L}}\right|$ =

Max gain (on resonance) $\left|\dfrac{t_1}{1 - r_{1,\mathrm{eff}}\, r_{2,\mathrm{eff}}}\right|$ =

Reflected gain $\left|\dfrac{E_\mathrm{refl}}{E_\mathrm{inc}}\right| = \left| -\,r_{1,\mathrm{eff}} + \dfrac{t_1^{\,2}\, r_{2,\mathrm{eff}}\, e^{-2 i k L}}{1 - r_{1,\mathrm{eff}}\, r_{2,\mathrm{eff}}\, e^{-2 i k L}} \right|$ =

Transmitted gain $\left|\dfrac{E_\mathrm{trans}}{E_\mathrm{inc}}\right| = \left|\dfrac{t_1 t_2}{1 - r_{1,\mathrm{eff}}\, r_{2,\mathrm{eff}}\, e^{-2 i k L}}\right|$ =

Finesse $\mathcal{F} = \dfrac{\pi}{2 \, \arcsin\!\left( \dfrac{1 - r_{1,\mathrm{eff}}\, r_{2,\mathrm{eff}}}{2 \, \sqrt{r_{1,\mathrm{eff}}\, r_{2,\mathrm{eff}}}} \right)}$ =