Michelson interferometer

Virtual Michelson interferometer laboratory: a laser beam is split by a beam splitter into two arms, each reflected by a mirror, and recombined on a screen to form an interference pattern (fringes). Mirror 2 can be displaced, the laser can be misaligned, and a gas cuvette with adjustable pressure can be inserted into one arm, changing its optical path length.

Δz moves mirror 2 along its interferometer arm (use the +/− buttons for 0.1 μm steps). λ adjusts the laser wavelength; θx/θy tilt mirror 1, misaligning the beam. "Insert cuvette" adds a fixed-thickness gas cell to one arm; when inserted, the gas pressure changes its refractive index and therefore the optical path length of that arm.

The interference pattern is obtained by superposing two Gaussian beams $$ U(\overrightarrow{r}) = A_0\dfrac{W_0}{W(z)} \times $$ $$ \times \exp\left[ -\dfrac{\rho^2}{W^2(z)} \right] \times $$ $$ \times \exp\left[ -ikz - ik\dfrac{\rho^2}{2R(z)} + i\eta(z)\right], $$ with a fixed Rayleigh range $z_0 = 20$ mm, beam waist $W_0 = 2$ mm, and zero Gouy phase, $\eta(z) = 0$. Dispersion effects are neglected; the refractive index $n$ of the gas inside the cuvette (10 mm thick) varies with pressure $P$ as $$ n = 1 + \alpha P, $$ where $\alpha = 2.75\times 10^{-7}$ mbar$^{-1}$, with $P$ in mbar.

Marco P. M. de Souza