Optical analogue of the Thomas effect in special relativity using Michelson-Gires-Tournois interferometer: Comprehensive error analysis and recovery of the direction of the Thomas rotation angle

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Previously, we reported a simple, low-cost, thin–film–based optical analogue of the Thomas Effect in Special Relativity (SR) using an ideal Michelson-Gires-Tournois interferometer (MGTI). This opens the door for other SR related phenomena to be studied analogously. Toward this goal, there are two important tasks. First, it is imperative to conduct a comprehensive evaluation of the technical limitations of this platform under two non-ideal (oftentimes unavoidable) operating conditions, namely: (i) an imperfect Gires-Tournois resonator (GTR), and (ii) the presence of interferometric error due to mismatch in the path-length arm difference of the MGTI. Second, it is also important to develop a technique to recover the direction information of the Thomas angle which is lost during the intensity measurement. Here, we report that (i) the GTR's imperfect back mirror must be fabricated with a minimum reflectance r0 value of greater than 0.9534 to limit the maximum phase deviation error by only less than 1%, (ii) the extracted Thomas angle is more sensitive to changes in interferometric error δl than the GTR imperfection. However, perfect extraction of the Thomas angle can be achieved for special range of the interferometric error δl, and (iii) the mimicked Thomas angle is distorted when the front reflectance coefficient r1 is greater than 0.7. Lastly, we introduce a method to recover the directional information of the Thomas angle by using a counter-intuitive additional positive/negative interferometric error. This method introduces no new optical components, and has high tolerance to fluctuation of the interferometric error.