Optical Analogue Between Relativistic Thomas Effect in Special Relativity and Phase Response of the Photonic Integrated Circuits-Based All-Pass Filter

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We report a link (or optical analogue) between the relativistic Thomas rotation angle effect found in the special theory of relativity (STR), and the phase response of an all-pass filter (APF), one of the building blocks of the rapidly evolving field of photonic integrated circuits. This link opens up the possibility of investigating STR phenomena in a ‘laboratory-on-a-chip’ setting. The Thomas effect is a spatial rotation of the reference frame due to Einstein’s velocity addition law of two successive velocities travelling in non-collinear directions. On the other hand, the APF is implemented with a microring resonator device with one waveguide bus. The analogue is established by associating two parameters. First, the transmission coupling coefficient τ of the APF is made to equal with the product of the two relativistic normalized velocities V1 and V2 (τ = V1V2), where the normalized velocities V1 = tanh [β1/2] and V2 = tanh [β2/2] with β1 (=tanh−1 (v1/c)) and β2 (=tanh−1 (v2/c)) being the rapidity values associated with the standard normalized speed. Second, the single-pass phase shift φ (or equivalently the phase detuning, Δφ or wavelength detuning, Δλ) parameter of the APF is related to the so-called generating angle θ of the two non-collinear relativistic velocities V1 and V2. We also introduce an additional photonic circuit to convert this phase-encoded Thomas angle into intensity for direct measurement. Lastly, other important and broader consequences of this link are briefly discussed.