Optical analogue between relativistic Thomas effect in special relativity and phase response of the photonic integrated circuits-based all-pass filter

• Published in: Journal of modern optics 2018-11, Vol.65 (19), p.2171-2178
• Main Authors: Dingel, Benjamin B., Buenaventura, Aria, Murakawa, Koji
• Format: Article
• Language: English
• Subjects: all-pass filter (APF); Coding; Coupling coefficients; Integrated circuits; microring resonator (MRR); Parameters; Photonic integrated circuits; Photonics; Relativism; Relativistic effects; Relativistic velocity; Relativity; Rotation; special relativity; Theory of relativity; Thomas effect; Velocity; Wigner angle
• ISSN: 0950-0340; 1362-3044
• DOI: 10.1080/09500340.2018.1502826

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 V 1 and V 2 (τ = V 1 V 2 ), where the normalized velocities V 1  = tanh [β 1 /2] and V 2  = tanh [β 2 /2] with β 1 (=tanh −1 (v 1 /c)) and β 2 (=tanh −1 (v 2 /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 V 1 and V 2 . 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.