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

ABSTRACT

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.

KEYWORDS:

• Photonic integrated circuits
• Thomas effect
• Wigner angle
• special relativity
• microring resonator (MRR)
• all-pass filter (APF)

Acknowledgment

We thank N. Madamopoulos and N. Labatique for their technical feedbacks.

Disclosure statement

No potential conflict of interest was reported by the authors.