Toward Special-Relativity-on-a-Chip: analogue of Einstein velocity addition using optical add-drop filter (OADF)

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We present an optical analogue of a central concept (not a specific relativistic effect) in Special Relativity (SR) that underlies many relativistic effects. This concept is the Einstein Velocity Addition (EVA) which plays a fundamental role in the development of SR. The photonic circuit analogue is between the EVA, and the complex electric field, through the output signal of the optical add-drop filter (OADF). The OADF is one of the key building blocks for wavelength filtering in photonic integrated circuits (PICs or photonic chip). This analogue strengthens the vision toward a Special-Relativity-on-a-Chip. The analogy is established by equating the two relativistic normalized velocities in EVA with the two transmission coupling coefficients of the two directional couplers in the OADF. Furthermore, the generating angle in the EVA is associated with the single-pass phase shift of the OADF. We analyze its magnitude and directional angle in detail. Lastly, other important consequences are also briefly discussed.