Frequency conversion by the transformation-optical analogue of the cosmological redshift

Vincent Ginis; Philippe Tassin; Ben Craps; Irina Veretennicoff

doi:10.1117/12.894065

9 September 2011 Frequency conversion by the transformation-optical analogue of the cosmological redshift

Vincent Ginis, Philippe Tassin, Ben Craps, Irina Veretennicoff

Proceedings Volume 8093, Metamaterials: Fundamentals and Applications IV; 80931M (2011) https://doi.org/10.1117/12.894065
Event: SPIE NanoScience + Engineering, 2011, San Diego, California, United States

Abstract

Recently, there has been a lot of interest in electromagnetic analogues of general relativistic effects. Using the techniques of transformation optics, the material parameters of table-top devices have been calculated such that they implement several effects that occur in outer space, e.g., the implementation of an artificial event horizon inside an optical fiber, an inhomogeneous refractive index profile to mimic celestial mechanics, or an omnidirectional absorber based on an equivalence with black holes. In this communication, we show how we have extended the framework of transformation optics to a time-dependent metric-the Robertson-Walker metric, a popular model for our universe describing the cosmological redshift. This redshift occurs due to the expansion of the universe, where a photon of frequency ω_em emitted at instance tem, will be measured at a different frequency ω_obs at time t_obs. The relation between these two frequencies is given by ω_obsa(t_obs) = ω_ema(t_em), where a(t) is the time-dependent scale factor of the expanding universe. Our results show that the transformation-optical analogue of the Robertson-Walker metric is a medium with linear, isotropic, and homogeneous material parameters that evolve as a given function of time. The electromagnetic solutions inside such a medium are frequency shifted according to the cosmological redshift formula. Furthermore, we have demonstrated that a finite slab of such a material allows for the frequency conversion of an optical signal without the creation of unwanted sidebands. Because the medium is linear, the superposition principle remains applicable and arbitrary wavepackets can be converted [V. Ginis, P. Tassin, B. Craps, and I. Veretennicoff Opt. Express 18, 5350-5355 (2010)1].

Citation Download Citation

Vincent Ginis, Philippe Tassin, Ben Craps, and Irina Veretennicoff "Frequency conversion by the transformation-optical analogue of the cosmological redshift", Proc. SPIE 8093, Metamaterials: Fundamentals and Applications IV, 80931M (9 September 2011); https://doi.org/10.1117/12.894065

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KEYWORDS

Electromagnetism

Frequency conversion

Dielectrics

Maxwell's equations

Electromagnetic radiation

Metamaterials

Free space optics

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