Broadband time-reversal of optical pulses using a switchable photonic-crystal mirror

Yonatan Sivan,John B Pendry

doi:10.1364/oe.19.014502

Abstract

Recently, Chumak et al. have demonstrated experimentally the time-reversal of microwave spin pulses based on non-adiabatically tuning the wave speed in a spatially-periodic manner [Nat. Comm. 1, 141 (2010)]. Here, we solve the associated wave equations analytically, and give an explicit formula for the reversal efficiency. We discuss the implementation for short optical electromagnetic pulses and show that the new scheme may lead to their accurate time-reversal with efficiency higher than before.

Highlights

We study the time-reversal scheme of [1] theoretically and compare it to previous non-adiabatic modulation-based schemes; we focus on time-reversal of ultrashort optical pulses, which as noted above, still has not been demonstrated experimentally
If one re-establishes the transmissivity once most of the energy of the forward wave has been converted to a backward wave, a time-reversed pulse is released backwards
In what follows we refer to these schems as switchable mirror (SM) -based reversal schemes

Summary

Principles of time-reversal using a switchable mirror

In order to understand the reversal schemes of [1, 18, 19], it is beneficial to adopt a somewhat heuristic interpretation. If one re-establishes the transmissivity once most of the energy of the forward wave has been converted to a backward wave, a time-reversed pulse is released backwards In a sense, this procedure transforms a perfectly transmitting medium into a “volume” mirror. In what follows we refer to these schems as switchable mirror (SM) -based reversal schemes This heuristic explanation clarifies why the zero-gap-based switchable-mirror (ZGSM) is equivalent to a homogeneous-medium-based switchable-mirror (HSM). In both structures a gap is opened due to the modulation (see [1, 19]) It is implied by the heuristic explanation (and later proved analytically in Section 2), that in both ZGSM and HSM, the wave-front is reversed, it is not conjugated. A final advantage of the HSM is that by choosing the proper modulation pattern, the reversal can be performed for any angle of incidence, for plane-waves as well as for beams, for high dimensional gratings or waveguide structures as well as for any incident carrier frequency

Analysis

Findings

Implementation