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arXiv:2104.10562 · Physical Review A

Slow and stopped light in dynamic Moiré gratings

Thomas E. Maybour, Devin H. Smith, Péter Horák

Published Jul 6, 2021• 4 citations
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Abstract

We investigate a theoretical model for a dynamic Moir\'e grating which is capable of producing slow and stopped light with improved performance when compared with a static Moir\'e grating. A Moir\'e grating superimposes two grating periods, which creates a narrow slow light resonance between two band gaps. A Moir\'e grating can be made dynamic by varying its coupling strength in time. By increasing the coupling strength the reduction in group velocity in the slow light resonance can be improved by many orders of magnitude while still maintaining the wide bandwidth of the initial, weak grating. We show that for a pulse propagating through the grating this is a consequence of altering the pulse spectrum, and therefore the grating can also perform bandwidth modulation. Finally we present a possible realization of the system via an electro-optic grating by applying a quasistatic electric field to a poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium.

DOI
10.1103/physreva.104.013503

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We investigate a theoretical model for a dynamic Moir'e grating which is capable of producing slow and stopped light with improved performance when compared with a static Moir'e grating. A Moir'e grating superimposes two grating periods, which creates a narrow slow light resonance between two band gaps. A Moir'e grating can be made dynamic by varying its coupling strength in time. By increasing the coupling strength the reduction in group velocity in the slow light resonance can be improved by many orders of magnitude while still maintaining the wide bandwidth of the initial, weak grating. We show that for a pulse propagating through the grating this is a consequence of altering the pulse spectrum, and therefore the grating can also perform bandwidth modulation. Finally we present a possible realization of the system via an electro-optic grating by applying a quasistatic electric field to a poled \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) nonlinear medium.
One of the key issues when dealing with slow light is the inevitable effect of dispersion, the result of which is to broaden a pulse upon propagation. Moreover, the dispersion tends to increase when the group velocity, the speed at which the pulse propagates, decreases. To see this, we note that if we write the group velocity vg ≡ c/ng, where ng is the group index, then we find that ng = n+ωdn/dω. Since for the materials we are interested in, the refractive index does not vary strongly in magnitude, and slow light is obtained when the derivative dn/dω is large and positive. However, as the variations in the magnitude of n itself are limited, the large derivative can only be maintained over a narrow bandwidth ∝ (dn/dω)−1. Therefore, a large delay implies a narrow bandwidth, and hence a limited pulse width. Here we discuss how to avoid this limit by using nonlinear effects in the form of gap solitons. Though this argument is quite simple, it can be made rigorous using the Kramers-Kronig relations. In this way it can be shown that the achievable delay in a linear, two-port device is subject to a limitation of the product of the delay and the bandwidth (Lenz et al., 2001).
The effect of slow light on second-harmonic generation in a periodically poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium is investigated theoretically. A linear $\ensuremath{\pi}$ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.