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Stopping and time reversal of light in dynamic photonic structures via Bloch oscillations

Dipartimento di Fisica and Istituto di Fotonica e Nanotecnologie del CNR, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milan, Italy

Phys. Rev. E 75, 026606 – Published 9 February, 2007

DOI: https://doi.org/10.1103/PhysRevE.75.026606

Abstract

It is theoretically shown that storage and time reversal of light pulses can be achieved in a coupled-resonator optical waveguide by dynamic tuning of the cavity resonances without maintaining the translational invariance of the system. The control exploits the Bloch oscillation motion of a light pulse in the presence of a refractive index ramp, and it is therefore rather different from the mechanism of adiabatic band compression and reversal proposed by Yanik and Fan in recent works [Phys. Rev. Lett., 92, 083901 (2004); 93, 173903 (2004)].

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References (25)

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For a sinusoidal modulation, Eq. (1) admits of a quasienergy band and the condition $J_{0} (α_{0} ∕ Ω) = 0$ corresponds to the collapse of the quasienergy band [M. Holthaus, Phys. Rev. Lett. 69, 351 (1992)]. More generally, for a fast sinusoidal modulation $α (t) = α_{0} (t) \sin (Ω t)$ of frequency $Ω$ much larger than $κ$ and amplitude $α_{0}$ which is slowly varying in time, by a multiple-scale analysis one can remove the rapidly varying terms in Eq. (1) and obtain the reduced equations $i d a_{n} ∕ d t = - κ_{e} (t) (a_{n + 1} + a_{n - 1})$ with an effective slowly varying hopping amplitude $κ_{e} = κ J_{0} (α_{0} ∕ Ω)$ [see, e. g., S. Longhi, Phys. Rev. B 73, 193305 (2006)]. A slow change of $α_{0}$ leads to an adiabatic change of the bandwidth of the waveguide. Light slowing down and stopping in this case is thus analogous to adiabatic band compression of Ref. [1]. The requested modulation frequency $Ω$ , however, turns out to be too high (larger than $κ$ ) to be reasonably achieved in practice.
In deriving Eq. (A3) we assumed that the relation $ω_{n} = n α (t)$ holds even for $n < 1$ and $n > N$ , though in practice the dynamic tuning of cavity resonances is applied solely for the cavities with index $n$ in the range $1 < n < N$ (see Fig. 1). However, taking into account that $α (t)$ vanishes outside the interval $[t_{1}, t_{2}]$ and that the size $N$ of the stopping box is large enough to fully contain the pulse during the delay interval—i.e., $a_{n} (t) ≃ 0$ for $n < 1$ , $n > N$ in the time interval $t_{1} < t < t_{2}$ —the previous assumption does not change the solution of the problem.

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Stopping and time reversal of light in dynamic photonic structures via Bloch oscillations

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