Abstract

The possibility of controlling the resonant properties of photonic structures via a small and dynamic refractive index change is a promising approach for an all-optical coherent control of light in nanophotonic structures. For instance, a temporal and translationally-invariant modulation of the refractive index in photonic crystals (PCs) and coupled- resonator optical waveguides (CROWs) produces an adiabatic change of the resonant properties of the structure which can be exploited to e.g. compress or slip the spectrum of an incoming pulse, thus realizing a few basic functionalities such as stopping, storing and time-reversing of light pulses [1,2], In this contribution a novel scheme of coherent and reversible light control in dynamic photonic structures, which does not necessarily require to maintain the translational invariance of the system, is presented. In particular, we demonstrate theoretically the possibility of stopping and time- reversing light pulses in a CROW structure with an imposed dynamic refractive index gradient. In this system, light stopping and reversal is not due to adiabatic shrinking and reversal of the waveguide band structure, as in Refs. [1,2], but it is a consequence of the coherent Bloch oscillation (BO) motion of the light pulse induced by the index gradient. It is remarkable that, thought temporal and spatial BOs and related phenomena have been studied to a great extent in several linear optical systems, they have been not yet proposed as an all-optical means to stop or time-reverse light pulses. We consider a CROW made of a periodic array of identical coupled optical cavities, and indicate by ω_n=ω_o+δω_n(t) the resonance frequency of the n-th cavity in the array, where δω_n(t) is a small frequency shift from the coimnon frequency ω₀ which can be dynamically and externally changed by e.g. local refractive index control. Practical implementations of CROW structures have been demonstrated in PCs with coupled defect cavities or in a chain of coupled microrings. Coupled mode theory can be used to describe the evolution of the field amplitudes a„ in the cavities and therefore the process of coherent light Control We assume that a ramp with a time-varying slope a(t) is imposed to the resonances of N adjacent cavities in the CROW, leading to a site-dependent frequency shift δω_n(t)=nα(t) for 1<n<N.[Fig. 1(a)]. After a pulse propagating along the CROW is fully entirely entered in the system, the index ramp is switched and the pulse undergoes a Bloch-like motion. If the ramp profile α(t) is chosen to be close to a rectangular shape [Fig. 1(b)] with duration τ=t₂-t₁C and amplitude a,,, pulse stopping for a duration x is obtained for an area y₀≈α₀,-, x equal to 2π (apart for integer multiplies of 2π). whereas if}+ is equal to n (apart for integer multiplies of 2π) the pulse is reflected and time-reversed. Examples of pulse stopping and time reversal, as obtained from numerical simulations, are shown in Fig. 1(c) and (d). Note that, in case of light stopping, the light pulse undergoes an effective back and forth Bloch motion which stores the pulse for a time x which is an integer multiple of the Bloch period τ_B=2π/α₀. Conversely, in case of pulse time reversal the light pulse undergoes a semi-integer multiple of the Bloch oscillation period and the structure acts as a phase conjugation mirror which reflects the pulse after reversal. In real physical units, consider for istance the case of pulse stopping at λ≈1.55μm and assume an index change dn/n≈5×10⁻⁴. The bandwidth of the waveguide and the transit time t_pass in Fig.l(c) are then given by ≈39 GHz ≈410 ps, respectively. For such parameter values, Fig.l(c) simulates the stopping of a ≈68 ps-long Gaussian pulse with a storage time τ≈1.75ns

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