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Optical and Quantum Sensing and Precision Metrology II

Front induced transitions in slow light and dispersive waveguides

Mahmoud Gaafar, Toshihiko Baba, Manfred Eich, Alexander Yu. Petrov

Published Feb 25, 2020• 0 citations
Publisher

Abstract

Moving refractive index fronts in waveguides with dispersion is a special type of spatio-temporal modulation. The interaction of light with that front allows frequency conversion, light stopping, optical delays, and bandwidth and pulse duration manipulation. Here, we present examples of signal transmission, reflection, trapping and stopping. We will geometrically consider indirect transitions in the dispersion relation using the phase continuity relation at the front and present numerical solutions of the linear Schrödinger equation which follows from the slowly varying envelope approximation of the wave equation.

DOI
10.1117/12.2540476

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Moving refractive index fronts in waveguides with dispersion is a special type of spatio-temporal modulation. The interaction of light with that front allows frequency conversion, light stopping, optical delays, and bandwidth and pulse duration manipulation. Here, we present examples of signal transmission, reflection, trapping and stopping. We will geometrically consider indirect transitions in the dispersion relation using the phase continuity relation at the front and present numerical solutions of the linear Schrödinger equation which follows from the slowly varying envelope approximation of the wave equation.
Moving refractive index fronts in waveguides with dispersion is a special type of spatio-temporal modulation leading to the change of signal frequency and wavenumber. The interaction of light with such fronts allows frequency conversion, light stopping, optical delays as well as bandwidth and pulse duration manipulation. We will present theoretical and experimental examples of signal transmission, reflection and trapping by the front and highlight special situations such as light stopping, time reversal or optical push broom effect. We will geometrically consider indirect transitions in the dispersion relation using the phase continuity relation at the front and present numerical solutions of the linear Schrödinger equation which follows from the slowly varying envelope approximation of the wave equation. In particular, for highly dispersive waveguides a temporal evolution of the spatial wave envelopes are considered in contrast to conventional spatial evolution of temporal envelopes. Further, we will present an overview of experimental results and estimate the maximal achievable effects for each of the application in different waveguide systems.
The dynamic manipulation of light can be achieved by the interaction of a signal pulse propagating through or reflected from a refractive index front. Both the frequency and the wave vector of the signal are changed in this case, which is generally referred to as an indirect transition. We have developed a theory to describe such transitions in integrated photonic crystal waveguides. Through indirect transitions, the following effects can be envisaged: large frequency shifts and light stopping and order of magnitude pulse compression and broadening without center frequency shift. All effects can be potentially realized with a refractive index modulation as small as 0.001. For the experimental realization, we have used slow light photonic crystal waveguides in silicon. The refractive index front was obtained by free carriers generation with a switching pulse co-propagating with the signal in the same slow light waveguide. The group velocities of the signal and the front could be varied arbitrarily by choosing the right frequencies of the signal and switching pulses. The indirect transition was unambiguously demonstrated by considering two situations: a) the front overtaking the signal and b) the signal overtaking the front. In both cases, a blue shift of the signal frequency was observed. This blue shift can only be explained by the occurrence of the expected indirect transition and not by a direct transition without wave vector variation.
We discuss how dynamic light stopping and pulse time reversal can be implemented in dispersive waveguides via indirect photonic transitions induced by moving refractive index fronts. The previous concepts of light stopping/time reversal either require complex local variation of the device’s refractive index or rely on the strict phase matching condition, which imposes limitations on the amount of manipulated information. Until now, only single pulses or continuous waves were manipulated experimentally. Our scheme is not limited by a strict phase matching condition and does not require local index variations, thus it can manipulate broadband signals in a single step process. Here, we present several numerically integrated results for pulse time reversal and stopping/storage via indirect front-induced transitions. The presented results are experimentally feasible using existing photonic waveguide technologies.
We demonstrate indirect photonic transitions in a silicon slow light photonic crystal waveguide. The transitions are driven by an optically generated refractive index front that moves along the waveguide and interacts with a signal pulse copropagating in the structure. We experimentally confirm a theoretical model which indicates that the ratio of the frequency and wave vector shifts associated with the indirect photonic transition is identical to the propagation velocity of the refractive index front. The physical origin of the transitions achieved here is fundamentally different than in previously proposed refractive index modulation concepts with fixed temporal and spatial modulation frequencies; as here, the interaction with the refractive index front results in a Doppler-like signal frequency and wave vector shift. Consequently, the bandwidth over which perfect mode frequency and wave vector matching is achieved is not intrinsically limited by the shape of the photonic bands, and tuning of the indirect photonic transitions is possible without any need for geometrical modifications of the structure. Our device is genuinely nonreciprocal, as it provides different frequency shifts for co- and counterpropagating signal and index fronts.
Nonlinearly generated refractive index fronts in waveguides can change the signal frequency and wavenumber leading to the indirect transitions. Here, we discuss how dynamic light stopping and pulse time reversal can be implemented in dispersive waveguides via these transitions. Our scheme, in contrast to previous concepts of light stopping and time reversal, is not limited by a strict phase matching condition and does not require local index variations, thus, can manipulate broadband signals in a single step process. The presented results are experimentally feasible using existing photonic waveguides technologies.
The process of an optical signal undergoing a transition between two modes of a photonic structure is referred to as a photonic transition. We show that a signal wave interacting with a free carrier front in a slow light waveguide experiences indirect photonic transitions leading to transmission or reflection from the moving front. Theory and experimental results are presented. The front induced dynamic frequency conversion is also compared to the frequency shifting based on other nonlinear effects like cross-phase modulation and four wave mixing.