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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Indirect transitions of a signal interacting with a moving refractive index front

Michel Castellanos Muñoz, Alexander Yu. Petrov, Liam O’Faoláin, Juntao Li, Thomas F. Krauss, Manfred Eich

Published May 1, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2051771

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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 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.
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.
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.
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.
Nonlinear degenerate four wave mixing and cross phase modulation are established approaches for all optical frequency manipulation in a silicon chip. These approaches require exact group velocity and/or phase velocity matching of pump, signal, and idler. On the other hand, several experimental demonstrations were presented recently, where frequency of light was changed by a free carrier front propagating in a silicon waveguide. This Doppler-like effect is less known, but has important advantages for frequency manipulation on chip. It requires no phase velocity matching and is not dependent on the shape and duration of the pump pulse. It also allows packet switching and can operate in a pump power independent regime. Here, we shortly review the work on front induced indirect transitions in silicon slow light waveguides. We consider three possible interaction regimes: transmission through the front, reflection from the front, and moving with the front called surfing. We derive analytical equations for the front with a linearly rising edge, which provide a unified description of the frequency shift in all three regimes. Finally, we compare the front induced dynamic frequency conversion to the frequency shifting based on nonlinear effects like cross-phase modulation and four wave mixing.
Dynamic manipulation of light has received considerable attention in recent years. 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 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.