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The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides

Rob J. P. Engelen, Yoshimasa Sugimoto, Yoshinori Watanabe, Jeroen P. Korterik, Naoki Ikeda, N.F. van Hulst, K. Asakawa, L. Kuipers

Published Jan 1, 2006• 163 citations

Abstract

We have studied the dispersion of ultrafast pulses in a photonic crystal waveguide as a function of optical frequency, in both experiment and theory. With phase-sensitive and time-resolved near-field microscopy, the light was probed inside the waveguide in a non-invasive manner. The effect of dispersion on the shape of the pulses was determined. As the optical frequency decreased, the group velocity decreased. Simultaneously, the measured pulses were broadened during propagation, due to an increase in group velocity dispersion. On top of that, the pulses exhibited a strong asymmetric distortion as the propagation distance increased. The asymmetry increased as the group velocity decreased. The asymmetry of the pulses is caused by a strong increase of higher order dispersion. As the group velocity was reduced to 0.116(9) .c, we found group velocity dispersion of -1.1(3) .10(6) ps(2)/km and third order dispersion of up to 1.1(4) .10(5) ps(3)/km. We have modelled our interferometric measurements and included the full dispersion of the photonic crystal waveguide. Our mathematical model and the experimental findings showed a good correspondence. Our findings show that if the most commonly used slow light regime in photonic crystals is to be exploited, great care has to be taken about higher-order dispersion.

DOI: 10.1364/oe.14.001658

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•Jan 1, 2009•0 citations

We have studied the dispersion of ultrafast pulses in a photonic crystal waveguide as a function of optical frequency, in both experiment and theory. With phase-sensitive and time-resolved near-field microscopy, the light was probed inside the waveguide in a non-invasive manner. The effect of dispersion on the shape of the pulses was determined. As the optical frequency decreased, the group velocity decreased. Simultaneously, the measured pulses were broadened during propagation, due to an increase in group velocity dispersion. On top of that, the pulses exhibited a strong asymmetric distortion as the propagation distance increased. The asymmetry increased as the group velocity decreased. The asymmetry of the pulses is caused by a strong increase of higher order dispersion. As the group velocity was reduced to 0.116(9) .c, we found group velocity dispersion of -1.1(3) .10(6) ps(2)/km and third order dispersion of up to 1.1(4) .10(5) ps(3)/km. We have modelled our interferometric measurements and included the full dispersion of the photonic crystal waveguide. Our mathematical model and the experimental findings showed a good correspondence. Our findings show that if the most commonly used slow light regime in photonic crystals is to be exploited, great care has to be taken about higher-order dispersion.

We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite-difference-time-domain Maxwell–Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse.

Slow light with a markedly low group velocity is a promising solution for optical buffering and advanced time-domain optical signal processing. It is also anticipated to enhance linear and nonlinear effects and so miniaturize functional photonic devices because slow light compresses optical energy in space. Photonic crystal waveguide devices generate on-chip slow light at room temperature with a wide bandwidth and low dispersion suitable for short pulse transmission. This paper first explains the delay-bandwidth product, fractional delay, and tunability as crucial criteria for buffering capacity of slow light devices. Then the paper describes experimental observations of slow light pulse, exhibiting their record high values. It also demonstrates the nonlinear enhancement based on slow light pulse transmission.

Slow light with a markedly low group velocity is a promising solution for optical buering and advanced time-domain optical signal processing.It is also anticipated to enhance linear and nonlinear eects and so miniaturize functional photonic devices because slow light compresses optical energy in space.Photonic crystal waveguide devices generate on-chip slow light at room temperature with a wide bandwidth and low dispersion suitable for short pulse transmission.This paper rst explains the delay-bandwidth product, fractional delay, and tunability as crucial criteria for buering capacity of slow light devices.Then the paper describes experimental observations of slow light pulse, exhibiting their record high values.It also demonstrates the nonlinear enhancement based on slow light pulse transmission.

Directional Waveguide Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Optical slow-wave structures such as coupled photonic crystal cavities, coupled microrings, coupled quantum wells, etc. are promising candidates for slow light devices because of the nature of their dispersion relationship which follows the tight-binding model well-known in solid-state physics. In a perfectly uniform structure, the slope of the dispersion curve, which defines the group velocity, is zero at the edges of the waveguide band, leading to slow light and enhanced light-matter interaction. Although the effects of group velocity dispersion (and higher-order dispersion) can limit the performance of slow light structures [1-4], the effects of dispersion can, in principle, be compensated by a variety ofmechanisms, including some ofwhich are used commonly in optical fiber communications.

We demonstrate ultrafast delay tuning of a slow-light pulse with a response time <10 ps. This is achieved using two types of slow light: dispersion-compensated slow light for the signal pulse, and low-dispersion slow light to enhance nonlinear effects of the control pulse. These two types of slow light are generated simultaneously in Si lattice-shifted photonic crystal waveguides, arising from flat and straight photonic bands, respectively. The control pulse blueshifts the signal pulse spectrum, through dynamic tuning caused by the plasma effect of two-photon-absorption-induced carriers. This changes the delay by up to 10 ps only when the two pulses overlap within the waveguide and enables ultrafast tuning that is not limited by the carrier lifetime. Using this, we succeeded in tuning the delay of one target pulse within a pulse train with 12 ps intervals.

Slow light with a markedly low group velocity is a promising solution for optical buffering and advanced time-domain optical signal processing. It is also anticipated to enhance linear and nonlinear effects and so miniaturize functional photonic devices because slow light compresses optical energy in space. Photonic crystal waveguide devices generate on-chip slow light at room temperature with a wide bandwidth and low dispersion suitable for short pulse transmission. This paper first explains the delay-bandwidth product, fractional delay, and tunability as crucial criteria for buffering capacity of slow light devices. Then the paper describes experimental observations of slow light pulse, exhibiting their record high values. It also demonstrates the nonlinear enhancement based on slow light pulse transmission.